- DOI: 10.4324/9780203014554.CH10
- Corpus ID: 11132246
Experimental modal analysis
- V. Ferrari , Paolo L. Gatti
- Published 12 November 1999
- Engineering, Physics
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Experimental modal analysis in research, modal analysis of structural vibration, experimental modal analysis of reinforced concrete square slabs, elastic characterization of glass by modal analysis, modal analysis a tool for design and optimization, damage detection of ferrocement tanks using experimental modal analysis and finite element analysis, experimental modal analysis of a flat plate subjected to vibration, estimation of modal parameters from frequency response function through global rational fraction polynomial method (grfp), experimental and finite element analysis to identify the source of vibration of a coach, vibration stability analysis of cantilever structure based on symbolic regression algorithm and modal analysis method, 6 references, global curve fitting of frequency response measurements using the rational fraction polynomial method, identification of the modal properties of an elastic structure from measured transfer function data, related papers.
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Experimental Modal Analysis
Vibration measurements and analysis
Experimental Modal Analysis (EMA) is an effective instrument for describing, understanding and modelling the dynamic behaviour of a structure. It can be carried out both to determine the natural frequencies and mode shapes of a structure and to verify accuracy and calibrate a finite element model (FE). Also, the EMA can be used in order to make a troubleshooting vibration problems.
Thanks to the best specialized softwares, SINT can carry out the PRE-TEST analysis (in order to chose the best set-up measurement) and the CORRELATION analysis (for the comparison of the Finite element model with the experimental model).
SINT Technology can determine the main modal parameters:
- Natural frequencies
- Mode shapes
The validation of the modes is done using the following:
- Modal Assurance Criterion (MAC)
- Complexity tools
- Modal Phase Collinearity (MPC)
- Mean Phase Deviation (MPD)
- Phase scatter
Some examples of the experimental modal analysis techniques that SINT Technology can use are:
- Impulse excitation (instrumented hammer)
- Controlled excitation (shaker)
- Operational Modal Analysis (OMA)
- Operational Deflection Shape (ODS)
Experimental Modal Analysis standards
Vibration and shock – Experimental determination of mechanical mobility – Part 2: Measurements using single-point translation excitation with an attached vibration exciter
Vibration and shock – Experimental determination of mechanical mobility – Part 5: Measurements using impact excitation with an exciter which is not attached to the structure
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Analytical and Experimental Modal Analysis
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This book covers the fundamentals and basic concepts of analytical and experimental approaches to modal analysis. In practice, the analytical approach based on lumped parameter and finite element models is widely used for modal analysis and simulation, and experimental modal analysis is widely used for modal identification and model validation. This book is inspired by this consideration and is written to give a complete picture of modal analysis.
- Presents a systematic development of the relevant concepts and methods of the analytical and experimental modal analyses.
- Covers phase resonance testing and operational modal analysis.
- Provides the relevant signal processing concepts.
- Includes applications like model validation and updating, force identification and structural modification.
- Contains simulations, examples, and MATLAB ® programs to enhance understanding.
This book is aimed at senior undergraduates/graduates, researchers, and engineers from mechanical, aerospace, automotive, civil, and structural engineering disciplines.
TABLE OF CONTENTS
Chapter 1 | 8 pages, introduction, chapter 2 | 64 pages, lumped parameter modeling of vibrating systems, chapter 3 | 32 pages, finite element modeling of vibrating systems, chapter 4 | 47 pages, analytical modal analysis of sdof systems, chapter 5 | 30 pages, analytical modal analysis of undamped mdof systems, chapter 6 | 40 pages, analytical modal analysis of damped mdof systems, chapter 7 | 28 pages, characteristics of frequency response functions, chapter 8 | 54 pages, signal processing for experimental modal analysis, chapter 9 | 35 pages, frf measurement using an impact hammer, chapter 10 | 29 pages, frf measurement using shaker excitation, chapter 11 | 55 pages, modal parameter estimation methods, chapter 12 | 16 pages, phase resonance testing, chapter 13 | 14 pages, operational modal analysis, chapter 14 | 17 pages, applications of experimental modal analysis, chapter 15 | 36 pages, finite element model validation and updating.
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Experimental Modal Analysis
| Course Status : | Completed | ||||
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| Density (g/cm ) . | Toughness K (MPa m ) . | Compressive strength (MPa) . | Young's modulus (GPa) . | Poisson's ratio (−) . | CL wave (m/s)* . |
|---|---|---|---|---|---|
| 3.90 | 3.5 | 3500 | 380 | 0.223 | 10 574 |
| Density (g/cm ) . | Toughness K (MPa m ) . | Compressive strength (MPa) . | Young's modulus (GPa) . | Poisson's ratio (−) . | CL wave (m/s)* . |
|---|---|---|---|---|---|
| 3.90 | 3.5 | 3500 | 380 | 0.223 | 10 574 |
* Longitudinal wave speed calculated according to elastic parameters
3. Sapphire window
In plate-impact experiments involving an alumina ceramic, sapphire plates are used as window material on the backside of the ceramic tile. Indeed, its impedance being very close to that of the alumina material allows minimizing the amplitude of the reflected wave at the back of the ceramic plate. The use of window material is common in plate-impact experiments 25 to increase the amplitude and duration of compression loading applied to the target. Indeed, without window material, only the elastic part of the signal could be analyzed. Tests without window materials would make it possible to characterize the HEL of the ceramic but not its plastic hardening (post-HEL) response. 26 The minimization of the reflected wave is very important if one wants to perform a Lagrangian analysis with the measured velocity signals. Indeed, a significant level of plastic strain must be reached in order to be able to carry out this analysis, and this level of plastic strain could not be achieved without window material. In addition, Lagrangian analysis being based on the calculation of the wave speed at any time, stronger uncertainties can be generated by using a window that is not suited for. 27
The sapphire plates used as window plates are squares 30 × 30 mm 2 long and 7.8 mm in thickness and are oriented according to plane A (cf. crystal orientation in Ref. 28 ). These plates are supplied by Saint-Gobain Company. A refractive index correction of 1.7284 29 was considered.
First, “classical” planar plate-impact tests were carried out to characterize the HEL of 316L steel from which the wavy flyer plate and the buffer further used are made. To do so, three plate-impact tests were carried out, using a 5 mm thick planar flyer plate. In the first test, an impact speed of around 500 m/s was selected. The velocity at the back of the sample was measured thanks to an optical probe and the PDV system.
The next goal was to investigate the effect of the wavy geometry of the flyer plate. In the tests involving a wavy flyer plate, a buffer is tapped to the front of the sample to homogenize the stress in the lateral direction. Homogenization of the stress field is important to ensure that the same loading is applied at any point of the ceramic front face. A shockless plate-impact test carried out at an impact speed of around 500 m/s is compared to a planar plate-impact test in Fig. 5 . In the test with a planar flyer plate, a very steep and almost instantaneous rising front is observed. In contrast, when the wavy flyer plate is used, a much longer rise time of around 0.8 μ s is noticed. Such long rise-time is desirable to be able to perform a Lagrangian analysis in further shockless plate impact. This rise time mainly reflects the plastic deformation process of the wavy flyer plate over time which generates a loading ramp.
Comparison of particle velocity profiles measured at the back face of targets made of 316L steel subjected to plate-impact test with an impact speed of about 500 m/s considering planar and wavy impactors.
Parameters of the Johnson–Cook plasticity model considered for 316L stainless steel according to Ref. 23 .
| (MPa) . | (MPa) . | . | . | . | ( ) . |
|---|---|---|---|---|---|
| 490 | 600 | 0.21 | 0.60 | 0.015 | 166 315 |
| (MPa) . | (MPa) . | . | . | . | ( ) . |
|---|---|---|---|---|---|
| 490 | 600 | 0.21 | 0.60 | 0.015 | 166 315 |
In the numerical simulation, it was chosen to work only with a half-period slice of the wavy flyer plate for symmetry reasons. Tests in Fig. 5 were numerically simulated to see whether the behavior of the wavy flyer plate can be predicted. To do so, the study was conducted using Abaqus explicit Finite-Element software. The element type considered for each solid (flyer plate, buffer, and sample) is a 8-node reduced-integration element (C3D8R). Solids are brought into contact via a penalty contact algorithm. An initial velocity corresponding to the impact speed measured in the experiment is imposed to the impactor. The mesh size of about 0.2 mm is small enough compared to the half-period. In the case of plane impact modeling, a ten times finer mesh is used to prevent filtering of highest frequencies that compose the rising edge.
The particle velocity is recorded at the back of the target to be compared with its experimental counterpart. Since the presence of the buffer allows the stress field to be homogenized along the sample width, the position of the measurement point on the rear edge of the specimen has little influence. A comparison between the experimental and numerical data from planar and shockless plate impact tests on 316L steel can be seen in Fig. 6 .
Comparison between experimental and numerical velocity profiles obtained in plate-impact tests conducted on 316L steel impacted at a speed of 500 m/s with planar and wavy impactors.
In the case of wavy-flyer plate impact, the slope of the velocity profile is lower in the numerical simulation than in the experimental data. A mesh analysis has shown that even with finer mesh size this problem persists. Nevertheless, it is observed that the numerical profile matches very well with the numerical prediction. Finally, this comparison provides a first validation of the numerical modeling to simulate plate-impact tests with wavy flyer before considering the ceramic sample. The behavior of “wavy impactors” can, therefore, be numerically predicted in the case of impactors manufactured in 316L steel.
A “double-thickness shockless plate-impact configuration” made of 316L steel was set up to assess whether a Lagrangian analysis could be conducted without a ceramic sample. To do so, two tiles of different thicknesses (5 and 6 mm) were bonded to a buffer made of the same 316L steel, and the whole target was impacted with a wavy-machined flyer plate. The particle velocity was measured at the back face of each tile. The impact velocity was set to 512 m/s. The data were then processed using Wave software to determine the particle velocity curve from the measured signals. The two velocity profiles used as input data of the Lagrangian analysis program are drawn in Fig. 7(a) . After adjusting the foot of the curves with an elastic model, a Lagrangian analysis was performed to deduce the (axial strain-axial stress) mechanical response of the material corresponding to a uniaxial-strain loading path [ Fig. 7(b) ].
Shockless plate-impact test applied to a target made of a buffer backed with two 316L steel plates of different thicknesses (5 and 6 mm), impacted at a speed of 500 m/s. (a) Particle velocity measured at the back face of each plate. (b) Result of the Lagrangian analysis.
This curve shows a bilinear response with a slope discontinuity that corresponds to the isentropic elastic limit (IEL), which is defined as the axial stress threshold above which an inelastic behavior is observed at a macroscopic scale in a case of isentropic compression under uniaxial-strain loading condition. The corresponding value of IEL (1.25 ± 0.3 GPa) is close to the elastic precursor (HEL) obtained in a planar plate-impact test and is not far from strength values obtained with another type of steel under shock compression and spalling. 31 This test validates the use of Lagrangian analysis to obtain the response of the material in a uniaxial strain loading path. This method will be subsequently applied to ceramics.
The material studied in the present work is of an alumina grade (F99.7). Although the planar plate-impact test gives access to the HEL, the shockless plate impact provides the isentropic elastic limit or IEL, 32 which corresponds to the axial stress threshold (in a uniaxial-strain loading path) above which the material no longer behaves elastically at the macroscopic scale.
Initially, in a similar way to what was done with steel, planar plate-impact tests were carried in order to determine the HEL of F99.7 alumina. This test was conducted with an impactor of 70 mm in diameter and 5 mm thickness fired at an impact speed of 583 m/s. The target is composed of an alumina sample of 8 mm thickness backed with a sapphire window. The rear velocity profile was measured at the interface between the alumina ceramic and the sapphire window.
Next, several plate-impact tests with a wavy flyer plate were carried out on targets made of a buffer tapped to F99.7 alumina tile with the aim of studying how the wavy-shape affects the rising time of the loading applied to the ceramic. These preliminary tests are necessary to set up the Lagrangian analysis. A test performed with a wavy flyer plate striking the target at an impact speed of 603 m/s is compared to the previous one (planar plate-impact) as in Fig. 8 .
Comparison of particle velocity profiles measured at ceramic–sapphire window interface in planar and shockless plate-impact tests both conducted at an impact speed of around 600 m/s. The planar plate impact test reveals a plateau around 145 m/s that corresponds to the ceramic HEL.
A plateau is noted on the planar plate-impact curve at around 145 m/s. From this plateau that corresponds to the U HEL , the HEL is deduced according to Eq. (3) . 26 Considering the impedance correction between the ceramic and the sapphire, the HEL can be deduced (6.7 ± 0.3 GPa). This result is quite close to the result of around 6.7 GPa obtained with a 99.5% pure alumina in Refs. 33 and 34 .
By comparing the two curves in Fig. 8 , it can be seen that the use of a wavy flyer plate has a strong influence on the rising time. Indeed, the rise time is almost 1 μ s longer than with a flat impactor. The maximum velocity achieved in the test with a wavy flyer plate is slightly higher than that in the test with planar impact, but this can be easily explained by the higher impact velocity of the flyer plate (603 instead of 583 m/s). Thus, as observed in plate-impact tests performed against 316L steel ( Fig. 5 ), the use of a wavy flyer plate allows increasing the rise time of the compression pulse, which is an essential parameter to ensure that a Lagrangian analysis can be performed. Nevertheless, to study the post-HEL or post-IEL response of alumina ceramic with the wavy flyer plate, it is necessary to reach a much higher stress level than the HEL (which is around 7 GPa) within the target.
On the other hand, it is possible to compare the experimental data with a numerical simulation to assess whether the effect of the wavy flyer plate is indeed the expected one. This comparison is proposed below.
Comparison of experimental velocity profiles measured in (a) planar and (b) shockless plate-impact tests with their numerical counterparts considering an EP (elasto-plastic) model for the ceramic and different values of strain-hardening coefficient ( n ).
In both (planar and shockless) types of plate-impact tests, the elastoplastic model seems to follow the experimental curve as closely as possible, particularly for a value of ( n ) equal to 0.215. In the case of shockless plate impact, the identification of n is more difficult as this parameter has less influence.
The correct representation of the EP model to model these plate impacts may be explained by the fact that the elastoplastic model with strain-hardening is sensitive to the plastic strain that varies during the test. The value of n = 0.215 obtained from the modeling of the planar impact test also seems appropriate here. Finally, it is concluded that the proposed geometry of the wavy-flyer plate provides a high enough rise time for carrying out a Lagrangian analysis to be applied to F99.7 alumina.
The following Lagrangian analysis configuration was developed. Two samples of different thicknesses (6 and 8 mm) were glued to a 316L steel buffer with sapphire tiles used as window material ( Fig. 10 ). The impact speed of the flyer plate was set to 862 m/s. The data were processed with the same software (Wave). The particle velocity profiles measured at ceramic-window interfaces are shown in Fig. 11(a) .
Shockless plate-impact testing configuration considered for Lagrangian analysis. From the bottom to the top: wavy-flyer plate, buffer plate, ceramic plates of different thicknesses, and window tiles.
Shockless plate-impact test applied to a target composed of two alumina samples of different thicknesses (8 and 6 mm) impacted at a speed of 862 m/s. (a) Particle velocity measured at the sapphire–ceramic interface. (b) Result of the Lagrangian analysis: the dashed lines correspond to the elastic response and to the elastoplastic response with linear strain-hardening.
A time lag is observed between the curves due to the difference in thicknesses between the two ceramic samples. A difference in the velocity profile can be seen at the very beginning of the curves. This can be explained by the poor ability of the software to estimate the speed for very low speeds. The elastic phase is clearly visible through the parallelism of the two velocity curves. The elastoplastic transition is not evident. Nevertheless, a trend does emerge. By plotting the two asymptotes relative to the elastic and plastic parts [ Fig. 11(b) ], it is possible to find the IEL. This method makes it possible to characterize the IEL that corresponds to the start of non-elastic response of the ceramic at the macroscopic scale. The obtained IEL of 9.0 ± 0.4 GPa is slightly higher than the value obtained by planar plate impact. Indeed, according to the previous tests, a HEL close to 6.7 GPa was found. This difference can be explained by the very progressive post-HEL strain hardening.
It is also possible to compare this result to its numerical counterpart obtained using the elastoplastic model with a work hardening n = 0.215 as mentioned earlier [Eq. (9) ]. Two numerical simulations were carried considering a half-period slice of the wavy flyer (cf. Fig. 1 ) impacting target made of a ceramic sandwiched between a buffer plate and a sapphire window. Two different thicknesses of ceramic tile (6 mm and 8 mm) were considered. Subsequently, the particle velocity at each interface between ceramic and sapphire tiles was recorded. These numerical data were then used as input of the Lagrangian analysis program to get the axial stress vs axial strain curve ( Fig. 12 ).
Comparison between the experimental axial stress vs axial strain response obtained from the Lagrangian analysis to its numerical counterpart obtained with an EP model.
The data processing derived from the numerical simulation provide a response close to the experimental measurements in the plastic phase. Once again, it validates the possibility of performing a Lagrangian analysis based on the shockless plate-impact test conducted with ceramic made of two different thicknesses.
In order to confirm the previous experimental result, a second test was carried out considering a configuration from the article of Forquin and Zinszner 16 according to which it is possible to use a wavy-buffer instead of a wavy-flyer plate. The particle velocity measurements used for the Lagrangian analysis are shown in Fig. 13(a) . The velocity curves are less smooth, with oscillations in the plastic response section. These curves, therefore, had to be smoothed in order to perform a Lagrangian analysis from these results. The oscillations are not due to data processing as they are physically present in the post-shooting data.
Shockless plate-impact test conducted in “reverse configuration,” with a target made of two samples of F99.7 alumina tiles of different thicknesses (8 and 6 mm) impacted at a speed of around 859 m/s. (a) Particle velocity measured at the sapphire–ceramic interface. (b) Result of the Lagrangian analysis.
The axial stress vs axial strain response [ Fig. 13(b) ] deduced from the Lagrangian analysis is somewhat different from that obtained in [ Fig. 11(b) ]. Here, the slope discontinuity is more pronounced. In addition, the overlapping curves make reading the IEL more complex. The IEL deduced from this test is 7.3 ± 0.3 GPa. This value is more consistent with the HEL deduced from a planar plate-impact test.
The previous results were compared with two GEPI tests carried out with another grade of alumina (A98). These results come from an internal CEA GRAMAT report. 36 A98 alumina is a 98% pure alumina with slightly different elastic properties compared to F99.7 ( Table III ).
Some properties of F99.7 and A98 alumina ceramics.
| . | A98 . | F99.7 . |
|---|---|---|
| (m/s) | 10 570 | 10 574 |
| (GPa) | 366 | 380 |
| 0.242 | 0.223 | |
| Purity | 98% | 99.7% |
| . | A98 . | F99.7 . |
|---|---|---|
| (m/s) | 10 570 | 10 574 |
| (GPa) | 366 | 380 |
| 0.242 | 0.223 | |
| Purity | 98% | 99.7% |
The two compression tests performed with the GEPI facility were carried out with electrode widths of 20 and 25 mm considering, in both tests, alumina tiles of thicknesses 3 and 4 mm. In these tests, LiF was selected as window material. Both tests achieved levels of axial stress of about 11 and 14 GPa (in absolute value). A Lagrangian analysis was carried out from particle velocities above 60 m/s. For lower speeds, the behavior was considered elastic.
As in the first results obtained on F99.7, the transition between elastic and plastic behaviors is not very clear ( Fig. 14 ). Based on the two GEPI tests, an IEL value of 7.5 ± 0.3 GPa was found. This value is similar to the values found in the tests carried out in the 3SR Laboratory. In particular, it is very close to the value of 7.4 ± 0.4 GPa obtained during the second test (inverted configuration). Moreover, these values also correspond to the order of magnitude of IEL that was found with AD995 alumina of 6.71 ± 0.08 GPa, whose purity is close to that of F99.7. 33 It, therefore, appears that the shockless plate-impact method developed at 3SR gives similar results to the GEPI tests with a Lagrangian analysis of data.
Results of the Lagrangian analysis obtained by GEPI tests at CEA-GRAMAT on A98 alumina.
The selected steel (316L) allows preventing a phase transformation in the considered range of pressure.
The test performed with wavy-flyer plate geometry generates a loading pulse applied to the sample with a large rising time.
The numerical simulation of the test conducted with a wavy-machined flyer plate and considering the Johnson–Cook plasticity model for the steel provides a correct description of the shockless shaping effect,
The test performed with a target made of two steel plates of different thicknesses confirms that a Lagrangian analysis of data can be achieved providing a consistent value of HEL as obtained from the classical plate-impact test as well as the axial stress vs axial strain response of the tested material.
The test performed with a target made of two alumina plates of different thicknesses processed with a Lagrangian analysis of data provided a HEL that is consistent with values obtained from the classical plate-impact test. It also provided the post-IEL (i.e., axial stress vs axial strain) response of the tested alumina.
An elastoplastic model with strain-hardening (Ludwick's law) allows reproducing the experimental data and seems to provide a reasonable description of the behavior of F99 alumina when subjected to a flat or wavy-plate impact test.
The authors would like to acknowledge Dr. A. Cosculluela from CEA CESTA for providing the alumina samples required for the experiments. This research received external funding from the CEA-CESTA, AID (Agence Innovation Défense), and the Brittle Codex Chair sponsored by Saint-Gobain Company. These supports are gratefully acknowledged.
The authors have no conflicts to disclose.
Julia Genevois: Data curation (lead); Formal analysis (supporting); Investigation (lead); Validation (supporting); Visualization (supporting); Writing – original draft (lead); Writing – review & editing (supporting). Pascal Forquin: Conceptualization (lead); Formal analysis (supporting); Funding acquisition (lead); Investigation (supporting); Methodology (lead); Project administration (lead); Supervision (lead); Validation (lead); Visualization (lead); Writing – original draft (supporting); Writing – review & editing (lead). Jean-Luc Zinszner: Data curation (supporting); Formal analysis (supporting); Methodology (supporting); Validation (supporting); Visualization (supporting); Writing – review & editing (supporting).
The data that support the findings of this study are available from the corresponding author upon reasonable request.
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Experimental Modal Parameter Evaluation Methods
- Living reference work entry
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- First Online: 27 November 2021
- Cite this living reference work entry
- R. J. Allemang 3 &
- A. W. Phillips 3
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Modern experimental modal analysis (EMA) methods provide a number of modal parameter solutions based upon different models, different model orders and different numerical processing of the redundant data and/or results. Evaluation of the modal parameter solutions provides a way of obtaining a single unique set of modal parameters that best represents the measured experimental data. The early portion of this chapter is a review of some of the experimental modal analysis (EMA) methods covered in detail in chapter “Experimental Modal Analysis in this handbook. This is followed by presenting a number of numerical tools that are used in connection with the EMA methods to evaluate and validate the number of modal parameters that can be estimated from a multiple input, multiple output (MIMO) set of measured data. Some tools like complex and multivariate mode indication functions (CMIF and MvMIF) can be used to determine the model order and/or number of modal frequencies that can be estimated from the experimental data. These tools can be applied independent of the EMA method that is used and are particularly useful when close or repeated modal frequencies are present in the experimental data. Additionally, various consistency diagrams, pole surface plots and modal parameter clustering methods are defined that become part of, and enhance, the EMA method used to estimate the modal parameters. Finally, the last portion of this chapter overviews methods that are primarily post processing tools to evaluate and validate the modal parameters that have been estimated. Methods include techniques for normalizing, conditioning and presenting the modal vectors, like the modal vector complexity plot (MVCP) along with techniques for using the estimated modal vectors to estimate other functions like the enhanced frequency response function (eFRF) which can be used to validate the physical validity of the estimated modal vectors. Orthogonality of modal vectors along with consistency of modal vectors, as measured by the modal assurance criterion (MAC), also falls into this category of evaluation and validation tools that are applied after the modal parameters have been estimated. The chapter finishes with a brief example of how several of the evaluation and validation tools can be combined into an autonomous modal parameter estimation method.
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Experimental Modal Analysis Methods
Uncertainty propagation in Experimental Modal Analysis
Abbreviations.
Number of inputs.
Number of outputs.
Short dimension (min( N i , N o )).
Long dimension (max( N i , N o )).
Number of spectral lines (frequencies).
Number of effective modal frequencies.
Number of modal frequencies.
Maximum frequency (Hz).
Frequency (rad/sec).
Maximum frequency (rad/sec).
Frequency resolution (Hz).
Complex modal frequency.
Observation period (sec).
Generalized frequency variable.
Model order for denominator polynomial.
Model order for numerator polynomial.
Residue, output DOF p, input DOF q, mode r.
Residual inertia, output DOF p, input DOF q.
Residual flexibility, output DOF p, input DOF q.
Companion matrix.
Denominator polynomial matrix coefficient.
Numerator polynomial matrix coefficient.
Identity matrix.
Frequency response function matrix. ( N o × N i )
Transformation matrix.
Left singular vector matrix.
Singular value matrix (diagonal).
Eigenvalue matrix (diagonal).
Right singular vector, or eigenvector, matrix.
First stage of modal parameter estimation.
Second stage of modal parameter estimation.
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Allemang, R.J., Phillips, A.W. (2021). Experimental Modal Parameter Evaluation Methods. In: Allemang, R., Avitabile, P. (eds) Handbook of Experimental Structural Dynamics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-6503-8_12-2
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DOI: https://doi.org/10.1007/978-1-4939-6503-8_12-2
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Learn about the theoretical and practical aspects of experimental modal analysis (EMA) methods for determining modal parameters of structural systems from input-output data. The chapter covers various EMA methods based on matrix coefficient polynomials, frequency response functions, and impulse response functions.
Experimental modal analysis is the process of determining the modal parameters of a structural system (frequencies, damping factors, modal vectors, and modal scaling values) from experimental input-output data, normally frequency response functions (FRFs) or impulse response functions (IRFs). This is in contrast to
The modal analysis is used for the determination of eigenmodes of structures. Due to artificial excitation of the structure and measurement of the resulting vibration the modal parameters (eigenfrequency, damping, vibration amplitude, and phase) of the eigenmodes are determined. Hence one can obtain the representation of motion of the different ...
Modal analysis is defined as the study of the dynamic characteristics of a mechanical structure. This applica-tion note emphasizes experimental modal techniques, specifically the method known as frequency response function testing. Other areas are treated in a general sense to intro-duce their elementary concepts and relationships to one ...
Modal analysis is the study of the dynamic properties of systems in the frequency domain. It consists of mechanically exciting a studied component in such a way to target the modeshapes of the structure, and recording the vibration data with a network of sensors. Examples would include measuring the vibration of a car's body when it is attached ...
The development of the tracking filter during the late 1950s was a major technical development that pushed nascent experimental modal analysis methods into the modern era. Besides, the experimental modal analysis could take off only after sensors were readily available and sufficiently stable and accurate to measure force and vibration response.
Modal analysis is used in the design of many types of structures, such as automotive structures, aircraft structures, spacecraft, computers, and tennis rackets. The most important measurement that is needed for experimental modal analysis is the frequency response function (FRF).
Experimental modal analysis (EMA) is a name for the technique of measuring frequency response functions and then using these FRFs to extract the modal parameters of the system (structure), namely the natural frequencies, damping ratios, mode shapes, and modal scaling constants. EMA is a very common application in vibration engineering, where it ...
The presented method is evaluated on ground vibration test data (i.e., experimental modal analysis) as well as flight vibration data (i.e., operational modal analysis) of an aircraft structure. In contrast to previous methods, the presented method can be easily used for various modal tests, since it can learn by itself to perform optimally with ...
Experimental modal analysis has grown steadily in popu-larity since the advent of the digital FFT spectrum analyzer in the early 1970's. Today, impact testing (or bump testing) has become widespread as a fast and economical means of finding the modes of vibration of a machine or structure.
Experimental modal analysis methodologies commonly use accelerometers as the main type of transducer, but can also be carried out using strain gauges [14]. Using accelerome ters will lead to the identication of the displacement mode shapes, while with strain gauges, the strain mode shape s are identied [9] instead.
Experimental modal analysis has grown steadily in popularity since the advent of the digital FFT spectrum analyzer in the early 1970's. Today, impact testing (or bump testing) has become widespread as a fast and economical means of finding the modes of vibration of a machine or structure. In this paper, we review all of the main topics associated with experimental modal analysis (or modal ...
SINT Technology offers vibration measurements and analysis services using experimental modal analysis (EMA) techniques. EMA can determine natural frequencies, mode shapes, damping and validate finite element models of structures.
In practice, the analytical approach based on lumped parameter and finite element models is widely used for modal analysis and simulation, and experimental modal analysis is widely used for modal identification and model validation. This book is inspired by this consideration and is written to give a complete picture of modal analysis. Features:
This paper discusses the application of Dynamic Mode Decomposition (DMD) to the extraction of modal properties of linear mechanical systems, i.e., experimental modal analysis (EMA). First, theoretical background of the DMD is briefly reviewed and its relevance to the Ibrahim time-domain method is discussed. Second, DMD is applied to a single ...
The basis of the theory for the experimental modal analysis is the equation of motion of the forced oscillation of the single-mass oscillator with velocity-proportional damping, a differential equation of second order (compare Eq. 15.1 ). Considering the different notations and multiplying by (−1), Eq. 4.1 becomes.
ABOUT THE COURSE: This course is about the fundamentals and basic concepts of Experimental Modal Analysis (EMA) and its applications. EMA, also known as Modal Testing, is a technique for experimentally determining the natural frequencies, mode shapes, and damping factors of a physical system or structure. One primary application of EMA is for ...
This research is focused on a comparison of classic and strain experimental modal analysis (EMA). The modal parameters (the natural frequencies, the displacement mode shapes (DMSs) and the damping) of real structures are usually identified with classic EMA, where the responses are measured with motion sensors (e.g. accelerometers).
Overview. Experimental Modal Analysis emerged in the late 1950's and gained steady popularity since the late 1960's. During that time period, researchers tried to solve a major structural issue referred to as the self-excited aerodynamic flutter problem, which is considered a critical issue for the aerospace industry.
In experimental modal testing, a measured force at one or more points excites the structure and the response is measured at one or more points to construct frequency response functions. The modal parameters can be determined from these functions by curve fitting with a computer. Various curve-fitting methods are used.
In the field of operational modal analysis (OMA), obtained modal information is frequently used to assess the current state of aerospace, mechanical, offshore and civil structures. However, the stochasticity of operational systems and the lack of forcing information can lead to inconsistent results. Quantifying the uncertainty of the recovered modal parameters through OMA is therefore of ...
The current Alphabet stock valuation looks attractive at its price point. The company trades at a slight premium to its price-to-earnings growth rate ratio of 1.2. This suggests that Alphabet's ...
Experimental modal analysis has grown steadily in popularity since the advent of the digital FFT spectrum analyser in the early 1970's. Today, impact testing (or bump testing) has become widespread as a fast and economical means of finding the modes of vibration of a machine or structure. Mechanical resonance is the tendency of a mechanical ...
The present experimental work provides the first experimental application and validation of the shockless plate-impact configurations theorized and numerically designed in Refs. 16 and 17 aiming at applying a Lagrangian analysis of data from plate-impact tests performed with ceramics. To do so, a multi-step strategy has been carried out.
Abstract. Modern experimental modal analysis (EMA) methods provide a number of modal parameter solutions based upon different models, different model orders and different numerical processing of the redundant data and/or results. Evaluation of the modal parameter solutions provides a way of obtaining a single unique set of modal parameters that ...
Abstract. The use of wind-assisted ship propulsion is regarded as one of the effective ways to reduce greenhouse gas emissions. This study combines wind tunnel experiments and advanced numerical simulations to investigate the model-scale effects and fluid-structure interaction (FSI) of a wingsail with a crescent-shaped profile. First, a wind tunnel test is carried out to study the aerodynamic ...