Summary
Steel structures are subject to large dynamic loads clearly reflected by generated vibration processes. The vibrations may affect state of serviceability of structures by lowering comfort of persons working there as well as possible reaching the level haz-ardous to safety of the structures. The effect of vibrations to structure is mainly manifested by additional stresses in a given cross-section, which are summed up with those resulting from static loads. The dynamic loads may cause damaging effects in buildings of various structural types or even lead to their destruction.
Judging the necessity of improving the quality assessment methods of building structures for purposes of estimation of their state as well as safety factors for brick structures, the author of this work undertook an attempt to investigate destruction pro-cess of selected object by using the method of experimental modal analysis.
Keywords: modal analysis, natural vibration frequency, stabilization diagram Introduction
Public modern building structures, production of silent-running machines and devices are asso-ciated with a high precision level of their manufacturing and appropriate selection of materials that greatly influence their quality, reliability and durability [7,19,21].
In investigating real systems (structures, buildings, machines, devices) the main problem is to determine quantity of energy stored, dissipated and transmitted by particular elements of the sys-tems. Knowledge of the quantities serves to assessing material effort, fatigue, diagnostic investigations as well as predicting noise levels, and also to facilitate designing system’s elements (e.g. vibration isolation) [1,5,12,17,20].
Development of measurement methods, especially those for measuring energy quantities, has substantially extended possibility of research on sound radiation by structures as well as made it possible to calculate sound power radiated to a remote field on the basis of close-field measurements. Methods for quantitative and qualitative research on vibroacoustic energy propagation within space of complex boundary areas have been developed. It has been connected with quantitative assessment of vibroacoustic energy stored in structural elements as well as assessment of energy radiated by the elements and also that transmitted in different ways [2,4,9,16,21].
Contemporary structural dynamics in building engineering makes use of various research tools from the state identification area such as : boundary element method, finite element method and modal analysis methods, which enable – by modelling and investigating state changes – to better understand behaviour of complex structures, perform their optimization during design process and assess their current, often hazardous, states [6,8,14].
Acknowledging necessity of improving research methods dealing with quality of brick building structures for purposes of assessing their state, as well as safety factors for brick structures (see
PN-research methods for quality assessment of destruction selected building structures by means of the experimental modal analysis method [12,13].
It is necessary to improve methods for research on dynamic characteristics of structures espe-cially those exposed on large dynamic loads. New materials and technology methods have been introduced to building engineering as well as novel structural solutions make it possible to increase productivity and quality of products, however they are accompanied with large, often dangerous dynamic loads. To the problems more and more attention has been presently devoted [13,17,18,19].
In building engineering, vibrations – a process which accompanies any motion – may be con-sidered in the categories of noxiuos, favor able or information containing vibrations. Vibrations are primary process and their (secondary) effect is acoustic signal in the form of longitudinal sound wave. Vibration and noise processes form the basis for a scientific research area – vibroacoustics. Modern building structures are accompanied by vibroacoustic phenomena which endanger people, environment, and their products. Trends of contemporary engineering and technology connected with rising dynamic loads, rotational speeds, minimization of weights and gabarites, make growing level of vibrations and noise invitable. The tendencies together with mass application of technical means provide hazards to people, natural and technical environment [2,7,10,13].
In most cases met in practice, analyses of dynamic properties are performed on the basis of analysis of structural model behaviour. Quality of the analysis depends on credibility of the model, which is measured by means of conformation of the object’s behaviour and the model, both subject to disturbances of the same kind. Structural model may be built in the process of analytical transfor-mations used for description of system’s dynamics or on the basis of results of experiments performed on a real object [3,8,9,20].
Analysis of dynamic properties of structure is carried out mainly by examining behaviour of dynamic model of a given structure, which is realized by using analytical description of quantities, which characterize system’s dynamics, or experimental methods directly applied to real objects [13,21].
Novel tools in this research area deal with possible application of modal analysis methods as well as a modern ways of achieving and processing vibration process for assessing quality of brick wall structures and elements which is the subject of considerations in this work. In practical appli-cations they make it possible to better understand behaviour of complex structures, optimize them during design process and assess hazardous states. In the latter area is contained the clue of the investigated problems, i.e. searching for assessment measures for degradation state of brick wall structures and elements, new and aged ones, and often those of unknown destruction state and safety factor values.
Modal analysis is widely used for investigating degradation state and fault location, modifica-tion of dynamics of tested structures, descripmodifica-tion and updating analytical model, as well as monitoring structural vibrations in aircraft and civil engineering. In the subject-matter literature the following notions can be found: modal analysis, experimental modal analysis and operational modal analysis [4,8,9,13,20]. In the majority of practical applications of modal analysis a multi-channel experiment and complex calculations connected with the processing of measured signals and esti-mation of model’s parameters, are required. The so seen application possibilities allows to distinguish the following kinds of modal analysis:
• theoretical – which requires to solve eigenvalue problem for a given structural model of in-vestigated object,
• experimental – which requires to control identification experiment during which object’s mo-tion (e.g. vibramo-tion) is excited and measurements of excitamo-tion and response are performed in many measuring points,
• operational – which is based on experiment carried out in real conditions, during which only system’s response is measured and object’s motion results from real operational excita-tions.
The experiment for identifying the destruction state of the studied wall elements is the basic source of information and on its basis the value of measures and the structure of the model can be established. The quality of the received model depends on one side of the quality of the results of experimental investigations, and on the other side of the structure of the identified model. The modal analysis experiment can be divided in the following stages:
1. Planning:
– the choice of way of extorting trembling on the studied elements and the points of application, – the choice of points of for measuring the trembling and the measuring apparatus,
– the choice of suitable measuring equipment,
– the choice of the modeling arrangement (the limitation of number of degrees liberty). 2. Calibration of the measuring track.
3. Acquisition and processing of the results.
The studied wall element shows the trembling force of signal extortion proportional to state of the destruction. The signal of extortion and the answer was used for further delimitation of the FRF function and the stabilization diagram.
The use of signals analyzer is the simplest machine with regard on service solution, however the most modern and gives the largest possibilities of specialized measuring interface on the working station. The basic operation that can be done by the signals analyzer is the regular analogue-digital processing, which makes possible applying digital technology in processing the modal analysis sig-nals [13,17,19].
The sensors that measure accelerations have considerably smaller mass and therefore do not influence the movement of the arrangement. The additional advantage of sensor use is the fact that they receive integrated acceleration signals of speed and trembling dislocation. The backwards op-eration depends on differentiating trembling, which can lead to large mistakes particularly in range of higher frequencies. With this regard the sensors have their own resonance, which limits the fre-quency in which they can be applied.
The selection of the place for fastening the sensor is very important as it has influence on results of modal investigations. Sensors should be fixed in such way that they will not influence the trem-bling of arrangements; as well they should be fixed in characteristic places of the construction.
The experimental modal analysis requires precise laboratory conditions for the execution of investigations. Model must be subjected from mountain well-known and put extortions. Extortions can run away from these, which they act on object in time of normal exploitation. During experiment realization we can encounter the difficulty behavior peaceable with reality of shore conditions: fastening studied object. In the case of large models the realization of this experiment is very expen-sive.
In this paper are presented research results of differentiated state of brick structure, obtained by applying the experimental modal analysis. For this aim was used the LMS SCADAS Recorder, the device which combines features of analyzer and classical recorder, as well LMS Test.Lab software
1. Vibrations in description of structures
Ob Theoretical modal analysis is defined as a matrix eigenvalue problem dependent on matrices of mass, stiffness and damping. It requires the eigenvalue problem for an assumed structural model of investigated structure to be solved [13,15,19]. The determined sets of natural frequencies, damp-ing coefficients for the natural frequencies and forms of natural vibrations make it possible to simulate behaviour of structure under arbitrary excitations, choice of steering means, structural mod-ifications and other issues.
Analysis of natural frequencies and vectors is obtained on the basis of motion equations (after neglecting terms which contain damping matrix and external load vector). Then the motion equation of natural vibrations obtains the following form:
0
=
+ Kq
q
B
For one d.o.f. system its solution is as follows:)
sin(
)
(
t
=
q
ϖ
t
+
ϕ
q
&
where:q
&
– vector of amplitudes of natural vibrations.
On substitution of the above given equation and 2nd derivative to the motion equation the
fol-lowing is obtained:
0
)
sin(
)
(
−
ϖ
2B
+
K
q
&
ϖ
t
+
ϕ
=
The equation is to be satisfied for arbitrary instant t then the set of algebraic equations is yielded as follows:
0
)
(
K
−
ϖ
2B
q
&
=
(
k
11−
ω
2m
11)
q
1+
(
k
12−
ω
2m
12)
q
2+
+
(
k
1n−
ω
2m
1n)
q
n=
0
(
)
(
)
(
2)
0
2 2 2 22 2 22 1 21 2 21−
m
q
+
k
−
m
q
+
+
k
n−
m
nq
n=
k
ω
ω
ω
….. …… ……. ……. ……(
k
41−
ω
2m
41)
q
1+
(
k
42−
ω
2m
42)
q
2+
+
(
k
nn−
ω
2m
nn)
q
n=
0
This way was produced the set of linear homogeneous algebraic equations, which has non-zero solution only when the condition:
0
)
det(
K
−
ϖ
2B
=
is fulfilled.On transformations the n-order polynomial is obtained. Among its roots multifold ones may be present, and the vector built from the set of frequencies
2
ϖ
ordered according to increasing value sequence is called the frequency vector, and the first frequency is called the fundamental one [23].]
....,
,
[
ϖ
1ϖ
2ϖ
nϖ
=
The theoretical modal analysis is mainly used in design process, i.e. when it is not possible to perform tests on objects. The traditional experimental modal analysis (EAM) makes use of input (excitation) to output (response) relation and it is measured in order to assess modal parameters consisted of modal frequencies and damping. However the traditional EAM has some limitations such as:
– in the traditional EAM, artificial excitation is used to measure vibration frequencies. – the traditional EAM is usually performed in laboratory conditions.
However in many cases a real state of degradation may greatly differ from those observed in laboratory environment. In experimental modal analysis the identification experiment consists in exciting object’s vibrations at simultaneous measuring excitation force and system’s response usu-ally in the form of vibration acceleration amplitude.
2. Measurement software
For the measurement waveforms extortion and response system and determine the most used functions FRF measurement equipment purchased for the project company under the name of LMS LMS TEST.XPRESS. This software enables you to easily perform a modal analysis of brick ele-ments, as well as any other building structures – fig.1.
Figure 1. Software manufacturer website
The next step is to define the system with all the data needed to calibrate the measurement path. For the purposes of studies carried out in this stage began by defining the number of active measur-ing channels. Their number is limited only by the number of inputs on the measurement, which is different for different models of measuring segments.
For the purposes of measurement using experimental modal analysis you defined two measure-ment channels. According to the theoretical experimeasure-mental modal analysis first sensor is reserved for the hammer modal (vibration force), and place 2 sensor piezoelectric sensor is connected (the answer key to force).
Figure 2. Calibration of sensor connection
The figure above shows the calibration window and defines of connection of sensors. Properties, that each sensor is connected to the segment defined by the window, visible on the right in the drawing (fig.2). There are characteristic values of the sensors, which can change as needed.
2.1. Creating a real model
This model is created by using one of two methods for modal analysis, which are based on measuring the vibration structure at a given forcing. Experimental modal analysis method assumes that the force shall be measured and to answer extortion. Both of these parameters are known. The position of using this method of modal analysis is shown in Fig.2. The second of the methods called operational modal analysis is also based on the measurement of vibration caused by natural forcing operational characteristic of the work of a machine or mechanical design.
It is important that each object considered as a rigid body. By this principle, and a number of other conditions and assumptions that must be met to be able to use this method, it is necessary to suspend the object in a way that is shown in Fig.2. The next thing is to choose the appropriate response measurement points and enforce proper place where this goes arouse the greatest amount of vibration studied mechanical design.
Assuming that the conditions are fulfilled go the study analyse the structure of the vibration stimulus to be forcing a pulse. That kind of coercion may be inflicted modal hammer or vibration exciter. Fig. 3 shows the mounting of the sensor responses and how enforcement structures modal hammer. In Fig. 4 and 5 show two graphs in the time domain from the hammer modal response of the sensor.
Figure 3. Measuring position
Figure 4. The signal from the modal hammer Figure 5. The signal from the sensor response
Modal hammer is equipped with a force sensor which enables the value of a given force. Reac-tion force the truss to the quesReac-tion is measured vibraReac-tion acceleraReac-tion sensor. Figure 6 shows the force value in the form of a pulse at a level above 100 [N]. The signal caused by forcing is received by a piezoelectric sensor response (fig.6). During the measurement of vibration with increasing fre-quency forcing amplitude changes occur at the measuring point.
Figure 6. Chart (from left) FRF spectral transfer function and coherence function chart COH
Despite constant during the exciting force, the answer to the question of the extortion strength-ened in some frequencies grill until achieving full compatibility between the frequency and force of its resonant frequency. Processing time signal to a frequency signal by fast Fourier transform (FFT) allows determine of the so -called spectral transfer function (FRF). This form of the signal allows for a much simpler form of the object of determining the resonant frequency. The appointment of these frequencies is even easier if you superimpose on the chart FRF plot coherence (Fig. 6). Data obtained in the form of spectral transfer function are used to estimation of individual modal para-meters including mode shapes. Fashion vibrations examined structure takes different forms
depending on the frequency of extortion. Each of the test structure of the natural resonant frequencies of vibration corresponds to a specific form (Fig.7).
Figure 7. Form lattice vibrations at a frequency of 2803, 25 [Hz] and attenuation at 0.06 [%]
Modal parameters of the model estimates of individual spectral transfer function (FRF). Each FRF is presented in the form of a graph, which is established to analyse the frequency range. The proces is shown on Fig.8.
Modal parameter estimation can be carried out in two areas: time and frequency. Currently leading a field in which the parameter estimates are carried modal frequency domain is also known as Polymax or in short pLSCFD. After preparing the measurement results for further analysis, their estimation is done by creating so-called stabilization diagram.
Figure 8. Summary and preparation spectral estimation function FRF modal parameters
This diagram consists of different fields marked: s – the field is stable, v – vector modal, f – frequency field, d – the field attenuation, o – blank. Diagram of stabilization on the basis of which were made of modal parameter estimation in the case of the truss is shown in Fig. 9.
Figure 9. Stabilization diagram
By his own assessment of the stabilization diagram obtained these fields choose stable (s), which, in our discretion properly will describe the state of our object. If you clear each individual field in the diagram we obtain the modal parameters in the form of natural frequencies, damping
factor and the form of vibrations, respectively. For analysis of grid summarizes the first two modal parameters in Table 1.
Table 1. Summary of natural frequencies and damping coefficients for the analysed structure after validation
Frequency Range: 0,7 – 5000 [Hz]
Form vibrations Frequency [Hz] Damping [%]
1 316,414 7,48 2 402,885 0,14 3 857,077 0,08 4 932,579 0,04 5 1020,852 0,08 6 1160,253 6,64 7 1433,557 0,05 8 1474,005 0,17 9 1814,810 0,14 10 2338,013 0,14 11 2408,325 0,05 12 2553,819 0,06 13 2803,254 0,06 14 3465,221 0,06 15 3784,573 0,04 16 3907,980 0,07
For each shown in Table 2 as a vibration is also assigned its graphical form, an example of which is shown in Fig.10. Other forms of vibration are summarized in the next section, as compared with figures obtained from the analysis of the vibration theoretical model Inventor.
Table 2. Tabulated results validate certain mode shapes
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B?EB <C #1 <C AEB=*>EA ;BD? ;;<D ;;?A ;=A> ;;D ;>DB <B<E ;D<D A=;C D?EB ;?AB ;;?A ?E=< ;;?> ;BCC ;ACE ; ;;?? ;;< ;?AE ;>A= <D=> ; <;AE< ;<C= ;A<A ?;E= ;A=B ?;;?BB<< =<A<= ;?D< ;;=B A; #1 A; AC;E*CB; A;>A DC>E =?D= <;<= <E=> ?=>> ?<;> D;<E ;;>A C<B= <><< <?=<? ;E< ;=B< ;;DA ;;>? ;?AA === A>=A AD;A ACCE ;?A= ?CE< ??D=D ;E<= ;?;C ?ED? ;=;B ?BB<< ?;; ?A;>A ;>B= EA? A? #1 A? =;C;*?D< ?;EE ?EA ;;E< DEE? ===D ;;=E ?==< ;DA< ==E= ?<AC> ;;;> ;<D< ;;= ;>C= ;?<? ??A= ;;A ;<? ;;;< ;=CD ;;EE ; ;>A= <>B<> ;?ED ;=AB ;?DD <C=> =<A<=?A;>A ?;; ;<DA ;<A? A< #1 A< =>>E*>BB ;D?E ;;EE ;ED> B?>B ;<CB ?A?= ;?AA ?DAE= >?=? ;?AA ; ?A<? ;;?= DBB> ;>DE ;DDC ;D;A ;?DE ;;>B ;DA> <BBD EDA= ;;<E ; ;C>A ;?<A ;>BD ;AA? ;?D< ;>B= ;<DA ?;; ?B;C AA #1 AA =E<E*B?> ;>AA <E;> ;;;? ;<;C =?D ?A<< ;;;= ;BE ACDC ;A<B ?=?A ;CCA ;ED< ;AEA ?A;< <C?E A;? ;>BE ;D?> <ABA ;DEC ;;?? ;;;< ;>B ;;;> ?CDE ;=C B?EB ;;=B EA? ;<A? ?B;C ?;;
Characters vibrations that were obtained were also validated by Automac to eliminate these forms, which are largely dependent on each other. Individual fashion vibration may be different in nature: the torsional and flexural torsion. The position of the natural frequencies and mode shapes due to the properties of the test structures described by the parameters such as mass, stiffness and damping. Vibration analysis of individual characters but not all the time is ambiguous. Therefore, to assess the correctness of the selected poles modal model Automac method is used.
Validated results are shown in Fig. 11 and in Table 2. After validation of the form 33 resulting vibrations is selected 16, which in the best extent reflect the current state of the test grid 16 statement of mode shapes are shown in Table 3.
Table 3. Tabulated results validate certain mode shapes
#1 #*F G, %" #1 ?A?D*=?=#1 <=;<*BB>#1 AB>E*;EE#1 =CA<*>EC#1 >?;<;*B><#1 D??D;*<>A#1 E?=AA*>>E#1 B?=E=*;;>#1 C?B?=*B?;#1 ?;<AAB*;?A#1 ??<=;B*A<>#1 ?<<>>A*B?C#1 ?A<B;A*<>=#1 ?=A=D>*<<?#1 ?>AEB=*>EA#1 ?D ? #1 ? A?D*=?= ?;; B=>;< ;=C= DD;=C ;<BC ?CCBC ?;CD ECE=C ==D? ;;;A ;;>D ; B?A=B ;;;= ;DD? ><< < #1 < =;<*BB> B=>;< ?;; ;;;< >E=EE ; ?DA<? ;<CB DDB=E AD> ;?>> ;?=D ;=>? E>?C= ;;;> ;;;= =;A? A #1 A B>E*;EE ;=C= ;;;< ?;; ;<<B AAB> EBBC =D;B ;;== ;;<A ;?B< >E=< ;AB= ;?EC ;=AC ;>>C ?=AEC = #1 = CA<*>EC DD;=C >E=EE ;<<B ?;; ;AAC AE<A ;<EE B==>? ?;DDC ;;AB ;;;= ;??= B>>C? ; <BDD ?<EC > #1 > ?;<;*B>< ;<BC ; AAB> ;AAC ?;; ;BCA EABD ;?A= ;?CD <AEA ;A;> ED=B ;;A ;;>< ;>DD DAB< D #1 D ??D;*<>A ?CCBC ?DA<? EBBC AE<A ;BCA ?;; =<CB ?E>E ;<>= ?<DA ;= =A?E ?;?A< <C=A ?;=? ;?EC E #1 E ?=AA*>>E ?;CD ;<CB =D;B ;<EE EABD =<CB ?;; ;;?> ;ADC ;?;= ;<;C ?=BD< ;A;D ;A>C ;;;< <==BB B #1 B ?=E=*;;> ECE=C DDB=E ;;== B==>? ;?A= ?E>E ;;?> ?;; ?;BE= ;<<? ;;?B ;;<= BBCE= ;;AE ?DAE ?;>D C #1 C ?B?=*B?; ==D? AD> ;;<A ?;DDC ;?CD ;<>= ;ADC ?;BE= ?;; ;CC? ;;<? ;?>C C>D ;;>D ;A<A ;;=E ?; #1 ?; <AAB*;?A ;;;A ;?>> ;?B< ;;AB <AEA ?<DA ;?;= ;<<? ;CC? ?;; ;;;D <<<D ;;?E ;;>> ;;<? A>A ?? #1 ?? <=;B*A<> ;;>D ;?=D >E=< ;;;= ;A;> ;= ;<;C ;;?B ;;<? ;;;D ?;; A>=DA ;;EC ;;DE ;?<C A>DE ?< #1 ?< <>>A*B?C ; ;=>? ;AB= ;??= ED=B =A?E ?=BD< ;;<= ;?>C <<<D A>=DA ?;; ;;;> BC>E ;>=E =;<C ?A #1 ?A <B;A*<>= B?A=B E>?C= ;?EC B>>C? ;;A ?;?A< ;A;D BBCE= C>D ;;?E ;;EC ;;;> ?;; ;;EC ; <;< ?= #1 ?= A=D>*<<? ;;;= ;;;> ;=AC ; ;;>< <C=A ;A>C ;;AE ;;>D ;;>> ;;DE BC>E ;;EC ?;; ??;> ?E=D ?> #1 ?> AEB=*>EA ;DD? ;;;= ;>>C <BDD ;>DD ?;=? ;;;< ?DAE ;A<A ;;<? ;?<C ;>=E ; ??;> ?;; ?C<< ?D #1 ?D AC;E*CB; ><< =;A? ?=AEC ?<EC DAB< ;?EC <==BB ?;>D ;;=E A>A A>DE =;<C <;< ?E=D ?C<< ?;;
3. A summary of the results of the actual and theoretical model
Modal study aims to determine the dynamic properties of lattice elements commonly used in the construction of harbour cranes to identify possible ways to diagnose and even modify these properties through structural changes, which would ensure a high quality of these objects. To per-form modal analysis lattice structure created a three-dimensional model of the selected item. For truss structures consist of suitable types of shapes or profiles associated disjoint or inseparable con-nections. Similarly was implemented the Inventor programme. Modelled the selected element truss port cranes, which has been associated with a geometric relationship according to the nature of co-operation between these elements. Thus created were analysed element via the "Stress Analysis". This module is one of the analytical computing subsystems Inventor and comes with the possibility of using the finite element method to carry out the theoretical modal analysis. Pre-preparation step in the calculation include:
• define how to support the test piece,
• conversion of the bonds resulting from the assembly and method of assembling blocks of individual elements to a form suitable for, and determine the number of mode shapes.
Table 4. Forty mode shapes for truss
Depending on the type of connection being present between the constructions elements have been replaced by so-called contact bound in the case of static and spring-type contacts for mobile connections.
Table 5. Comparison the results of analysis natural frequencies for the FEM model and tactual model
Shape
Vibration frequency [Hz] The
discrepancy results [%] Experimental studies FEM analysis 1 316.414 326,05 2,96 2 402.885 478,13 15,74 3 857.077 893,46 4,07 4 932.579 925,14 0,8 5 1020.852 1037,42 1,6 6 1160.253 1136,29 2,07 7 1433.557 1449,69 1,11 8 1474.005 1480,90 0,47 13 1814.810 1890,93 4,03 16 2338.013 2296,25 1,79 18 2408.325 2391,88 0,68 19 2553.819 2547,10 0,26 21 2803.254 2802,87 0,01 25 3465.221 3426,64 1,11 30 3784.573 3769,07 0,41 33 3907.980 3937,71 0,76
Inventor analysis is based on the finite element method (FEM). The result of this analysis is the natural frequency and vibration forms without attenuation coefficient. The following Table 3 shows the results of the analysis of the truss structure in the environment of Autodesk Inventor. The as-sumptions of the analysis determined the frequency range from 0.7 to 5000 [Hz] and a maximum of 40 characters vibration.
Figures vibration frequency for these, are shown in comparison to results obtained in real model. Based on experimental studies identified modal parameters. The results obtained were compared with the results of FEA grid and compared in Table 5.
Comparing the results of FEA and experimental studies, it was found that the results are satis-factory and the resulting discrepancy can be traced resulting in a slightly different way of restraint lattice with finite element analysis in relation to the restraint of the grid used in the experimental study. Nevertheless, it is possible to observe significant similarities between the different forms of vibration.
Graphical representation of individual normal modes for the FEM model and experimental stu-dies are compared in Fig. 12 to 15.
Figure 12. Comparison of the results (from left) FEA and experimental studies of the first form of vibrations
Figure 13. Comparison of the results (from left) FEA and experimental studies of the third form of vibrations
Figure 14. Comparison of the results (from left) FEA and experimental studies sixteenth mode shapes
Figure 15. Comparison of the results (from left) FEA and experimental studies Thirty-third of the normal modes
The need to improve the dynamic performance of mechanical structures, in particular, port cranes, force designers need to identify the dynamic characteristics of the design already on the road. The studies support the use of FEA, the results of which are specific feedback during the design phase. FEA results can be the basis for changing the geometry of the structure.
As commonly used in the practice of testing technique of dynamic properties, modal analysis allows the identification parameters of the mechanical properties, and hence possible to predict their behaviour as a result of imbalances.
4. Conclusions
The results points the fact that it is possible to distinguish between material properties, which has an impact on the ability to distinguish between their mechanical properties. The study also con-firmed the usefulness of the LMS test apparatus using operational modal analysis performed on the lattice steel structure.
By obtaining graphical charts and a later their comparison it is possible to observe their diver-sity. These charts are different for materials that are in good condition, and damaged, which demonstrates the ability to assessment of the destruction of a lattice steel structure.
It practically verified the sensitivity of assessment of modal analysis to degree of brick struc-ture degradation.
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WYKORZYSTANIE ANALIZY MODALNEJ DO OCENY SPAWANYCH KONSTRUKCJI STALOWYCH
Streszczenie
Konstrukcje stalowe są naraĪome na działanie duĪych obciąĪeĔ dynamicznych wyraĨnie odzwierciedlonych przez generowanie procesów wibracyjnych. Wibracje mogą wpływaü na stan uĪytkowalnoĞci konstrukcji poprzez obniĪenie komfortu osób tam pracujących, a takĪe moĪliwe osiągniĊcie poziomu zagroĪenie bezpieczeĔstwa. Wpływ drgaĔ na strukturĊ przejawia siĊ głównie wystĊpowaniem dodatkowych naprĊ-ĪeĔ w przekroju poprzecznym, które są sumą wynikającą z obciąnaprĊ-ĪeĔ statycznych. Dynamiczne obciąĪenia mogą powodowaü szkodliwe skutki w budynkach o róĪnych typach konstrukcyjnych lub nawet doprowadziü do ich zniszczenia.
Dostrzegając koniecznoĞü poprawy metod oceny jakoĞci konstrukcji budowlanych w celu oszacowania ich stanu oraz współczynników bezpieczeĔstwa dla konstrukcji murowanych, autor tej pracy podjął próbĊ zbadania procesu niszczenia wybranego obiektu za pomocą metody eksperymentalnej analizy modalnej.
Słowa kluczowe: analiza modalna, czĊstotliwoĞü drgaĔ własnych, diagram stabilizacji
Mariusz ółtowski
Katedra Informatyki w Zarzdzaniu Wydział Zarzdzania
Uniwersytet Technologiczno-Przyrodniczy w Bydgoszczy e-mail: mariusz.zoltowski@utp.edu.pl
Bogdan ółtowski Michał Liss
Zakład Pojazdów i Diagnostyki Wydział Inynierii Mechanicznej
Uniwersytet Technologiczno-Przyrodniczy w Bydgoszczy e-mail:bogdan.zoltowski@utp.edu.pl
