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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
The practical, clear, and concise guide for conducting experimental modal tests Modal Testing: A Practitioner's Guide outlines the basic information necessary to conduct an experimental modal test. The text draws on the author's extensive experience to cover the practical side of the concerns that may arise when performing an experimental modal test. Taking a hands-on approach, the book explores the issues related to conducting a test from start to finish. It covers the cornerstones of the basic information needed and summarizes all the pertinent theory related to experimental modal testing. Designed to be accessible, Modal Testing presents the most common excitation techniques used for modal testing today and is filled with illustrative examples related to impact testing which is the most widely used excitation technique for traditional experimental modal tests. This practical text is not about developing the details of the theory but rather applying the theory to solve real-life problems, and: * Delivers easy to understand explanations of complicated theoretical concepts * Presents basic steps of an experimental modal test * Offers simple explanations of methods to obtain good measurements and avoid the common blunders typically found in many test approaches * Focuses on the issues to be faced when performing an experimental modal test * Contains full-color format that enhances the clarity of the figures and presentations Modal Testing: A Practitioner's Guide is a groundbreaking reference that treats modal testing at the level of the practicing engineer or a new entrant to the field of experimental dynamic testing.
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Veröffentlichungsjahr: 2017
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Table of Contents
Cover
Title Page
Copyright
Dedication
Preface
About the Companion Website
Part I: Overview of Experimental Modal Analysis using the Frequency Response Method
Chapter 1: Introduction to Experimental Modal Analysis: A Simple Non-mathematical Presentation
1.1 Could you Explain Modal Analysis to Me?
1.2 Just what are these Measurements called FRFs?
1.3 What's the Difference between a Shaker Test and an Impact Test?
1.4 What's the Most Important Thing to Think about when Impact Testing?
1.5 What's the Most Important Thing to Think about when Shaker Testing?
1.6 Tell me More About Windows; They Seem Pretty Important!
1.7 So how do we get Mode Shapes from the Plate FRFs?
1.8 Modal Data and Operating Data
1.9 Closing Remarks
Chapter 2: General Theory of Experimental Modal Analysis
2.1 Introduction
2.2 Basic Modal Analysis Theory – SDOF
2.3 Basic Modal Analysis Theory – MDOF
2.4 Summary
Chapter 3: General Signal Processing and Measurements Related to Experimental Modal Analysis
3.1 Introduction
3.2 Time and Frequency Domain
3.3 Some General Information Regarding Data Acquisition
3.4 Digitization of Time Signals
3.5 Quantization
3.6 AC Coupling
3.7 Sampling Theory
3.8 Aliasing
3.9 What is the Fourier Transform?
3.10 Leakage and Minimization of Leakage
3.11 Windows and Leakage
3.12 Frequency Response Function Formulation
3.13 Typical Measurements
3.14 Time and Frequency Relationship Definition
3.15 Input–Output Model with Noise
3.16 Summary
Chapter 4: Excitation Techniques
4.1 Introduction
4.2 Impact Excitation Technique
4.3 Shaker Excitation
4.4 Comparison of Different Excitations for a Weldment Structure
4.5 Multiple-input, Multiple-output Measurement
4.6 Summary
Chapter 5: Modal Parameter Estimation Techniques
5.1 Introduction
5.2 Experimental Modal Analysis
5.3 Extraction of Modal Parameters
5.4 Mode Identification Tools
5.5 Modal Model Validation Tools
5.6 Operating Modal Analysis
5.7 Summary
Part II: Practical Considerations for Experimental Modal Testing
Chapter 6: Test Setup Considerations
6.1 Test Plan?
6.2 How Many Modes Required?
6.3 Frequency Range of Interest?
6.4 Transducer Possibilities?
6.5 Test Configurations?
6.6 How Many Measurement Points Needed?
6.7 Excitation Techniques
6.8 Miscellaneous Items to Consider
6.9 Summary
Chapter 7: Impact Testing Considerations
7.1 Hammer Impact Location
7.2 Hammer Tip and Frequency Range
7.3 Hammers for Different Size Structures
7.4 How Does Impact Skew and Deviation of Input Point Affect the Measurement?
7.5 Impact Hammer Frequency Bandwidth
7.6 Accelerometer ICP Considerations for Low Frequency Measurements
7.7 Considerations for Reciprocity Measurements
7.8 Roving Hammer vs Roving Accelerometer
7.9 Picking a Good Reference Location
7.10 Multiple Impact Difficulties and Considerations
7.11 What is “Filter Ring” during an Impact Measurement?
7.12 Test Bandwidth Much Wider than Desired Frequency Range
7.13 Why Does the Structure Response Need to Come to Zero at the End of the Sample Time?
7.14 Measurements with no Overload but Transducers are Saturated
7.15 How much Roll Off in the Input Hammer Force Spectrum is Acceptable?
7.16 Can the Hammer be Switched in the Middle of a Test to Avoid Double Impacts?
7.17 Closing Remarks
Chapter 8: Shaker Testing Considerations
8.1 General Hardware Related Issues
8.2 Stinger Related Issues
8.3 Shaker Related Issues
8.4 Concluding Remarks
Chapter 9: Insight into Modal Parameter Estimation
9.1 Introductory Remarks
9.2 Mode Indicator Tools Help Identify Modes
9.3 SDOF vs MDOF for a Simple System
9.4 Local vs Global: MACL Frame
9.5 Repeated Root: Composite Spar
9.6 Wind Turbine Blade: Same Geometry but Very Different Modes
9.7 Stability Diagram Demystified
9.8 Curvefitting Demystified
9.9 Curvefitting Different Bands for the Poles and Residues
9.10 Synthesizing the FRF from Parameters from Several Bands Stitched Together
9.11 A Large Multiple Reference Modal Test Parameter Estimation
9.12 Operating Modal Analysis
9.13 Concluding Remarks
Chapter 10: General Considerations
10.1 An Experimental Modal Test: a Thought Process Divulged
10.2 FFT Analyzer Setup
10.3 Log Sheets
10.4 Practical Considerations: Checklists
10.5 Summary
Appendix: Logbook Forms
Chapter 11: Tips, Tricks, and Other Stuff
11.1 Modal Testing Primer
11.2 Impact Hammer and Impulsive Excitation
11.3 Accelerometer Issues
11.4 Curvefitting Considerations
11.5 Blue Frame with Three Plate Subsystem
11.6 Miscellaneous Issues
11.7 Summary
Appendix A: Linear Algebra: Basic Operations Needed for Modal Analysis Operations
A.1 Define a Matrix
A.2 Define a Column Vector
A.3 Define a Row Vector
A.4 Define a Diagonal Matrix
A.5 Define Matrix Addition
A.6 Define Matrix Scalar Multiply
A.7 Define Matrix Multiply
A.8 Matrix Multiplication Rules
A.9 Transpose of a Matrix
A.10 Transposition Rules
A.11 Symmetric Matrix Rules
A.12 Define a Matrix Inverse
A.13 Matrix Inverse Properties
A.14 Define an Eigenvalue Problem
A.15 Generalized Inverse
A.16 Singular Value Decomposition
Appendix B: Example Using Two Degree of Freedom System: Eigenproblem
Appendix C: Pole, Residue, and FRF Problem for 2-DOF System
Appendix D: Example using Three Degree of Freedom System
Appendix E: DYNSYS Website Materials
E.1 Technical Materials Developed
E.2 DYNSYS.UML.EDU Website
Appendix F: Basic Modal Analysis Information
F.1 SDOF Definitions
F.2 MDOF Definitions
Part III: Collection of Sets of Modal Data Collected for Processing
Appendix G: Repeated Root Frame: Boundary Condition Effects
G.1 Corner Supports Set #1
G.2 Midlength Supports Set #2
G.3 Modal Correlation between Set #1 and Set #2
Appendix H: Radarsat Satellite Testing
H.1 Data Reduction Set 1: Reference BUS:109:Z, BUS:118:Z, PMS:217:X and PMS:1211:Y
H.2 Data Reduction Set 2: Reference PMS:217:X and PMS:1211:Y
Appendix I: Demo Airplane Testing
I.1 Impact Testing
I.2 SIMO Testing with Skewed Shaker
I.3 MIMO Testing with Two Vertical Modal Shakers
Appendix J: Whirlpool Dryer Cabinet Modal Testing
Appendix K: GM MTU Automobile Round Robin Modal Testing
Appendix L: UML Composite Spar Modal Testing
Appendix M: UML BUH Modal Testing
Appendix N: Nomenclature
Index
End User License Agreement
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Guide
Cover
Table of Contents
Preface
Part I: Overview of Experimental Modal Analysis using the Frequency Response Method
Begin Reading
List of Illustrations
Chapter 1: Introduction to Experimental Modal Analysis: A Simple Non-mathematical Presentation
Figure 1.1 Structural dynamics vs modal analysis.
Figure 1.2 Signal flow diagram showing modal filtering of input resulting in output.
Figure 1.3 Simple plate excitation–response model.
Figure 1.4 Simple plate response due to sinusoidal sweep excitation.
Figure 1.5 Simple plate frequency response function.
Figure 1.6 Overlay of time and frequency response functions for the simple plate structure.
Figure 1.7 Simple plate sine dwell response.
Figure 1.8 3 DOF beam: (a) model for input–output frequency response function matrix and (b) magnitude, (c) phase, (d) real, and (e) imaginary portions of the frequency response matrix.
Figure 1.9 3DOF beam: (a) drive point FRF (magnitude) for reference 3; (b) cross FRFs (magnitude) for Reference 3.
Figure 1.10 3DOF beam: (a) Mode 1 from third row of frequency response matrix; (b) Mode 1 from second row of frequency response matrix; (c) Mode 2 from third row of frequency response matrix; (d) Mode 2 from second row of frequency response matrix.
Figure 1.11 Waterfall plot of 3DOF beam frequency response functions.
Figure 1.12 Test scenarios for frequency response matrix for the 3DOF beam. (a) roving impact hammer test, (b) shaker test.
Figure 1.13 Anatomy of an FFT analyzer for typical experimental modal test measurements.
Figure 1.14 Hammer tip choice: (a) hammer tip insufficient to excite all modes; (b) hammer tip adequate to excite all modes.
Figure 1.15 Exponentially decaying window to minimize leakage effects.
Figure 1.16 Shaker testing: random excitation with Hanning window.
Figure 1.17 Burst random excitation without a window.
Figure 1.18 Sine chirp excitation without a window.
Figure 1.19 Input–output measurement locations.
Figure 1.20 Plate mode shapes for Mode 1: peak pick of FRF.
Figure 1.21 Plate mode shapes for Mode 2: peak pick of FRF.
Figure 1.22 Breakdown of a frequency response function.
Figure 1.23 Curvefitting different bands using different methods.
Figure 1.24 Curvefitting a typical FRF.
Figure 1.25 Schematic overview of the input–output structural response problem.
Figure 1.26 Measured operating displacements.
Figure 1.27 Excitation close to mode 1.
Figure 1.28 Excitation close to mode 2.
Figure 1.29 Excitation somewhere between mode 1 and mode 2.
Figure 1.30 Broadband plate excitation.
Figure 1.31 Schematic of the SDM process.
Figure 1.32 Overall dynamic modeling process.
Figure 1.33 Modal model characteristics.
Figure 1.34 Operating data characteristics.
Chapter 2: General Theory of Experimental Modal Analysis
Figure 2.1 SDOF model.
Figure 2.2 S-plane nomenclature.
Figure 2.3 Pole migration through the S-plane for a SDOF system with increasing damping (time and frequency plots are not to scale and are for illustration purposes only).
Figure 2.4 The dynamic amplification and phase for an SDOF system: (a) dynamic amplification; (b) phase.
Figure 2.5 Magnitude plot depicting the half power method.
Figure 2.6 Time response depicting the log decrement method.
Figure 2.7 SDOF FRF effects of different damping values.
Figure 2.8 SDOF FRF force balance. Sinusoidal excitation is (a) much less than natural frequency; (b) at natural frequency; (c) higher than natural frequency.
Figure 2.9 System transfer function for a single degree of freedom system.
Figure 2.10 Illustration plots of the acceleration frequency response function: (a) Bode, co-quad and Nyquist plots; (b) half power points for the co-quad and Nyquist plots.
Figure 2.11 Laplace transform, S-plane and frequency response function projections.
Figure 2.12 Stiffness, damping and mass controlled portions of the magnitude of the FRF.
Figure 2.13 Forms of the FRF and slopes of stiffness and mass controlled regions: (left) D/F; (center) V/F; (right) A/F.
Figure 2.14 D/F FRF with real, imaginary, magnitude, phase and Nyquist forms of the FRF.
Figure 2.16 A/F FRF with real, imaginary, magnitude, phase and Nyquist forms of the FRF.
Figure 2.17 Complete D/F FRF with pole and conjugate pole.
Figure 2.18 Relationship of transfer function, h(s) and frequency response function, h(jω).
Figure 2.19 Complex frequency response function evaluated at resonance.
Figure 2.20 2DOF system: (left) schematic; (right) free body diagram.
Figure 2.21 A general “n” multiple degree of freedom system: (a) a simple lumped mass model; (b) a more detailed finite element model.
Figure 2.22 Graphical representation of roots of determinant.
Figure 2.23 Schematic for eigensolution for mode 1.
Figure 2.24 Schematic for eigensolution for mode 2.
Figure 2.25 Modal transformation converting coupled MDOF system into SDOF modal systems.
Figure 2.26 Mode 1 modal response projected to all physical DOFs for mode 1 contribution.
Figure 2.27 Mode 2 modal response projected to all physical DOFs for mode 2 contribution.
Figure 2.28 Schematic of the transformation of the physical/coupled MDOF system into equivalent SDOF systems.
Figure 2.29 FRF for Multiple DOF system: (a) summed FRF; (b) individual mode contributions.
Figure 2.30 Transfer function and FRF for 3DOF system: (left) phase and magnitude; (right) real and imaginary; (main image) system transfer function.
Figure 2.31 FRF composition of SDOF FRFs summed together.
Figure 2.32 D/F FRF with real, imaginary, magnitude, phase and Nyquist forms of the FRF.
Figure 2.34 A/F FRF with real, imaginary, magnitude, phase and nyquist forms of the FRF.
Figure 2.35 Sinusoidal excitation lower than natural frequency: (top) contribution of each of the FRFs; (bottom) time domain responses.
Figure 2.36 Sinusoidal excitation at mode 1 natural frequency: (top) contribution of each of the FRFs; (bottom) time domain responses.
Figure 2.37 Sinusoidal excitation between mode 1 and 2 natural frequency: (top) contribution of each of the FRFs; (bottom) time domain responses.
Figure 2.38 FRF broken down by mode, showing FRF both in residue equation form and shape equation form.
Figure 2.39 3DOF cantilever beam with first three mode shapes.
Figure 2.40 3DOF cantilever beam FRF matrix: magnitude, phase, real, imaginary parts of the FRF.
Figure 2.41 3DOF cantilever beam FRF matrix, highlighting h
33
.
Figure 2.42 3DOF FRF showing drive point measurement; complete FRF and contribution by mode.
Figure 2.43 3DOF cantilever beam FRF matrix, highlighting h
32
.
Figure 2.44 3DOF cantilever beam FRF matrix, highlighting h
31
.
Figure 2.45 Roving impact test with stationary reference accelerometer at point 3.
Figure 2.46 Roving accelerometer test with stationary reference shaker force at point 3.
Figure 2.47 FRF matrix (magnitude) with each mode contribution shown individually.
Figure 2.48 FRF matrix (magnitude) with all modes combined.
Figure 2.49 3DOF FRF matrix: third column highlighting mode 1 shape.
Figure 2.50 Waterfall plot illustrating mode shapes for 3x3 FRF matrix.
Figure 2.51 Physical, time impulse, FRF and SDOF model for each mode.
Figure 2.52 Simple cantilever beam impulse and response schematic for small wind turbine blade.
Figure 2.53 Illustration of modal responses projected to physical space: (a) mode 1; (b) mode 2; (c) mode 3.
Figure 2.54 Overview of the entire physical, modal response and expansion to finite element model space. (animation is available on the book webpage).
Figure 2.55 Overview of analytical and experimental modal analysis.
Chapter 3: General Signal Processing and Measurements Related to Experimental Modal Analysis
Figure 3.1 Time/frequency representations for a sinusoidal signal.
Figure 3.2 Basic configuration of an FFT analyzer.
Figure 3.3 Anatomy of the FFT measurement process.
Figure 3.4 Schematic showing ADC bits, possible levels, dynamic range.
Figure 3.5 Analog signal digitized to obtain digital representation: (a) analog signal; (b) digital representation.
Figure 3.6 Amplitude distortion when capturing a pure sine wave with (a) 4 bit ADC; (b) 6 bit ADC.
Figure 3.7 Signal distortion due to fixed resolution for (a) large amplitude and (b) small amplitude sine waves at two different frequencies. (c) Poor use of ADC range with a small amplitude sine signal.
Figure 3.8 Signal distortion due to overloading of the ADC: (a) proper voltage range setting; (b) inappropriate setting and overload.
Figure 3.9 Signal showing need for AC coupling to remove large dominating DC signal.
Figure 3.10 Time step sampling of a sine wave.
Figure 3.11 Relationship of time resolution, frequency resolution, number of samples and bandwidth.
Figure 3.12 Illustration of distortion of data (red) when inappropriate sampling rates are specified.
Figure 3.13 Graphical representation of the time frequency relationships.
Figure 3.14 Schematic showing aliasing and the wrap around error.
Figure 3.15 A general random signal.
Figure 3.16 Several simple sine waves with corresponding frequency representations.
Figure 3.17 Actual time signal, sampled and reconstructed along with the resulting frequency spectrum from the FFT for properly sampled data.
Figure 3.18 Actual time signal, sampled and reconstructed, along with the resulting frequency spectrum from the FFT for improperly sampled data.
Figure 3.19 Sampling clearly showing discontinuity from sample to sample.
Figure 3.20 Conceptualization of windows weighting functions to reduce leakage.
Figure 3.21 Distortion effects of windows to reduce leakage.
Figure 3.22 Rectangular window frequency signature for (a) log mag and (b) linear mag.
Figure 3.24 Flattop window frequency signature for log mag (a) and linear mag (b).
Figure 3.23 Hanning window frequency signature for (a) log mag and (b) linear mag.
Figure 3.25 Comparison of the rectangular, Hanning and flat top windows with periodic signals satisfying and not satisfying the periodicity requirement of the Fourier transform process.
Figure 3.26 Overlaid plot of the rectangular, Hanning and flat top windows.
Figure 3.27 Illustration of (a) force and (b) exponential windows.
Figure 3.28 Schematic of the convolution of the theoretical window with the actual signal in the frequency domain.
Figure 3.29 Typical input–output measurement situation.
Figure 3.30 Time signal (top) and power spectra (bottom): (a) input; (b) output.
Figure 3.31 Power spectra: (a) input; (b) output; (c) cross power spectrum.
Figure 3.32 Power spectra: (a) input; (b) cross power spectrum; (c) output; (d) computed frequency response function.
Figure 3.33 Computed frequency response function (bottom) with coherence (top).
Figure 3.34 General input–output noise model.
Chapter 4: Excitation Techniques
Figure 4.1 Overall measurement process for impact test.
Figure 4.2 Overall measurement process for shaker test.
Figure 4.3 Impact and response shown over sample block T.
Figure 4.4 Several common impact hammer configurations. Courtesy of PCB Piezotronics, Inc.
Figure 4.5 Input time pulse (blue) and resulting frequency spectrum (red) for a metal tip, hard plastic tip, soft plastic tip, and rubber tip.
Figure 4.6 Typical FRF from an impact measurement.
Figure 4.7 Typical FRF with coherence from an impact measurement.
Figure 4.8 Typical FRF and coherence with the input force spectrum from an impact measurement.
Figure 4.9 Ideal FRF and coherence with the input force spectrum from an impact measurement.
Figure 4.10 Sampled force with force window applied.
Figure 4.11 Comparison of force spectrum, with and without pre-trigger delay.
Figure 4.12 Two different double impact time pulses and corresponding frequency spectra.
Figure 4.13 Time response due to an impact excitation requiring an exponential window.
Figure 4.14 Time response due to an impact excitation with two time response blocks: one requiring an exponential window and one not requiring an exponential window.
Figure 4.15 Frequency response matrix data collected for a roving hammer (row, red) and a stationary hammer (column, blue) shown with reciprocal FRF measurements schematically depicted.
Figure 4.16 Roving hammer modal test with three separate accelerometer reference locations.
Figure 4.17 Three separate hammer input reference locations with all accelerometers fixed.
Figure 4.18 Optical telescope modal test with 100 accelerometers and multiple impact locations, showing time streamed data collection for three accelerometers and 25 samples acquired.
Figure 4.19 Typical impact measurement setup for blue frame structure.
Figure 4.20 Measurements for 800 Hz with 400 spectral lines impact force (top left); input force spectrum (top right) time response (bottom left); FRF (bottom right).
Figure 4.21 Measurements for 200 Hz with 800 spectral lines: impact force (top left); input force spectrum (top right); time response (bottom left); FRF (bottom right).
Figure 4.22 Measurements for 400 Hz with 400 spectral lines: impact force (top left); input force spectrum (top right); time response (bottom left); FRF (bottom right).
Figure 4.23 Measurements for 400 Hz with 800 spectral lines with damping window: impact force (top left); input force spectrum (top right); raw time response (middle left); windowed time response (bottom left); FRF (bottom right).
Figure 4.24 Measurements for 400 Hz with 400 spectral lines with heavy damping window: impact force (top left); input force spectrum (top right); raw time response (middle left); windowed time response (bottom left); FRF (bottom right).
Figure 4.25 Measurements for 100 Hz with 800 spectral lines with very light damping window: impact force (top left); input force spectrum (top right); raw time response (middle left); windowed time response (bottom left); FRF (bottom right).
Figure 4.26 Measurements for 800 Hz with 800 spectral lines: input force spectrum (top); FRF (middle); coherence (bottom).
Figure 4.27 Measurements for 200 Hz with 800 spectral lines with metal tip: input force spectrum (top); FRF (middle); coherence (bottom).
Figure 4.28 Measurements for 200 Hz with 800 spectral lines with very soft tip: input force spectrum (top); FRF (middle); and coherence (bottom).
Figure 4.29 Impact time force (upper traces), time response (middle traces) and FRF (bottom traces) for a measurement with slightly too much damping window applied (left), definitely too much damping window applied (middle) and improved resolution with little damping window applied (right).
Figure 4.30 Reciprocity measurement.
Figure 4.31 Typical shaker configuration used for vibration qualification testing.
Figure 4.32 Typical modal shaker system configuration.
Figure 4.33 Typical shaker setup schematic (top) with pieces of the modal shaker/stinger (middle) and an actual shaker (bottom) attached to a test structure in the lab.
Source:
Image courtesy of PCB Piezotronics, Inc.
Figure 4.34 Assortment of shaker stingers.
Source:
Image courtesy of PCB Piezotronics, Inc.
Figure 4.35 Comparison of deterministic and non-deterministic excitation.
Figure 4.36 Schematic of typical input force (top), output response (middle), and FRF (bottom) for random excitation.
Figure 4.37 Input force (top) and output response (bottom) on left and coherence (top) and FRF (bottom) on right for random excitation.
Figure 4.38 Schematic of typical input force (top), output response (middle), and FRF (bottom) for random excitation with Hanning window.
Figure 4.39 Input force (top) and output response (bottom) on left and coherence (top) and FRF (bottom) on right for random excitation with Hanning window.
Figure 4.40 Schematic showing effective use of data with 50% overlap processing.
Figure 4.41 Schematic of typical input force (top), output response (middle), and FRF (bottom) for pseudo-random excitation.
Figure 4.42 Schematic of typical input force (top), output response (middle), and FRF (bottom) for periodic-random excitation.
Figure 4.43 Schematic of typical input force (top), output response (middle), and FRF (bottom) for burst random excitation.
Figure 4.44 Input force (top) and output response (bottom) on left and coherence (top) and FRF (bottom) on right for burst random excitation.
Figure 4.45 Schematic of typical input force (top), output response (middle), and FRF (bottom) for sine chirp excitation.
Figure 4.46 Input force (top) and output response (bottom) on left and coherence (top) and FRF (bottom) on right for sine chirp excitation.
Figure 4.47 Schematic of typical input force (top), output response (middle), and FRF (bottom) for stepped sine excitation.
Figure 4.48 Weldment structure used for comparison measurements.
Figure 4.49 Input force (top) and output response (bottom) on left and coherence (top) and FRF (bottom) on right for random excitation.
Figure 4.50 Input force (top) and output response (bottom) on left and coherence (top) and FRF (bottom) on right for random excitation with Hanning window.
Figure 4.51 Input force (top) and output response (bottom) on left and coherence (top) and FRF (bottom) on right for burst random excitation.
Figure 4.52 Input force (top) and output response (bottom) on left and coherence (top) and FRF (bottom) on right for sine chirp excitation.
Figure 4.53 Comparison of FRF with random with a window, burst random, and sine chirp excitations.
Figure 4.54 Comparison of FRF and coherence with random and burst random excitations.
Figure 4.55 Comparison of FRF overlaid with coherence with random and burst random excitation.
Figure 4.56 Zoomed in FRF on mode 1, showing difference between FRF from random and burst random excitations.
Figure 4.57 Linearity check with sine chirp excitation (FRFs).
Figure 4.58 Comparison of SISO and MIMO reciprocal data sets collected with random excitation with a Hanning window and burst random excitation.
Figure 4.59 Schematic for two separate SISO tests (top) vs MIMO test (bottom).
Figure 4.60 SVD for two shaker inputs (left) and two force spectra overlaid (right).
Figure 4.61 Multiple coherence (top) related to two FRFS (bottom) for two input locations.
Figure 4.62 SISO measurement (top) and MIMO measurement (bottom) with broadband FRF shown on left and expand into first two modes on right.
Figure 4.63 Frame structure with separate attached modally active components.
Figure 4.64 SISO and MIMO test setup configurations.
Figure 4.65 SISO test setup and results for one shaker location.
Figure 4.66 MIMO test setup and results for MIMO configuration.
Chapter 5: Modal Parameter Estimation Techniques
Figure 5.1 A typical set of data used for a least squares analysis.
Figure 5.2 Straight line fit passing through zero (left), straight line fit with offset (middle) and straight line fit with some data removed (right).
Figure 5.3 Illustration of curvefitting with band of interest and adjacent bands.
Figure 5.4 Typical FRF with selected band for estimation of parameters.
Figure 5.5 FRF for a 2DOF system with different damping and frequency closeness.
Figure 5.6 FRF for a 2DOF system: well separated and lightly damped.
Figure 5.7 FRF for a 2DOF system: closely separated and lightly damped.
Figure 5.8 FRF for a 2DOF system: well separated and heavily damped.
Figure 5.9 FRF for a 2DOF system: closely separated and heavily damped.
Figure 5.10 Frequency domain representation (left) and time domain representation (right).
Figure 5.11 Schematic showing peak picking technique.
Figure 5.12 Schematic showing circular representation in the Nyquist plot (right) for SDOF system.
Figure 5.13 Schematic showing curvefit for an SDOF system.
Figure 5.14 Schematic showing mass and stiffness residual effects used for curvefitting.
Figure 5.15 Schematic showing curvefit for an MDOF system.
Figure 5.16 Transform of FRF measurement to obtain equivalent time domain data.
Figure 5.17 FRF broken down by mode, showing FRF both in residue equation form and shape equation form.
Figure 5.18 Summation function showing several peaks over a limited bandwidth.
Figure 5.19 MMIF showing several dips over a limited bandwidth with primary MIF in blue and secondary MIF in red.
Figure 5.20 CMIF plot with three references indicating multiple roots.
Figure 5.21 Stability diagram from the 1990s with summation function.
Figure 5.22 Stability diagram with summation, MMIF, and CMIF with a pseudo-repeated root.
Figure 5.23 Stability diagram for Canadian Space Agency Radarsat satellite test in 1993.
Figure 5.24 Stability diagram for Canadian Space Agency Radarsat satellite test in mid-2000 using PolyMAX.
Figure 5.25 Synthesis comparison for two cross measurements for a structure with very directional modes.
Figure 5.26 Modes (poles and residues) combined from band #1, band #2, and band #3, along with the lower residual from band #1 and upper residual from band #3 to synthesize the frequency response function.
Figure 5.27 Synthesis comparison for drive point measurement for the Canadian Space Agency Radarsat satellite: (a) with both local and global modes; (b) with mainly global modes.
Figure 5.28 MAC table and 3D matrix comparing mode shapes from two different modal tests with two different boundary conditions.
Figure 5.29 Typical experimental modal test measurements in matrix form.
Figure 5.30 Typical experimental modal test configuration.
Figure 5.31 Typical operating modal test configuration.
Figure 5.32 Schematic showing output only response scenario with unknown force and FRF shown.
Chapter 6: Test Setup Considerations
Figure 6.1 RR frame structure with two different boundary condition setups.
Figure 6.2 Shock plate tested with two different support conditions.
Figure 6.3 Mass and inertia ratios to achieve a built-in boundary condition for a CX-100 turbine blade.
Figure 6.4 Very large wind turbine blade low frequency experimental modal test.
Figure 6.6 Very small jet engine turbine blade simulation, high frequency experimental modal test.
Figure 6.5 Medium sized academic structure experimental modal test.
Figure 6.7 Space frame structure with various combinations of measurement locations.
Figure 6.8 Plate model with two input and three output locations.
Figure 6.9 Coupled plate model with one component not measured.
Figure 6.10 Poor distribution of points: mode 1 and mode 3 not distinguishable.
Figure 6.11 Poor distribution of points: RBM 1 and mode 1 not distinguishable.
Figure 6.12 Poorly selected reference locations for nine reference accelerometer locations.
Figure 6.13 Mode shifting due to air bag pressure changes during SISO shaker testing.
Figure 6.14 Typical accelerometer test locations.
Figure 6.15 Symmetric configurations: orientation necessary.
Figure 6.16 Illustration of simple tuned mass absorber.
Figure 6.17 Schematic of dynamic coupling effects of modes.
Figure 6.18 Effect of very small change to test setup.
Chapter 7: Impact Testing Considerations
Figure 7.1 Time pulse and frequency spectrum for several hammer tips.
Figure 7.2 Comparison of tips of different hardnesses with different impact strengths.
Figure 7.3 Impact test setup for a large wind turbine blade.
Figure 7.4 Wiring layout for modal test of a large wind turbine blade.
Figure 7.5 Typical flap and edge mode shapes for large wind turbine blade tests.
Figure 7.6 Modal and operating testing on a large optical telescope.
Figure 7.7 Schematic of golf club testing with small impact hammer configured with a small camera tripod.
Figure 7.8 Measurement for (a) a good impact excitation (b) a skewed impact excitation.
Figure 7.9 Measurement for (a) a good impact excitation (b) an inconsistent impact excitation.
Figure 7.10 Comparison of impact force spectrum for specified bandwidth and four times the specified bandwidth.
Figure 7.11 Comparison of two bandwidth settings with two different tips over two different frequency ranges.
Figure 7.12 Soft hammer tip used for wider frequency range.
Figure 7.14 Suitable hammer tip used for desired frequency range.
Figure 7.13 Very hard hammer tip used for narrow frequency range.
Figure 7.15 Illustration of hammer energy distribution beyond the bandwidth of interest.
Figure 7.16 Illustration of hammer energy distribution beyond the bandwidth of interest with (a) hard and (b) soft tip.
Figure 7.17 Comparison of two DC accelerometers and an ICP accelerometer for very low frequency application.
Figure 7.18 Schematic showing reciprocal measurements from shaker test and roving impact test.
Figure 7.19 Small structure setup for reciprocal measurements.
Figure 7.20 Close-up of ball bearings used to improve accuracy of reciprocal measurements.
Figure 7.21 Multiple reference impact test: roving hammer test (left) and stationary hammer test (right).
Figure 7.22 MACL frame with directional modes: FRFs (left) and shapes (right).
Figure 7.23 Single impact excitation: excitation (top) and response (bottom)
Figure 7.24 Single impact excitation: input spectrum (top) and FRF (bottom)
Figure 7.25 Single impact excitation: coherence (top) and FRF (bottom)
Figure 7.26 Multiple impact excitation: excitation (top) and response (bottom)
Figure 7.27 Multiple impact excitation: input spectrum (top) and FRF (bottom)
Figure 7.28 Multiple impact excitation: coherence (top) and FRF (bottom)
Figure 7.29 Frequency response and coherence for 200 mV/g accelerometer for single impact (left) and multiple impact (right).
Figure 7.30 Frequency response and coherence for 1 V/g accelerometer for single impact (left) and multiple impact (right).
Figure 7.31 Effects of filter ring depending on bandwidth selected: 400 Hz BW (left) and 1600 Hz BW (right).
Figure 7.32 Measurement over 2 kHz with 500 Hz range to be analyzed.
Figure 7.33 Frequency excitation to 500 Hz.
Figure 7.34 Measured response to 1 kHz.
Figure 7.35 Impact response for one sample.
Figure 7.36 User perception of impact averaged response.
Figure 7.37 FRF and coherence from initial measurements.
Figure 7.38 Impact response from structure standpoint.
Figure 7.39 Good FRF and coherence from proper technique.
Figure 7.40 Excitation (top) and response (bottom) with sensitive accelerometer and exponential window for case 1.
Figure 7.41 FRF (bottom) and coherence (top) with sensitive accelerometer and exponential window for case 1.
Figure 7.42 Excitation (top) and response (bottom) with sensitive accelerometer and exponential window for case 2.
Figure 7.43 FRF (bottom) and coherence (top) with sensitive accelerometer and exponential window for case 2.
Figure 7.44 Excitation (top) and response (bottom) with sensitive accelerometer and exponential window for case 3.
Figure 7.45 FRF (bottom) and coherence (top) with sensitive accelerometer and exponential window for case 3.
Figure 7.46 Comparison of hard tip and soft tip force spectrum.
Figure 7.47 FRF and coherence for hard tip.
Figure 7.48 FRF and coherence for soft tip.
Figure 7.49 Typical mode shapes shown with MAC comparing both sets of data collected.
Figure 7.50 Comparison of single and double force spectrum.
Figure 7.51 Mode shapes for structure.
Figure 7.52 Typical FRF for harder impact tip (left) and for softer tip (right).
Chapter 8: Shaker Testing Considerations
Figure 8.1 Typical shaker/amplifier configuration for experimental modal testing.
Figure 8.2 A typical modal shaker with trunnion (left) and a test setup with skewed excitation input (right).
Figure 8.3 Typical shaker measurement setup.
Figure 8.4 Good alignment (left) and bad alignment (right) for a shaker stinger attachment.
Figure 8.5 Stinger installation sequence: extend stinger (left), screw into force gage (middle), tighten lock nuts (right).
Figure 8.6 Stinger attachment: last step after structure setup and instrumentation attached.
Figure 8.7 Shaker settling: initial setup (left) and sag in system after several hours (right).
Figure 8.8 Structure shaker misalignment requiring shaker adjustment.
Figure 8.9 Correct force gage configuration (left) and incorrect force gage orientation (right).
Source
: Image courtesy of PCB Piezotronics, Inc.
Figure 8.10 Incorrect orientation (left) and correct orientation right for measurement.
Figure 8.11 Resulting measurement with incorrect configuration (left) and correct measurement (right).
Figure 8.12 Comparison of FRF with: offset accelerometer (top left); accelerometer aligned as well as possible (lower left); impedance head (lower right).
Figure 8.13 A typical shaker measurement setup with stinger.
Source
: Image courtesy of PCB Piezotronics, Inc.
Figure 8.14 FRF with short stinger.
Figure 8.15 FRF with longer stinger.
Figure 8.16 Stinger tuned absorber effect. Shapes not to scale and sketched to show expected effect of stinger rotational stiffness coupled to main structure.
Figure 8.17 Comparison FRF for different stinger lengths.
Figure 8.18 Reciprocity measurement between upper and lower SISO measurements.
Figure 8.19 Intentional stinger misalignment.
Figure 8.20 Poorly fabricated stinger assembly.
Figure 8.21 Four stinger lengths shown.
Figure 8.22 Stinger length comparisons.
Figure 8.23 Stinger type comparison.
Figure 8.24 Sleeved vs unsleeved stinger comparison.
Figure 8.25 MACL frame mode shapes.
Figure 8.26 Horizontal and vertical drive point measurements, showing the directional nature of the modes.
Figure 8.27 Skewed input excitation to overcome directional shape characteristics.
Figure 8.28 Skewed impedance measurement with geometry notation.
Figure 8.29 Laboratory structure with isolated components.
Figure 8.30 SISO vs MIMO FRF drive point measurement.
Figure 8.31 SISO vs MIMO FRF cross measurement.
Figure 8.32 Laboratory structure with isolated components.
Figure 8.33 FRF component (1) to frame (F) reference.
Figure 8.35 FRF frame (F) to frame (F) reference.
Figure 8.36 Close-up of several FRFs, showing inconsistency.
Figure 8.37 Laboratory structure with isolated components.
Figure 8.38 Stability diagram for combined SISO FRFs.
Figure 8.39 Stability diagram for three separate SISO tests.
Figure 8.40 Stability diagram for MIMO FRFs.
Chapter 9: Insight into Modal Parameter Estimation
Figure 9.1 SUM for 2 references and 15 accelerometers.
Figure 9.2 MMIF (left) and CMIF (right) for 2 references and 15 accelerometers.
Figure 9.3 Stability diagram for FRF data.
Figure 9.4 First six planar modes of MACL frame with a typical FRF measurement.
Figure 9.5 Three modes with distortion due to local curvefitting.
Figure 9.6 Composite spar structure and test geometry (left), summation function with single mode approximation (top), and two mode approximation (bottom).
Figure 9.7 Comparison of two large turbine blades.
Figure 9.8 Fit of data with obvious outlier.
Figure 9.9 Fit of data with outlier removed.
Figure 9.10 Set of fairly linear data.
Figure 9.11 Estimates of the slope for: (a) first order; (b) second order; (c) third order; (d) fourth order fit of data.
Figure 9.12 Typical stabilization diagram.
Figure 9.13 System transfer function and FRF.
Source
: Image courtesy Vibrant Technology, Inc.
Figure 9.14 Example of simple straight line fit.
Figure 9.15 Conceptual SDOF curvefit.
Figure 9.16 Conceptual MDOF curvefit.
Figure 9.17 Similar bands used for curvefitting for poles and residues.
Figure 9.18 One all encompassing band used for curvefitting for residues.
Figure 9.19 Band 1 fit data.
Figure 9.21 Band 3 fit data.
Figure 9.22 Modes (poles and residues) combined from band 1, band 2 and band 3, along with the lower residual from band 1 and upper residual from band 3 to synthesize the frequency response function.
Figure 9.23 RADARSAT1 test geometry.
Figure 9.24 Summation function and mode indicator function using all references along with stability diagram over the entire band.
Figure 9.25 Stability diagram for three different bandwidths using all references: (a) 12.6–20.6 Hz; (b) 36.7–40.6 Hz; (c) 44.1–48.1 Hz.
Figure 9.26 Typical synthesized FRF using all references.
Figure 9.27 MAC of modes using all references.
Figure 9.28 Modes of the RADARSAT1 satellite: first 25 modes of the structure.
Figure 9.29 Modal participation matrix of the RADARSAT1 satellite.
Figure 9.30 Summation function and mode indicator function using selected references.
Figure 9.31 Stability diagram for three different bands using selected references: (a) 12.6–20.6 Hz; (b) 36.7–40.6 Hz; (c) 44.1–48.1 Hz.
Figure 9.32 Typical synthesized FRF using selected references.
Figure 9.33 MAC of modes using selected references.
Figure 9.34 Multivariate mode indicator function and the complex mode indicator function using all references.
Figure 9.35 Stability diagram using PolyMAX and all references.
Figure 9.36 Selective synthesized frequency response functions.
Figure 9.37 MAC of modes using PolyMAX.
Figure 9.38 Stability diagram and first five modes of frame from a MIMO shaker test.
Figure 9.39 Stability diagram and first five modes of frame from an OMA spatially broad excitation with wide frequency band.
Figure 9.40 Stability diagram and two modes of frame from an OMA localized excitation with wide frequency band.
Figure 9.41 Stability diagram and five modes of frame from an OMA localized excitation complemented with additional shaker excitation with wide frequency band.
Chapter 10: General Considerations
Figure 10.1 Overview of analytical and experimental modal analysis.
Figure 10.2 Possible gear for portable testing.
Figure 10.3 Test lab portable chair/desk, ADC cart and large test situation.
Figure 10.4 Test setup with a “rats nest” of cabling.
Figure 10.5 Sample of three forms for a logbook (full size samples are shown at the end of the chapter).
Chapter 11: Tips, Tricks, and Other Stuff
Figure 11.1 Assortment of commercially available impact hammers. Image courtesy of PCB Piezotronics, Inc.
Figure 11.2 Small hammer configured with camera tripod.
Figure 11.3 Pendulous mass configuration.
Figure 11.4 MIMO test setup with two sets of measurement points.
Figure 11.5 MIF for data from first test.
Figure 11.6 Stability diagram for data from first test.
Figure 11.7 Typical curvefit from first test.
Figure 11.8 MIF for tests 1 and 2 combined.
Figure 11.9 Stability diagram for tests 1 and 2 combined.
Figure 11.10 Schematic planar beam modal test.
Figure 11.11 Schematic for 9 m wind turbine blade test.
Figure 11.12 Schematic for large wind turbine blade test.
Figure 11.13 Aerospace structure with FRFs and several modes.
Figure 11.14 Schematic depiction of measurement selection.
Figure 11.15 Extraction and synthesis of FRFs: (a) poor; (b) good.
Figure 11.16 Blue frame with three plates (top) with the test geometry (bottom).
Figure 11.17 The typical flexible modes for the blue frame with three plate subsystems.
Figure 11.18 Some possible reference points for the blue frame with three plates.
Figure 11.19 Typical test setups for shaker test and impact test with data acquisition system.
Figure 11.20 Reciprocity measurements: (a) between the red plate and the green plate; (b) between the red plate and the blue plate; (c) across the frame.
Figure 11.21 Stability diagram for blue frame with all references (top) and one reference (bottom).
Figure 11.22 MIMO test setup and results for MIMO configuration for shakers on frame.
Figure 11.23 Stability diagram from multiple-input, multiple-output test for blue frame structure.
Figure 11.24 MIMO test setup and results for MIMO configuration for shakers distributed on structure.
Figure 11.25 Test structure axis labels.
Figure 11.26 Frequency response function written on a mode by mode basis using the residue formulation and the mode shape formulation.
Appendix B: Example Using Two Degree of Freedom System: Eigenproblem
Figure B.1 2-DOF system.
Appendix C: Pole, Residue, and FRF Problem for 2-DOF System
Figure C.1 2-DOF system.
Figure C.2 D/F FRF (a), V/F (b), A/F (c) FRF for drive point H
11
FRF with real, imaginary, magnitude, phase, and Nyquist forms of the FRF.
Figure C.3 D/F FRF (a), V/F (b), A/F (c) FRF for H
21
cross FRF with real, imaginary, magnitude, phase, and Nyquist forms of the FRF.
Appendix D: Example using Three Degree of Freedom System
Figure D.1 3-DOF system.
Appendix E: DYNSYS Website Materials
Figure E.1 Website front page.
Figure E.2 The filemap page.
Appendix F: Basic Modal Analysis Information
Figure F.1 Damping estimates: (a) half power method; (b) log decrement method.
Figure F.2 System transfer function.
Figure F.3 Frequency response function.
Figure F.4 System transfer function/frequency response function/S-plane.
Figure F.5 FRF written in partial fraction form.
Appendix G: Repeated Root Frame: Boundary Condition Effects
Figure G.1 Rectangular frame with closely spaced (or pseudo-repeated) modes.
Figure G.2 Summation function for corner support modal test.
Figure G.3 MMIF function for corner support modal test.
Figure G.4 CMIF function for corner support modal test.
Figure G.5 Zoom for stability diagram for corner support modal test.
Figure G.6 Stability diagram for corner support modal test.
Figure G.7 Test locations with extracted frequencies for corner support modal test.
Figure G.8 Synthesized drive point FRF for corner support modal test.
Figure G.9 Summation function for midlength support modal test.
Figure G.10 CMIF function for midlength support modal test.
Figure G.11 Zoom for stability diagram for midlength support modal test.
Figure G.12 Stability diagram for midlength support modal test.
Figure G.13 Test locations with extracted frequencies for midlength support modal test.
Figure G.14 Synthesized drive point FRF for midlength support modal test.
Figure G.15 MAC Comparing the modal data from the two different boundary conditions.
Appendix H: Radarsat Satellite Testing
Figure H.1 Canadian Space Agency RADARSAT satellite mock up test: (a) photo; (b) test geometry.
Figure H.2 Summation function using all four references.
Figure H.3 Stability diagram using all four references.
Figure H.4 Modal data extracted using all four references.
Figure H.5 Synthesized drive point FRF using using all four references.
Figure H.6 Summation function using only two z and y references.
Figure H.7 MMIF function using only two z and y references.
Figure H.8 CMIF function using only two z and y references.
Figure H.9 Stability diagram using only two z and y references.
Figure H.10 Synthesis of drive point FRFs using only two z and y references.
Appendix I: Demo Airplane Testing
Figure I.1 Demo airplane modal test measurement points.
Figure I.2 Summation function for demo airplane impact data.
Figure I.3 MMIF function for demo airplane impact data.
Figure I.4 CMIF function for demo airplane impact data.
Figure I.5 Summation function for demo airplane impact data.
Figure I.6 Synthesis of drive point FRF for demo airplane impact data.
Figure I.7 Demo airplane modal test measurement points.
Figure I.8 Summation function for demo airplane skewed shaker data.
Figure I.9 MMIF function for demo airplane skewed shaker data.
Figure I.10 CMIF function for demo airplane skewed shaker data.
Figure I.11 Summation function for demo airplane skewed shaker data.
Figure I.12 Demo Airplane modal test measurement points.
Figure I.13 Summation function for demo airplane MIMO data.
Figure I.14 MMIF function for demo airplane MIMO data.
Figure I.15 CMIF function for demo airplane MIMO data.
Figure I.16 Summation function for demo airplane MIMO data.
Appendix J: Whirlpool Dryer Cabinet Modal Testing
Figure J.1 Whirlpool dryer cabinet: (a) photos; (b) test geometry.
Figure J.2 Whirlpool dryer cabinet test set up.
Figure J.3 Summation function using all four references.
Figure J.4 Stability diagram using all four references.
Figure J.5 Modal data extracted using all four references.
Appendix K: GM MTU Automobile Round Robin Modal Testing
Figure K.1 Typical automotive modal test setup.
Figure K.2 Summation function using all four references.
Figure K.3 Stability diagram using all four references.
Figure K.4 Modal data extracted using all four references.
Appendix L: UML Composite Spar Modal Testing
Figure L.1 Typical modal test set up.
Figure L.2 Summation function.
Figure L.3 Orthogonal polynomial fit for six modes.
Figure L.4 Orthogonal polynomial fit for 1 mode over 308 Hz to 352 Hz band.
Figure L.5 Orthogonal polynomial fit for 2 modes over 308–352 Hz band.
Figure L.6 Single mode and two mode extracted mode shapes.
Appendix M: UML BUH Modal Testing
Figure M.1 Typical BU modal test set up.
Figure M.2 Summation function using all seven references.
Figure M.3 CMIF using all seven references.
Figure M.4 Stability diagram using all seven references.
Figure M.5 Modal data extracted using all seven references.
Figure M.6 First twenty finite element mode shapes (for reference only).
List of Tables
Chapter 6: Test Setup Considerations
Table 6.1 Cross-MAC illustrating boundary condition effects
Table 6.2 Maximum channel voltage distribution
Chapter 7: Impact Testing Considerations
Table 7.1 MAC comparing reference data with “hybrid” data
Table 7.2 MAC comparing reference data with softer hammer tip data
Chapter 9: Insight into Modal Parameter Estimation
Table 9.1 Modal parameter comparison for SDOF polynomial curve-fit
Table 9.2 Modal parameter comparison for MDOF polynomial curve-fit
Table 9.3 MAC of MIMO modal test and operational modal test with spatially broad excitation
Table 9.4 MAC of MIMO modal test and operational modal test with localized excitation
Table 9.5 MAC of MIMO modal test and operational modal test with localized excitation
Chapter 10: General Considerations
Table 10.1 Checklist for necessary equipment for remote testing
Table 10.2 Typical equipment list for a sample modal test
Table 10.3 Channel/accelerometer information and channel voltage settings for impact test
Table 10.4 Initial spreadsheet showing measurements required
Table 10.5 Intermediate test spreadsheet showing measurements completed
Table 10.6 Final spreadsheet showing all measurements obtained
Table 10.7 Typical modal test report Table of contents
Modal Testing
A Practitioner's Guide
Peter Avitabile
University of Massachusetts Lowell, USA
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Preface
This is a book about experimental modal analysis. Yes…there are other text books on this subject but this one is different. Other books have deep theoretical developments that researchers and PhDs all relish but do not get to the core of what is needed, from a practical standpoint, to provide practitioners with the critical information needed to perform the day to day modal test and develop a model from measured data.
This book is really written for the novice, manager, engineer and technician; the novice that may come in any shape or form.
•
the newbie to modal testing and needs basics to get started
•
the engineer that has not been involved in experimental dynamic testing
•
the research/graduate student who has a need to make measurements and no one to guide them
•
the engineer in a small company that gets tasked to perform modal tests
•
the engineer promoted to fill the shoes of a well-seasoned modal test engineer who moves to management or retires
•
the manager who needs to understand basics to properly secure funding to support important projects
•
the engineer that needs to write test plans, conduct tests and extract useful information from data acquired
•
the technician who needs to acquire data that is useful for development of a model
•
for all to understand what each needs to do in order to be able to provide a model that can be used to evaluate systems, understand dynamic characteristics and solve complicated structural dynamic problems
While this book is not written to impress those well versed in modal analysis, many of the theoretical oriented folks will find very useful practical information regarding modal tests if they have never actually worked in a lab environment and have only developed theoretical approaches to solve these problems. But this text is also good for the graduate students who have research that has a need for experimental structural dynamic models to be developed but the PhD candidate is not focused on experimental modal analysis directly and his advisor is not familiar either – but there is a need for the PhD student to make meaningful measurements but not get bogged down with the intricate details of experimental modal analysis.
This book is also useful as a textbook for an undergraduate course to introduce very basic concepts necessary to perform an experimental modal test – possibly as a laboratory related class or as an addition to a vibrations class or for a graduate class on structural dynamics. This book definitely has sufficient material to be used as a first introduction to experimental modal analysis as an upper level undergraduate class or beginning graduate level class.
This book is meant to focus on the practical aspects of experimental modal analysis. Only limited theory is presented in the text in order to illustrate or expound upon certain methodologies of experimental modal testing that have their roots in the underlying theory. In many cases, the theory (or final equation of a long derivation) is just presented; this text is not about developing the details of the theory but rather applying the theory to solve real problems. There are an abundance of good textbooks in the area of vibrations but very few contain even a small piece of the content of this book. There are some textbooks on experimental modal analysis but most concentrate on the theoretical side of modal analysis assuming the implementation of a real test is easy and straightforward.
