Note on resonance testing

343

NOTE ON RESONANCE TESTING

By R. E. D. Bishop* and

J.

W. Penderedt

THE B A S I S O F RESONANCE TESTING

IN THE MOST RUDIMENTARY FORM of resonance testing, a

structure is excited harmonically and the driving frequency is adjusted until a resonant state is found. The resonance frequency is assumed to be a natural frequency of the structure, the resonant vibration is assumed to take place accurately in the corresponding principal mode (which can thus be identified and measured) and the resonant magni- fication-or, alternatively, the variation of response with driving frequency around the resonant condition-can be made to give a figure for the damping associated with that mode.

The underlying theory is both simple and very well known, being effectively that of a lightly damped system having one degree of freedom. The technique is commonly used in industry and is often perfectly adequate. It can be used, for instance, with alternator rotors (which are housed in their bearings but not rotating) as a means of estimating or checking critical speeds.

PRACTICAL DIFFICULTIES

Unfortunately there are some engineering systems whose natural frequencies and principal modes (if not their levels of damping) have to be measured, but for which simple resonance testing is utterly inadequate. This is par- ticularly true of aircraft structures.

There are several reasons why this difficulty may arise, but they all amount to the same thing-the real structure is inadequately represented by an ideal system having one degree of freedom. I n particular, the structure may possess close natural frequencies which will not permit violent vibrations to be excited separately in their cor- responding principal modes. An airliner on the ground may well have 30 natural frequencies and principal modes in the range 0-25 c/s.

There are other problems which may confront the resonance tester. One of these is the presence of heavy damping and another is damping which may couple the The M S . of this paper (which is an introduction to the three papers which follow i t ) was received at the Institution on 2nd October

1963.

* Kennedy Professor of Mechanical Engineering, University College London. Associate Member and Member of Council of the Institu- tton.

t

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principal modes. Yet again, even with a well-behaved system it is possible to miss resonances if the exciter is sited badly.

Resonance testing of aircraft structures was introduced in this country before the last war. And, by the end of the war, the difficulties that have been mentioned were well recognized, both here and in the United States of America, though no satisfactory way of overcoming them had been found. Fresh impetus was given to resonance testing after the war by the discovery of progress made during the period of hostilities by the Germans. Since then, several papers have been published on the subject.

THEORETICAL A N D EXPERIMENTAL INVESTIGATIONS

A critical survey of linear resonance testing techniques

has been published*. The basic theory was developed and the various techniques which have been suggested from time to time were examined in the light of it. It was pointed out that techniques are essentially of two sorts: (1) A simple system of excitation produces response data which, with aircraft structures at least, are usually extremely complicated. The tester then has to face a dif- ficult task of analysis if he wants to extract modes and frequencies.

(2) A complicated system of excitation produces a response which occurs accurately in a principal mode at the appropriate natural frequency. In this case, little effort is required by way of analysing results.

It seems probable to the present authors that, of these two possibilities, the second may well prove to be the more acceptable for aircraft structures. Although some progress has been made towards devising a suitable tech- nique, however, the theoretical side alone is by no means straightforward.

So far, however, the first possibility has proved by far the more tractable. The techniques in use today are almost invariably of this kind. Now one of the main obstacles to progress in devising a practical technique is the lack of published experimental data obtained under controlled

4 BISHOP, R. E. D. and GLADWELL, G. M. L. ‘An investigation

into the theory of resonance testing’, Phil. Trans. A 1963 255

(no. 1055), 241.

344 R. E. D. BISHOP AND J. W. PENDERED

conditions. In fact the literature on resonance testing appears to be almost entirely theoretical.

It was to meet this need of experimental data that a series of experimental research studies was put in hand, and some of the work that was done is recorded in the three papers which follow this note. Of course, the task of providing an experimental background to a subject like this is very large. The question of presentation also raises

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difficulties. Here, each paper takes up one particular topic so that each is self-contained, though this has inevitably led to some overlapping. A further investigation has been completed in which a system having, in effect, two natural frequencies was resonance tested; the system was adjusted, for successive tests, so that one of the frequencies gradu- ally ‘passed through’ the other. This last investigation will be reported later.