Lifetime concept of plaster panels subjected to sonic boom

",

LIFEI'IME CONCEPT OF PLASTER PANELS SUBJECTED TO SONIC BOOM

Ju,ly,

1974.

by ~ .... .. .-.... -

..

-.

"" . . . ~t.'... '" Barry R. Leigh _{1"'-1'"' '''''''' . __ ~. 1 - C~' , FT} _~M 1 U:J. 197~

lJrIAS Technical Note

No.

191

CN ISSN 0082-5263

LIFErlME CONCEPT OF P;LASTER PANELS SUBJECTED TO SONIC BOOM

by

Barry R. Leigh

Manuscript received, Ju1y 1974.

Acknowle~ements

I should like to extend my sineere thanks to Dr. I. I. Glass and Dr. R. C. Tennyson, my staff supervisors for their guidance and patience throughbut this project, which was suggested by Dr. H. S. Ribner.

Dr. N. D. Ellis was a continuing source af inspiration.

The effort exerted by Mr. J. J. Göttlieb during the development of the

travelling wave sonic boom simulator is greatly appreciated.

Thanks are offered to Mr. A. Perrin and Mr. J. Unger for their advice in electronic design.

To Dr. H. S. Ribner, Mr. W. Richarz and Mr. D. Sutton thanks are extended for their help in the design of the acoustic shaker.

The invaluable assistance of Mr. R.Gnoyke in carrying out experiments and manufacturing plaster panels is greatly appreciated.

I wish to thank Mr. M. Millan and Mr. E. Mills for their advice and assistance in modifying the horn structural cut-out.

To Mr. J. Morton of the Canadian Gypsum Company I offer thanks for

supplying plaster for use in the tests and fer giving much useful information about plaster.

1 wish to sincerely thank Miss E. Whitney for her help in typing the

manuscript.

Special thanks are extended to NRC and Mar/TDA for supplying the funds

necessary to conduct this research.

---

-Abstract

Relè.ti vely pure gypsum plaster panels we re mounted in the side of the

UTIAS travelling-wave sonic boom simulator 'in order to simulate a plaster wall

subjected to sonic boom. The dynamic response of the plaster panels (16 in x 16 in x 3/8 in), subjected to sonic booms of up to ],,5 psf peak overpressure

and of

5

ms to 1000 ms durat;ion, was moni tored by mea.ns of strain gauges attached at the centre of each panel. The maximum Je vel of response was found to be well below that required for yield in the plaster.

In order to test the "Lifetime Concept" of plaster panels and. to

simulate aging effects on plaster in bUild1ngs the following tests wereperformed.

An

siN

curve was obtained by loading the ·plaster panels to failure ' at different cyclic loading levels by means of a loudspeaker-driven acoustic shaker. A number of these plaster panels were also subjected by the acoustic shaker to 10

7

load-ing cycles at a level slightly higher than the peak strain induced in the panels

by a 10 psf, 100 mssimulated sonic boom. Tne prefatigued panels were then sub-jected to 1000 such booms. Their loading effect was judged to be more severe than booms generated by present-day SST. FinallY,.the prefatigued and repeatedly

-boomed panels then received an additional 10

7

loading cycles in the aCQustic shaker. Visible cracking or a change in response behaviour were deemed to

con-stitute failure of a plaster panel. It was f01.md that of the thirteen panels

so t~sted only one failed,-possibly because of excessive static èlamping stresses

induced by the attachment scheme.

On the basis of these tests it can be concluded that it is unlikely that plaster in good repair will be significantly damaged by repeated exposure to sonic booms generated by SST overflights.

List of Symb.ols

a length of the sides of a square

Ao unstrained resistance of a strain gauge

~ strained resistance of the nth strain gauge

6A change in resistance due to strainingof a st~ain gauge

b width ofa beam

c speed of sound

CT

timing capacitor in a monostable circuit

DAF dynamic amplification ,factor '

E Young's lllQdulus of elasticity of a material

E(f) energy spectral density of a transient inpressure

E output 'offset voltage 'of an amplifier

os f

n

nth natural frequency of a mechanical sY$tem

F force

GF gauge factor of a strain gauge:

h thickness of a plate', or beam

M

GF =

€A

~ iriput biascurrent of ~ operational amplifier

in nth current

-,-i input offset current ofanoperational amplifier

os

I second moment of area of a beam cross-section

I eurrent through a current source

' -

.

,

~ eurrent delivered by a current source to a load

In eurrent through the nth current .s01,lrce

óJ difference between the eurrentsthrough two eurrent sources

-k differential voltage gain of

a

differential amplifier

1 length

M aireraft flight Mach number

M bending moment"" in bearn or distributeq, bending moment in plate

M , x N

~

Rf RL R n R 0

~

S T T P v v n v 0 v _os v o+ V o-w s x, y M

Y distributed bending moments about x, y axes, respectiv~ly

number of loading cycles to failure in a fatigue test, hence

siN

nth transistor'in a circuit

feedback resistor load resistor nth resistor

unstrained resistance of a strain gauge timing resisto~ iÏl a monostal;>le cfrcui t

intensity of cyclic loading in a fatigue test, hence

siN

duration of a pressure tr~sient, or, more properly, time between the

two shocks of a sonic boom or "N-wave" _

pulse width in time for an activated, monostable circuit nodal voltage

nth voltage output voltage

input offset voltage of an operational amplifier

output voltage of an operational amplifier in pos i tive saturation

output of an operational ampl~fier in negative saturation

deflection of the centre of ,a plate

components of a 2-dimensional coordinate system GREEK SYMBOLS

5

n

a constant relating geometry and load to deflection of the centre of a plate

a constant relating geometry and load to stress induced at the centre of a pl!ite

maximum shear strain

shear strain in the x, y plane

ratio of resistance change due to strain to the unstrained resistance in a strain gauge: 5 = € • GF

E EL E ma.x ET E E X' _Y El €2 v P CT CT

e

CT T CT ,CT X Y

CPn

strain

longitudinal strain·in a specimen uniaxially ~oaded

maximum strain

-transverse, or ~ateràl, strain in a specimen uniaxially loaded

l0ngi-tudinally

components of strainin' the x, y coord1nate system

principal strains in a 2 .. d1nlensional state· of strain

~oisson's ratio of a material

density of a material stress

compression stress require~ to cause yield in a material

tensile stress required to cause yield in. a material

components of stress in the

x,

y coordinate system

a constant relating geometry and the. nth resonant frequency of a plate

1. 2.

3.

4.

5.

6.

8.

Table of> Contents Acknowledgements INi'RODUCTION MECHANICAL PROPER~IES SIMULATION

ELASTIC ANALYSIq OF THE PLASTER PANEL PLASTER PANEL RESPONSE TO SONIC BOOM FATIGUE PROGRAMME

CONCLUDING REMARKS AND RECOMMENDMIONS REFERENCES

APPENDIX Al: Strain Gauge Amplifier

ti

A2: Delayed Trigger Circuit "

_A3:

Acoustic Shaker

"

A4:

,

Level Detector Circuit

i i 1 3

6

9

i4

15

17

19

.'

- -- - -

-1. INTRODUCTION

The advent of supersonic transports (SST's) such as the Anglo-French Concordeand the Russian Tu-144 has led to the inmri.nent possibility of their

introduction into service· on Canad,ian air routes. Within a wide corridor on the

groWld centered on the flight path of an aircraft flying at supersonic speeds,

a transient pressure wave known as sonic boom can be experienced. For a Concorde

cruising at M =.1.78, Md an altitude of 43,000 feet, . the width of this corridor

is tY];lically forty miles in S1.UllIDer (Ref .1). The character and intensity of the

boom experienced on the ground depends, for a given aircraft under given flight

conditions, on the proximity of the observer .to the centre of the corridor, on

atmospheric conditions such as winds, air turbulence, and temperature gradients ,

and on the nature of the local terrain (Ref. 2). Figure 1 presents the pressure

signature of a tY];lical Concorde sonic boom. as recorded on the grcund under the

flight path. The "peaked", "normal" and "Ilounded" booms shown in Fig. 2 were each

generated by the same aircraft UIider same ·fl:i,ght 'condi tions. Differences in boom

peak overpressure, rise time, impulse and duration can be seen. Tqese differences

effect the response of a given building to a given sonic boom. Variations in

the character of a sonic boom have been attributed to atmospheric eff~cts such

as winds, a.ir turbulence, and tem.Pera~ure gradients, (Ref. 3). Boom overpressure

measured at stations across the corridor typically has a "bell" shaped profile,

with sudden cut-off at the edges of the corridor and a maximum at the centre

(Fig. 3).

As a sonic boom sw~eps ov~r a building, the building is subjected to a

time- and position-dependent forcing function. Pressure meàsured on outside walls

facing the direction of flight can be up to three times the measured free ground

overpressure • . This effect hasbeen attributed to multiple reflections. Pressures

on oppositeoutside walls are typically three-fourths the free ground overpressure

due to snadowing and diffraction of the sonic bOQm pressure wave (Ref •. 2). The

magnitude of the bu:i,lding' s response is greatly influenced by the relative

direc-tion of the supe:rsonic overflight. For example, the greatest response might be

expected for a flight vector perpendicular to the building' s longes t wal1.

The sonic boom subjects the building to é\. "racking" displacement whereby

the structure distorts in the shear mode relative to the foundation. The pressure

difference between the interior and exterior of walls, ceilings, and roofing

ele-ments causes them to disto:rt in the plate mode. Pressure disturbances are trans

-mitted into the interior of the building through open windows and doors and through

its structura.l elements é\.ccording to the:i,r flexibilities and sound transmissibilities.

The variou,s rooms, doors and windows of the building form a system of coupled

Helmholtz resonators whereby the transient acoustic energy of a sonic boom causes

the air in a room to resonate in the form of a damped sine wave, of ten of higher

peak overpressure than the incident N-wave (Ref. 5).

Theoretical and experiment al investigations of this phenomenon are

des-cribed in Refs.

6,

7 and 8. Figure 4 shows the pressure 'measured inside a building

acting as a Helrnholtz resonator excited by sonic boom during a Swedish test series.

Figure 5 represents an electronic analogue simulation of an essentially similar

event~

A building is a coll~ction of ~y discrete structural elements. The

displacements of these e lements are coupled and the bui lding itself is capable of

response in many mode shapes, each with its own natural frequency. Furthermore,

Helmholtz effects tend to form part of the overall dynamic ooupling (Refs. 5,7,8).

Figure 6 demonstrates the coupled modal responses of a floor and an adjoining wall.

A sonic boom contains energy over a wide range of frequencies (Fig. 7) :and is

capable of exciting many of the modes of vibration of a typical building. Figure 8 shows the displacement and acceleration with time of the centre of a wall excited

by sonic boom during the Edwards Airforce Bas"e sonic boom tests in 1966-67. The

Dynamic Amplification Factor (DAF) has been defined by Crocker (Ref. 9) as the

ratio of response to a pressure transient divided by the response to a static load

of the same pressure. The DAF of a given structural element depends on the period

and character of a transient and the natural frequency and damping of the element.

Figure

9

is a plot of DAF for the exterior structural elements of a building as

measured during the Edwards AirforreBase -series. Response is seen to peak when f

= l/T.

Computer-aided analyses of the response of structures to sonic booms have

been conducted using the finite element displacement method, with relatively

accurate results (Refs. 10,11).

It is known from the experience of sonic boom test series conducted in

the United States and Europe (Refs. 2,6,12,13) that some damage can be expected

in buildings exposed to sonic boom, even at relatively low overpressure • Experience shows that the damage will occur randomly to secondary structural elements such

as window panes, paint, wallpaper, and plaster. The cost of repairs of such

damage from sonic booms would naturally have to be paid for by the operators of

the supersonic aircraft responsible. For airlines, this would represent an added

cost of operation of SST' s •

When a structure is deformed by a sonic boom, damage can occur only

when specific elements are loaded beyond their yield stresses. In the case of

plaster, the situation is complicated by the existence of large numbers of stress

concentrations in corners, at the junction of ceilings and walIs, around wire

mesh reinfor.cement~ and at existing cracks (Ref.

6).

Some methods of construction

have relatively fewer inherent stress concentrations. Old structures can be

ex-pected to have more stress concentrations than new. Investigators of sonic boom

induced damage have remarked that in most instances, the general state of repair

of the structures involved was poor and that the boom of ten serves as a "trigger" for damage (Refs. 2,6).

For damage-prone materials such as plaster it is necessary to consider

other sources of loading than sonic boom. In essence, the problem must be

con-sidered as one of material fatigue, especially in light of the possibility of

repeated sonic boom loading from SST's in airline service over land. Diurnal and

seasonal changes in temperature provide cyclic loading and reversal of load.

Foundations can shift wi th the seasons. Blasting operations, thunder, wind

gust-ing, door slamming, running and walking indoors, and the passage of traffic and heavy machinery provide transient loading which can be at least as severe as that

of sonic boom (Refs. 1,6,14-16).

It would therefore be impossible to assess the effect of sonic booms

on the serviceability of plaster without having an understanding of the fatigue-life properties of the material. With such ~owledge, it becomes possible to include sonic boom loading in the list of enviro:rurental factors which degrade plaster, and which ultimately require i ts repair or r epIacement • Tbi s proces s

2. MECHANICAL PROPERTIES

Plasters are manufactured from the' natural mine ral gYl?sum, the main

constituent of' Wbich is calcium sulfate dihYc4'ate (caS0

₄

.2H₂0). ASTM C 22-50

(Ref. 18) specif'ies that gYl?sum 'be at least

70%

pure. The mineral is crushed

and ground to the desired fineness and heated at atmospheric pressure 300-350oF.

This process, called calcination, changes the state of hydration of the mineral

to the so-called hemi-hydrate form (caS0

4

.1/2H20). Additives may be added to

control the time of setting of· the plaster. Additional refining processes are

undertaken in the manufacture of the more exotic plasters 8.J."1d plaster cement s. ASTM c-28-68 (Ref. 18) specifies that calcinated gYl?sum for the building industry

be at least 6&/0 pure hemihydrate. In the ready nûx form, the plastermay contain

up to 3 ft3 of aggregates per 100 lb. calcined gYl?sum. Aggregates are essentially

added bulk which reduces the cost of the prOduct, which must set wi thin 1-1/2 to

8 hours. The aggregates include pure sand, vermiculite, perl;i te, . and wood fibre.

Neat plaster' is a calcined gYl?sum intended for base coats. The buil der

mayor may not add aggregates to suit his Pu.r:P0se. Gauging plaster is a calcined

gYl?sum of specified fineness which is ip~ended to be mixed with lime on the

build-ing site for use as a finish coat. Bond plaster is a relatively pure calcined

gYJ?sum

(9J'1o

hemihydrate, 2-5% lime) to te used as a coat over concrete.

All these various plasters,.in combination with aggregates or not,have

specified minimum physical strengths , and they all share one comon property:

when wa-re r is added to them in the right proportion, they can be made into pliable, workable slurries which af ter a period harden.

In the process of setting a plaster, (Ref.20) water must be added to

the "hemihydrate". Initially, water 'fills the gaps between the grains of plaster

and floats them apart. Àided by manual'-or machine mixing, hemihydrate dissolves

in the water. From this slurry of plaster and water supersaturated wi th

hemi-hydrate, entrapped air bubbles tend to float. Seed crystals ofdihydrate begin

to preciJü tate from the solution,. and on them grow an interlocking mass of crystals .

This is the period called hydration of the setting plaster. During this time, noticeable heat is evolved. The chemicai reaction may 'he described as:

hemihydr ate water <iihyrate heat

In the wet state, the interstices between the crystals are filled with the excess

water used to prepare the batch. Later,thesevoids will be occupied by air. The relative volume of these voids or pores defines the "porosity" (Ref. 19).

Theoretically, only 18.6g of water are required for complete hydration

of lOOg of hemihydrate, but in practice, more is required to f~oat the plaster

grains apart and to IlBke a fluid mixture. Ifnot Enough water is added, then

the resultant batch will be dough-like and will contain lumps of only slightly

damp plaster. Af ter setting, . incomplete hydration will have taken place and

the final product will be next to useless. If too much water is added, then the plaster will be excessively runny and the excess water will tend to separate f'rom the mixture. The final product will be flaky, çrumbly and excessively weak. The water to plaster percentage ratio is known in the gYJ?sum industry as tbe

"consistency" (Ref. 20).

Over its normal consistency range a given plaster will exhibit acceptable

properties when set. Indeed, the many various gypsum plaster types may be

classi-fied according to their normal consistency ranges. Ordinary building plaster has a

nor:rnaJ.. consistency range of abou·t 70 to 90; special purpose hard plasters for making

dies and case moulds may have consistencies as low as 20 to 30.

Different brands of building plaster have been found to have different

optimal consistencies (Ref.2l). Furthermore, the allowable consistency range of a

plaster tends to decrease with time due to the adsorption of water vapo1,lr (Ref .22).

Gypsum manufacturers recommend that plaster be stored in a warm, dry place and that

the oldest plaster be used first (Ref. 23). strength, density, and Young's modulus

are all controlled by porosity which, as we have seen, is controlled by consistency.

Figure 10 is a collection of data from Refs. 19, 23 showing the typical properties

of gypsum with varying consistency and porosity. In essence, higher consistency

means higher porosity, and lower strength, density and Young's modulus.

Referenc~ 21 points out that the strength of a set plaster is a function

of the stirring rate and the stirring time of the batch. Ridge (Ref. 24) found

that the temperature at which a plaster is set can affect i ts strength. For example,

specimens cast at OOC were about 1'2!'/o stronger than those cast at 29°C. He observed

that the structure of plaster cast at lower temperatures was finer grained and that

the average pore size is smaller. Apparently, at the lower temperatures there are

many more sites of nucleation. .

Thus it can readily be seen that there are many variables that affect

the mechanical properties of a set plaster. Conditions on the building site are

not well controlled. The ambient conditions are variable. The plaster is made

by different manufacturers, has been stored for different lengths of time, is

rarely mixed wi th carefully measured porti ons of water, and' the rate and time of

mixing are highly variable. One would not expect quite so large variations in the

properties of. a given manufacturer's plaster wallboard, however.

One effect which no one seems-to have investigated in gypsum. is agitation

and cyclic loading during the time when a plaster is setting. On a construction

site, as we known, all manner of 1dbrations are induced by heavy trucks,

construc-tion machinery, and blasting operations. Before the plaster is set and while it

is still wet,its strength is much lower than when it is set. Furthermore, its

densi ty is higher because of the excess wate r content. It is therefore more highly

susceptible to low frequency vibrations. One can imagine that the not yet completely

tied together crystals of the plaster might be damaged, but one. can only speculate

as to what effect this will have ·on the ~laster's strength and elastic properties

af ter it is completely set.

There is little or no existing data on the fatiguing properties of

gypsum or on the mechanism at work during failure by fatigue of plasters.

In short, therefore, plaster' is a mate rial of uncertain chemie al

compo-si tion, uncertain microscopá.c structure, and of widely varying mechanical properties • The material chosen for all the tests conducted in this pro gramme was

moulding plaster supplied by the Canadian Gypsum Company. ASTM standard C59-50

(Ref .18) specifi.es that moulding plaster be at least 8Cf1/o pure "hemihydrate", that

at least 9Cf1/o of it shall be finer than a 149 micron sieve, and that it set within

20-40 minutes. This plaster is essentially a purer version of building plaster.

- - - -

---(Ref .20). For these tests, consistency was mainta:in ed constant at 80 grams of wa'ter

per lOOg of plaster.

The procedure for' making the pi_aster was adopted i'rom Rei'. 25 as follows.

Tap water was allowed to sit at room tempera'ture for some tim~ to release as much

as possible of its dissolved gases. The water fqr a batch was carefully measured

and poured into the mixing container. The weighed portion of plaster was sifted

through wire mesh onto the surface of the water and allowed to so~ up water and

to sink. ' At this point, the side of the mixi~g container would be gently tapped

to help release entrapped air bubbles and wet the plaster grains. Two to three

minutes af ter all the plastèr had been added, to the water, the mixture was hand

stirred wi th a plastic pa,ddle for about 20 seconds. The plaster was then free

of l'lllll's and of about the same fluidity as tlÏick cream. It was then ready for

pouring.

A testing programme was undertakento determine the typical mec~nical

properties of the plaster formulation descr:î:l?ed above. Where possible, the re ..

sults obtained from the tests arecolllj?ared with data, taken from the li'teratttre,

summarized in Table 1.

Young's modulus and Poisson's ratio were determined withthe use of

strain gauges applied to a cantileverplaster beam deflected by a tip load.' The

stress generated at the mountirig point of the gauges ~y be calculated by simple

beam theory.

Mh

0'

=

21

where 0', M, h, I are stress, bending moment, beam thickness and beam cross-section's

secondmoment of area, respectively.,

Now, M

=

Fl

where F is the tip load anEl 1 isthe distancè from the load to 'tne strain gauge.

For a rectangular beam of width b:

I

=

3 bh

12 '

Strain is measured directiy trom thestrain ga,uges. A plot of stress versus

longi-tudinal strain is shawn in Fig. 11. On the same figure is a plot of transverse strain

(€T) yersus longitudinal strain (€L). Young's modulus, E and Poissop's ratio, v

are defined as follows:

a,nd

0'

E =

-~

v

=1

The beam roay then be tip loaded by fine inc-rements until failure occurs. This

experiment will yield the failure stress of the material in the specimen. Plaster is a brittle material which has a quite linear stress/strain curve right up to

failure.

Like many other brittle materials (such as concrete, glass, and even

cast iron) i t is much stronger in compression than in tension • Hence in the

bending mode, failure will almos·t always occur starting on the side of the

speci-men which is in ,t ension. In order to determine the compression strength, cubes

of the material were crushed by a Tinius-Olsen Universal Testing Machine at

con-stant rate of displacement until the first reversal of force. The stress of failure in compression was defined as the,ratio of this peek force to the gross

cross section area of the cube under test.

The density,p, of a large number of specimens of simple geometric shape was determined.by weighing them and comparing weight to volume.

3. SIMULATION, .

It was previously noted that sonic boom can be a contributing factor to the damage of plaster in builclings. The simple nechanical properties of plaster have already been investigated. The Lifetime Concept of plaster subj ected to

sonic boom will now be examined. In order to simulate the conditions in a

build-ing loaded by sonic boom, two factors must be present. The plaster must be sub-jected to a prior lbading history and then to the severe transient of sonic boom.

Af ter repeated sonic boom loading, the extent of damage must in some way be de-termined. In addition,.it would be useful to determine the fatigue life of the material for varying degrees of repeate~ loading.

The, UTIAS travelling wave sonic' 'boom horn-type simulator (Refs. 27,28) was the means used to provide sonic boom loading on plaster. The horn may be used in two modes: with a shock tube driver or with an airmass-flow valve. For several reasons, the bulk of sonic boom testing was conducted with the air mass-flow

valve. Though the tapered shock tube gives a "clean" N-wave pressure signature i t is, as employed in this facili·ty, incapable of generating N-waves of sufficiently long duration to be of use in sonic boom structural testing of full-scale speci-mens. Furthermore, the rise time of the shock tube N-wave is much shorter than that of a supersonic aircraft. In addition to having the capability of generating

simulated sonic booms of any duration from less than 100 ms to greater than 1 s,

up to large overpressures, the mass-flow valve can be operated automatically at a programmable rate which is limi ted, in practice, by the ability of the air com-pressors to' maintain pressure in the air reservoir'tanks. This is of extreme im-portance in fatigue testing, wherelarge numbers of loading cycles are to be ad-ministered during a test. However, the pressure signature of the mass-flow valve-generated N-wave is not nearly as "clean" as that of the tapered shock tube. Due to the high flow velocities through the valve a broad spectrum envelepe of jet noise is superimposed on the pressure signature of the simulated sonic boom. The intensity of the jet noise increasëi with the duration of the simulated sonic boom and increases relative to the boom as overpressure is increased (Ref. 27). It has been noted (Ref .28) that the addition of fiberglass boards as filters into the horn near the apex will reduce the jet noise content at the expense of some increase in boom rise time.

Figure 12 is an exterior view of the travelling wave horn-type sonic boom simulator, 80 ft. long and 10 ft. sq'lJ,are at the open end where an impedance-matching, moving porous piston (Fig. 13) is mounted to minimize reflections of the

pressure wave (Ref. 27).

In Fig.

14,

the control roam"is shown, cam,plete with auxiliary equip-ment and with the mass-flow valve in p~ace at the apex of the horn. Figure 15 is a view of the test room showing the cutout, or horn window, and 'the reflec-tion eli:m;inator.

F~gure 16 i~ a simplified functional diagram,of the facility. The l;l.orn window, which is

6

ft., high and

12ft.

long, has been modif1ed by the

addi-tion of a steel pl,ate perimeter with evenly spaced tapped holes to faciJ,.itate the attachment of a wide variety of structures.

Nine aluminum I-be~, 6' in. deep with

3-1/2

in. x

3/8

in. ,flanges

were milled so that one flange is 2 in •. wide. These beams were moun"tfed

verti-cally in the cutout with the small flange facing into the hom" 16 in. between centres. Aluminum arcpitectural channel sections, 2 in. w~de, 1 in. deep~

1/8

in. thick, were placedhorizontally," in'between the I-beams, and also on 16 in. centres.

This structurally stiff network was taken to simulate 2 x

4

wooden

studs, with wooden' cross-braces ('or "firestops") 'Qacked by a poured concrete, concrete bloek, or brick wall. According to typical construction practice,

plaster wallboard is nailed,' in place', on the studs. In corners and at the joints

between adjacent wallboards, various reinforcements s,+ch as adhesive tapes, are of ten applied. And over"thewallboard is applied asmooth, thin 'layer of plaäter "hard coat". The finisl;l.ed wall is theref'ore a continuous structure • Here,

however, discrete plaster panel specime~s were used.

, Perimeter frames, 16 in. square, of galvanized sheet steel bent into 1 in. ,x

3/8

'in. x 1/2 in.' channel sectiohs were fabricated. The process of making a plaster panel follows: the frame is laid flat and a 14 in. square bottom plate of the same sheet metal as the frame is inserted in the frame. Plaster slurry is poured into the frame until it is level with the hottom of the

top flange (Fig. 17). The table on which the ,frame sits is gently agitated for

about 5 min. with an uncounterbalanced electric motor to free entralllled air bubbles. The plaster is allowed to set. Af ter the heat of hydration has been dissipated, the panel is, lifted end the bottom plate remoyed. The panel is then

allowed to dry in a drying rack for at least two weeks before use.

For use in sonie boom testing, the panels are attached tq the stru c-tural network in the hom cv,tout by means of 1 in. x

1/4

in. aluminum bar stoc$. and machine screws. The attachment seheme'is graphically described in Fig.

18.

There is roam for 'up to

32

panels to be"mounted in the cutout at one time. Such an attachment scheme is a good simulation of the boundary eon-ditions encounterec;l on a continuous ,wallof plaster, wbich can be thought of as a, number of panels with edges clamped a't the studs limd f~re~tops, providing that mot ion of the whole wall can be neglected. Fo~ wood-framed buildings and forlarge interior walls without masonry backing, the ass~tion of no wall movement is not a good one. Nor is it large wood-framed ceilings. The extra flexibility of such structures allows them to be excited by sonie boam in the

simple plate mode.

On the other hand, the panels, though of relatively high quality and uniformi ty, have the benefit" of nei thaI' :the ,p,aper :reinforcement of plaster

wallboard nor the dense, strong plaster hard coat. Furthermore, the superimposed '

jet nois.e contains a.large percentage of its energy. in the resonant. range of the

plaster panels. In addition, the acoustic back-'loading of air cavi ties behind

the plaster' board in a real \ wall affords more support ·than offered to the freely

suspended panels of this test series. The panels are mounted in the hern wi nd ow ,

parallel to the direction of propagation.

For parallel mounting of the panels, the pressure loading is rende red non-uniform in position, because i t takes finite time for the wave to traverse

the panel. However, because the panel length is. much smaller than .the wavelength

of a simulated sonic boom, there should be li ttle difference between parallel and normal mounting. For theshort wavelength of shock tube N-waves, this is not true.

A strain gauge mounted, on the centre of each panel was the means of

measuring response. It. will be shown that centre strain and centre displacement

are equivalent for response modes symmetric 'àbout the centre. A . strain-measuring

electronic circuit was built, as described in Appendix Al.

Pressure was measured with a Ë '&K model UA 027L 1/2 in •. sonic boom

microphöne and by a KistIer model 206 piezotron •

. An electronic control box with the capability of ·.ma.nual or aut~tic

firing of the air mass flow valve was constructed by the UTIAS electronics

tech-nician. An electromagnetic totalizer was attached to the cöntrol box to

indi-cate the numberof booms applied during a test series.

·In order to ·facilïtate the recording .of an event'occurring in the

test end of the horn, but initiated at the control room, an electronic delayed

trigger was constructed (Appendix A2). In practice, 'a trigger pulse from an

inexpensive ceramic microphone activates the.circuit which, af ter the desired

delay, triggers' the sweep of an oscilloscope. The delay required is the time

from initit;l.tion of the sonic boom to its arrival time at the test section.

In order ·to simulate other' sources of leading encountered by plaster

and as a means of determining the fatigue life of plaster, the plaster panels

were loaded sinusoidally by an acoustic shaker as described in Appendix

A3.

In short, therefore, the facility employed for this test series is

capable of generatingpressure transients ofa similar character to the sonic

boom generated by an aircraft flying at supersonic speeds and of delivering that transient to a matrix of structural members which simulate the wall

of a typical Canadian house. The technique of using discrete panels allows

many loading tests to be run simultaneously • . The short cycle time of the

mass-flow valve/high capacity compressor systeIil/automaticfiring system allows

many booms to be administered in a short, no~-tedious period of time.

However; it should be nóted that a complete separation (or "uncoupling")

of phenomena .is weIl nigh impossible. For example, one can never be sure that

the plaster does not contain weakening lill!;ps or unseen .. internal bubbles. The

panels are never perfectly planar and severe static stress fields can· be

gene-rated in the panel when it is clamped in place in either the horn window or the acoustic shaker. It would be possible, even for a perfectly planar panel, to crush the plaster behend yield by excessive tightening of re'taining screws.

properties are functions of arnbient conditions such as temperature and especially humidity.

The silnulated sonic boom is not necessarily öf the same character as

the pressure transient to which the plaster of a:IJ.y give~ house is subjected by

sonic boom. However, depending on aircraft headi'ng and on the degree of acoustic

coupling from open or closed windows and doors, the interior pressure transient

induced by sonic boom will vary with a given buil~.

4.

ELASTIC ANALYSIS OF TEE PLASTER PANEL

This ~ection uses the mechanical properties of plaster and the geometry

of the plaster panel as the basis for an analysis of the behaviour of the· plaster

panel under various loads and with various .. support ronditions. Tt relates strain

measurements to other possibly mó-re meaningful. quantities. Small deflection, thin

plate theory is used throughout.·,

For small deflection-theory to be accurate, the maximum deflection of

the plate must be much smaller.than its thickness. Otherwise stretching of the

middle surface of the plate must be taken into account. For thin plate theory to be accurate, the thickness of the plate must be small compared to its edge dimensions. Otherwise shear deformations through the plate thickness must be

taken into account. . Rough ,an.d seemingly lenient criteria (Ref. F9) requj,.re tha:t

the thickness be at least five times the maximum deflection and. that the shortest

side of the plate be at least five times the thickness for small deflection, thin '

plate theory to be applicable. .

First, an interprëtation of the strain readings obtained from the plaster panels must be given. Strain is measured by a strain gauge placed along thë diago-nal of the panel, at the centre. In the acoustic shaker the panel is narmally

subjected to a plane wave in pressure-,' at a frequency which will exci te the

funda-mental mode which is symmetrie about the centre of the panel. In the horn, under sonic boom loading, the situationis more cOIlI]llicated. The loading is a traI).sient

and, in the case of our simulator, contains ·broad band jet noise (Fig.

19).

The

sonic boom sweeps along the plate. The loading is, therefore, not only time de-pendent, as in the shaker, but a}-so dependent on posi tion on the plate.

This is not a problem during the lineat decay position of the wave be-cause the wave length is longer than the dimensions of the panel. However, it is

a problem with the sudden rise of t~e.sonic boom which, in this case, is typically

3 ros, corresponding to approximatelY '3'~eet which is of the same order as the panel

dimensions. In addition, the ~igh frequency content of the jet noise will surely

excite bther modes than the'fundamental, both symmetrie and asymmetrie about the .

centre of the panel. For mode shapes symmetrie about the c.entre . of a square panel,

it is clear that the strain measured by á strain . gauge mounted at the centre will

be equal to the strain measured by a gauge placed perpendicular to it. With this in mind, consider two coordinate systeros with origins on the surface of the plate at its centre (Fig. 20). One sys-tem (x,y) is on the diagonal; the other (Xl ,yl),

rotated somewhat. Postulate shear s,trains in the plane of the panel at that point.

They are called ?' and '1' I I for the (x,y) and (x' ,y' -) coordinate systems

res-x.y x .y

pectively. For a third 'coordinate system, called the principal a:xes sy-stem, no

such shear exists, by definition (Ref. 30).

For the (x,y) system,

€

_max

and with E

=

E ,

X Y

1~---2~j

=

EX: El

i-~l....;€X~

'

~_€....IIY:"")+.( r~y)

r

=

E + l~l

x 2 (1)

where E is the maximum strain in the principa:J,. axis eoordinate system. max

(2)

where (r/2)max is the maximum shear s'train to be eneouz:ttered for any orientation ofaxes at the centre.

A similar set of equations ean be developedfor the (x', y') system:

E

=

' E ₊ Ix'y'

max x:': 2

(~

)

~

rx''l.'

2 (4 )

Now eOllIJ?are equations (t) , (3) :

E + 1 r

~'l.

I

~

E

-

₁ rx''l.'

I

=

₀

X x' 2 (5a)

but,

r_xy

~(~)

,

=

!.EL

I;

thus E

=

_Ex'

T

2 x

max

( 5b)

Therefore, the strain ga~ge reading at the centre of the square panel, with symmetrie defleetion modes will be independent of orientation. Refer now

te the general two-dimensional equations of elastieity (Ref. 31).

cr _x

=

E

-·2

1 - v

cr y E.

= ...

'

--~

₂

1 - ~ (6b)

where cr , cr are si:;resses in thex,y directions, vis Poisson'.s ratie, and Eis

x y YoU!l€;' s modulus.

Since €

=

€

=

€ •

X Y •

(we measure € with a strain _gauge)

cr =cr =cr

=

E € (6c)

x y

1

-

v

Fer E

=

6.5 x

105

psi, v.

=

.235:

cr

~ 8~50

x

105

psi _• €

This is an interpretation of the strain gauge re!;l.dings. For bending mements

M ,M imposed on a plate'at a given poi:q.t,the stressés at the surfa.ce are

x y

given by (Ref.

32):

6M

CT ..

=

-.:J:.

Y7

where h isthe pla,tethickness.

For a simply supported squar~ plate 'lUlder a statie uniform transverse

pressure laad, the deflect10n w and distributed moments M and M at the centre

s . x y

are given by (Ref. 29):

·w

s

. 2 .

M=M =M =(3aISP

. x Y'

where ~ is the pressUfe, a is the length ef a side.

For the plaster· panels, :

.

11

end, for v = .25 thus, end, a = 16 ins. E = 6.5 x 105 psi h =

.4

in. nominal:

ex

= .0457

13

= .0460 (Ref .29) w

=

.0719 in/psi .6P s M

=

11.8 in2 • 6P

Now, supposing we want to calculate the deflection of the centre of the simply supported panel, knowing the strain. From equations. (6c, 7,8,9):

'w

=

s

2.

a ex

6(1-v)l3h • E

Substituting the known values of a,

ex, 13, v,

h yields the expression: 2

w

=

1.38 x 10 in. E

s

(10)

for any deformation of the square, simply supported panel which is of the same

shape as that of statie pressure .loading.

In the shaker, the support condition was found to be close to simple

support. The fundament al mode shape is nearly identical to the statie, constant

pressure mode shape. Therefore, the above expression is a valid meens of esti-mating deflection for a known strain. Plaster yield occurs at about

or, from equation (6c),

whenoe,

(J

=

300 psi

E

=

354 ~in/in ~t the centre,

w

s

=

4.88 x 10-2 _in

Since the maximum value of w is much smaller than h, small deflection thin plate theory can be expected to ~eld accurate results.

Now consider the cas·e of clamped edge support for the plaster panel. Th:is cöndi tion is fairly accurately met when the panels are mounted in the horn window. Recalling equations (8, 9) for the clamped boundary condition with

v

=

.25 nominal (Ref. 29):

ex

=

.0143

~

=

.0220

One might want to predict the st;rain induced at the centre of the clamped plaster panelfer a given uniform static pressure load. This may serve

as a "ballpark" guess

'

at

the effect 'of a given somc boom and will, in addition, af ter sonic boom dynamic strain measuremènts have been made, teIl us the Dynamic An!Plification Factor (DAF) of somc boom on the plaster panel with cl~ed edges.

From Equations (6c, 7, '9): €

=

6~Cl

- v) a 2 Eh2

=

,249 Ilin/i.n/ps~ .liP

=

,1.73 ~in/in/psf' liP for the known values of ~,

v,

a, E, h.

(11)

One cannow proceed to estimate the natural frequencies of the square plaster panel for the two boundary conditions-of simply supported and clamped edges. From Ref. 29, the fi~st natural frequency is:

cfJ

l

f

=

-1 2

a 12p(1 - v ) 2'

where p is the material density. · Fo~ simple support,

hence,

f

l

=

120 Hz

For clamped edges,

hence,

(12)

.An interpretation of strain measurements has been made and the use of thin plate small deflection theory has been -justified. The static pressure response and the natural frequencies of the p:j..aster panel for both simple and clamped support have-been computed.

5.

PLASTER PANEL RESPONSE TO SONIe BOOM

The response (as measured with strain gauges) of the plaster panels mounted

in the horn cutout to simulated sonic boom will nCl>i be examined. In this phase of

the test programme, the intensity and 'duration of t~ sonic boom to be used for

fatigue testing was chosen. The nature of the panel response was examined. The

effect of superimposed jet nois~ was found to be significant. The panels were loaded

by mass-flow-valve-simulated' booms of varying duration and by tapered shock

tube-genera:ted booms. That the boundary conditions of the panels mount ed in the horn

are close to clamped was verified.

For reasons to be described later, the boom chosen for fatigue testing

was of 10 psf overpressure and 100ms duration. Figure 21 shows the response in

strain to such a boom, with both no electronic filtering (Fig. 2la.) a,nd with

high-pass filtering (Fig. 21b). The unfiltered trace shows that the panel closely follows

the rise in pressure accarqpanying the sonic boom' s front shock. The pa,nel begins

to oscillate, because of the combined effects of the shock transient and the

super-imposed jet noise. Dynamic An!>lification factor for the panel can be dete rmined.

E

DM'

₌

]2eak

Estatic

=

30 _17.3 ~in _~in in _in

=

1.73

The response of the panel can be considered to liein two regimes. For loading at frequencies well below res onance, the panel can be said to respond quasistatically. Consider Fig. 2lc which is the trace of pressure outside the horn, 6 in. behind the panel minus the pressure inside the horn, with lew pass filtering, cut-off at 40 Hz, which is well below panel resonanee, and of the 40 Hz

low pass response in strain of the panel. Notice the similari ty in phase and

shape for the two traces. Ac.c.ording to plate theory, the panel strain for 6.55

psf statie pressure should be:

E

=

11.3 ~in/in

We measure:

E·

=

12.7 ~in/in

which is in reasonable agreement.

Loading at frequencies near resonance will excite the panel quite severely. Figure 22 shows band pass electronic filtering 0f the 10Oms, 10 psf simulated sonic boom from 150 Hz to 250 Hz, the resonant range forthe plaster panels with clamped

edges. The peak pressure of this envelope reaches 1.6 psf (16% af the peak pressure

of the N-waves). Figure 23 is an expanded trace of strain response of a plaster panel. It indicates that the natural frequency of this particular panel is approxi-mately 200 Hz. For mass-flow-valve generated sonic booms, then, the response of

the plaster panel may be ';thought of as a quasi-statie following of the general

One would expect that, were the jet noise reduced, the strain +esponse would be reduced as well. Figure 24 shows the response in strain due to simulated

sonic booms with varying degrees of jet noise filtering. The filtering, of the type described in Ref. 28, consists of the insertion of fiberglass boards into the horn both longitudinally and transversely at ab out the 16 ft. station where flow velocities are still quite high. The response in strain is indeed reduced by the addition of jet noise filtering.

;Figures 25a to 25f show typical response in strain of the plaster panels for a wide range of N-wave durations and Fig. 25g is a plot of DAF for varying N-wave duration as derived from Figs. 21a and 25a-f.

Figure 25a shows the panel capàble of rise time of approximately 2 ms.

For booms greater than 100 ms duration, the dominant loading effect is jet noise. One must ncw examine the response of damaged panels. Because with damage the stiffness and thus the natural frequency of a panel drops and because the peak in energy content of a 100ms boom occurs at 10Hz (Ref. 4) and falls at essentially 6 dB/octave thereafter, onewould expect considerably more response from broken panels than from intact panels. Figure26a is the trace of tesponse of the intact panel. A simple crack has developed in Fig. 26b. The panel, originally square, has thus been rendered into two panels, one triangular, the other a parallelogram with three clamped edges, and one edge with the nonlinear support of the crack. This edge will scrape and rock when excited and thus will provide some damping. The natural frequency of the parallelogram (on which is mounted a strain gauge) has dropped from 170 Hz to 150 Hz and the DAF has in-creased from 2.6 to 3.7. In Fig. 26c the crack has been opened up to eliminate these fretting effects. The natural frequency is thereby dropped to 110 Hz and the DAF increased to 5.4.

The vari ous sonic boom response phenomena have been investigated, in-cluding the effects of low frequency content of the simulated sonic boom, the intermediate frequency jet noise, and the high frequency drive of the shock tube N-wave. It has been shO'ln that. cracking can be detected by a change in the character of a panel's response.

6.

FATIGUE PROORAMME

It has been shown in the preceding section that the peak strains induced

in the plaster panels by sonic boom are well below the strain required for the material to yield. However, central to the "Lifetime Concept" is the concept of fatigue. In order to determine the degrading effect of sonic boom on plaster, one must apply repeated booms so that the damage becomes cumulative. Furthermore, other damaging influences, as was previously noted, must be taken into account.

The first part of tne fatigue programme was an experimental dei:e rmination of a sinq:>le S/N curve for the])laster. Theplaster panels were loaded sinusoidally in the acoustic shaker. For each panel, a particular value of peak strain was

imposed at panel resonance until the panel failed. Panel failure is accompanied by a downward shift in panel resonant frequency and, since the shaking frequency is not changed during a test, the strain drops. The onset of failure towards the end of a test has been observed to be quite sUdden, requiring only a few seconds or less.

Panel failure has been arbitrarily defined to occur when the peak strain

has fallen to

80%

of its value at the beginning of a fatigue test. The drop to this

level of peak strain is sensed by an electronic level detector circuit (described

in Appendix A4), which then t,è-rminates the experiment. Such aut0Inatic monitoring

is necessary because some of the fatigue tests requirèd on the order of one week

for completion. Figure 27 is aphotograph of the fatiguing apparatus. The results

of the fatigue tests are l'lotted in Fig. 28. A line was curve-fi tted to the data using a least squares computer algorithm. The empirical equation of this line is:

E

= 345 - 21.9 log N

where E is the peak strain imposed apd N is the expectation of the number of cycles

at that strain to failure in fatigue. The large amount of scatter seen in the

figure is typieal of fatigue testing. More confidence could be attached to such

a curve and its standard deviation (51.6 ~in/in) were more specimens to be tested.

One rather encouraging feature of the curve fit is that if an extrapolation is

made to one loading cycle (N

= 1) then,

E

=

345 ~in/in

This compares well wi th the yield strain of the material which was

eomputed to be oceurring at a measured strain at the centre of 354 ~in/in. The

material appears to have quite excellent fatigue properties , gaving the

expecta-tion of enduring almost one half of its yield strength for 10 loading cycles.

The second half of the fatigue testing programme consisted of subjecting

the plaster panels to combined preloading, sonic boomloading and .postloading.

The preloading and postloading consisted each of 10

7

loading cyeles at

50 ~in/in peak strain, which is slightly higher than the typical peak strain

in-duced in the plaster panels by a 10 psf, 100ms simulated sonic boom. The

pre-loading simulates the prior damaging influences to which the walls of a building

might be subj ected. The postloading serves as an indicator of the pJa ster' s

abili ty to continue to withstand normal, everyday loading af ter repeated exposure

to sonic boom. A panel's serviceability oould be established if it survived the

sonie boom tests and the shaker· tests without appreciable shift in i ts mechanical properties , most notably i ts natural frequency in the shaker and the power a.n:q:>li-fier output voltage required for a given level of strain at resonance.

The sonic boom loading consisted of 1,000 simulated sonie booms, each 100 ms in duration and 10 psf in overpressure. No jetnoise filtering was applied. Compared to a Concorde SST sonic boom these booms have four to five

times the overpressure and about 40 to

50%

of the duration. The mass of air

re-quired for a 100ms simulated boom is considerably lower than for the 250ms

simu-lated boom (the duration typieal of a Coneorde boom). The repetition rate is therefore faster for the short er duration boom. Furthermore, the jet noise is

of considerably lower amplitude for the 100ms simulated boom. The use of

rela-tively high overpressure boom can be justified as a means of simulating Helmholtz

effects which .often amplify the overpressure of the incident sonic boom.

The booms were applied at a rate of 100 per hour. Af ter each set of

100 booms, the panels ~ were vi sually inspected for cracks and the response of each

panel to sonic boom was monitored. In fact, response was found to be a better

clue of damage than eracking, which is extremely difficult to detect. Of the

The results of the test are s·ummarized in Table 2.

The slight shifts in resonant frequency and sensitivity ·to power amplifier

voltage are considered to be insignificant and can be . attributed to changes in

clamping force.

The response of the panel which failed is illustrated in Figs •. 26a <á.nd

26b. In Fig. 29, by contrast, we see the response of a panel which did not fail

t 0 i ts fir st, 500th , ~d 1000tl1 s oni c boom'. .

Assume that the modelling was accurate except that the strain induced by

a 25Oms, 2 psf Concorde boom on plaster is twice that induced by the' 10Oms, 10 psf

simulated boom, and assum~ that the plaster of a ~alJ,. oscillates in strain at that

peak level of 100 Ilin/in for four times' the Concordeboom· duration; that is, for

about one seconde This gives the wall panel, fór a Il0Ininal natural frequency of

200 Hz, 200 loading cycles,at 100 Ilin/in peakstrain. Now assume that there are

no other

4

1oading influences on the wall but 30 Concorde sonic booms per day, or

about 10 booms per year. The wall panel is thereby subjected to 2 x 106 löading

. cycles per year. Now assume that the plaster' in the .wall, lies on the lower standard

deviation line of the SiN curve. From Fig. 28, this would give' the plaster a

fatigue life of 108 cycles at '100 !lin/in strain; req1.Ûring 50 years of exposur e

to 30 booms per day before the occ-urrence of a crack.

On the other hand, the plaster damage problem ,is strongly pointed out by

the fact that one of thirteen tèst panels did break under the influence 0f sonic

boom loading. It is quite likely that the failure occurred due to excessive

clamp-ing pressure from the retainer strips used to secure the panel in the horn w:in dow. When this static stress field had the dynamic stress field due to sonic boom

superimposed 0n :i,..t, the result could well have been very close to yield stress.

7 • CONCLUDING REMARKS AND RECOMMENDATIONS

It has been shown, within the limitations of the technique of simulation used here, that damage would be tinlikely to plaster walls and ceilings in properly

maintained buildings subjected to repeated sonic b00ms generated by SST overflights ~

Nevertheless, claims of plaster damage 'induced by sonic boom have been made and the

agencies responsible for the supersonic aircraft involved have reimbursed claimants,

at least in part. Table 3 is apartial, listing of available data on supersonic

overflights of populated areas and the resulting payments for boom-induced building

damage. Variations in the percentage of claims that were · accepted and in the specific

cost per boom can be attributed to differinginvestigation practices for different countries and agencies.

The relative amount of plaster damage will vary with differing construction practiees and state of repair of buildings. Although i t is felt that t he sonie boom may act as a trigger for incipient damage, i t is a diffieult problem to apportion responsibility when a sonie boom eauses damage to a plaster wallor eeiling. Many

aged plaster struetures may be--'ready to collapse with virtually any transient.

This ean arise from the eomhined fatiguing action of the operation of construction

maehinery, the passage of traffie, thunder or door slarimling. It is not reasonable

to expeet that an airline opèrating SST' s should pay all costs of renovation

beeause one of its aireraft triggered the damage'in a strueture ready to collapse

in any event. Fear of sonie bóom aften leads owners to inspect earefully their buildings af ter a supersonic overflight. In many cases the damage they find may not

have been caused by the sonic boom at all, but may have occurred earlier due to some

other cause. Such an event may. appear statistically (Table 3) as an unsettled

sonic boom-:i.nduced damage claim.

Future simulations of boom-induced plaster damage should, unlike the

present work, attempt to include built-in stress concentrations such as corners,

window and door frames and existing cracks. Furthermore, tl1ey might include coupled

responses such as Helmholtz effects and entire wall motions • In addition, all the

various plaster construction tec_hniques, using lSYl?sum plasters with added aggregates

and gypsum wallboard could be tested. However, . in view of the present optimistic

results , perhaps onl-Y the most -vulnerable of these might be attempted.

Alterna-tively, it would be useful to formulate a workable computerized technique of coupled

structural and acoustic analysis of building response. Such a techruique could be

applied to a wide variety of construction methods a,.nd building layouts to deter:rn:in e

their response to sonic boom and to 10cate potentia1 areas of stress concentration.

Experimental fatigue data on construction materials could serve as computer inputs

to estimate the damaging inf1uence of sonic boom on buildings. This procedure might

save a good deal of experimentation.

In smmnary, the results of the tests performedindicate that tl:e sonic

boom-induced building damage prob1em is not significant for plaster in we11-maintained

structures. These results agree with the conclusions of most researchers in this

I ' , 1. MilIer, W. D. 2. Lilley, G. M. 3. Frobose, M.

4.

5.

6.

7.

8.

9. 10. Parmentier, G. Mattieu, G. Rigaud, P. Franke, R. Evrard, G. Clarkson, B.' L. Mayes, W. H. Wilhelmsen, A. Larsson, B. . Lin, S. Slutslty, S. Arno1d, L. Crocker, M. J. Hudson, R. R. Craggs, A. 11. Popp1ewell, N. 12. Weber, G. M. Ry1ande~, R. (ed.) 13. Nixon, C. W. Borsky, R. N. REFERENCES

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De~ember, 1970.

Report,in five parts on the Somc Boom prepared for

the OECD Conference on Sonic Boom Research. Part 2. Variations in the sonic boom pressure signature due

atmosphèric ',conditions and ground reflectiom.

Part 3. Response , of struc'tures to sonic boom.

Bäng Sonique de Concorde 001. variations de pres sion au sol.

, ~e systeme auditif du Cobaye.

ISL Rapport Technique RT3/72.

Enregistrement des Etude des effets sur Istres, mai 1971.

Somc Boom Experiments at Edwards Air Force Base.

Prepared by the Stanford' Research Insti tute for 'the

Na'tional Sonio Baom Evaluation Office, Report NSBEO-1-67,

J\üy·1967.

Boom-induced Buildings Responses and Damage. JQurnal of the Acoustical Society of Amer:i,.ca, 51,1972.

Sorï:i.c Booms and Structural. Damage. Nationa1 Swedish

:süilding Research, Document D3: 1973 (Engl1sh Translation) Sonic Boom Analogues for Investiga'ting Indoor Waves

'and Structural Response. lFrIAS TN 158, Nov 1970.

EXperimental-Ana1ytic Dynamic Techniques fer Application

to Sonic Boom Struct\lI'al end Acoustic. Response

Determi-nat~,on. NYU-AA-70-1~, July, 1970.

Struçtural Response to S0111c Booms. Journ~ of Sound

and'V~bration, NO.9, 1969.

The Response of a Simply Supported Plate to "N" Waves at Oblique Incidence. Jrurnal of Sound end Vibration,

Vol.' 16,. 1971.

The Response of Box Type Structures to Somc Booms,

,NASA CR 66887,-1970.

Sonic B00Ill Exposure Effects : Rep0rt from a' Workshe:p

on Methods and Criteria, Stockholm, 1971. II.l:

structures and Terrain. Journal of Sound and Vibration,

Vol. ,20, No.4, Feb 1972.

Effects

ot

Sonic Boom on People. The Jouna1 of

~he AcousticaI Society of America, Vol. 39, No.5, 1966.

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