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E-raamat: Modal Testing: A Practitioner's Guide

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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.

Preface xv
Part I: Overview of Experimental Modal Analysis using the Frequency Response Method 1(220)
1 Introduction to Experimental Modal Analysis: A Simple Non-mathematical Presentation
3(34)
1.1 Could you Explain Modal Analysis to Me?
6(4)
1.2 Just what are these Measurements called FRFs?
10(7)
1.2.1 Why is Only One Row or Column of the FRF Matrix Needed?
13(4)
1.3 What's the Difference between a Shaker Test and an Impact Test?
17(4)
1.3.1 What Measurements do we Actually make to Compute the FRF?
18(3)
1.4 What's the Most Important Thing to Think about when Impact Testing?
21(1)
1.5 What's the Most Important Thing to Think about when Shaker Testing?
22(2)
1.6 Tell me More About Windows; They Seem Pretty Important!
24(1)
1.7 So how do we get Mode Shapes from the Plate FRFs?
25(4)
1.8 Modal Data and Operating Data
29(7)
1.8.1 What is Operating Data?
29(4)
1.8.2 So what Good is Modal Data?
33(1)
1.8.3 So Should I Collect Modal Data or Operating Data?
34(2)
1.9 Closing Remarks
36(1)
2 General Theory of Experimental Modal Analysis
37(56)
2.1 Introduction
37(1)
2.2 Basic Modal Analysis Theory-SDOF
38(18)
2.2.1 Single Degree of Freedom System Equation
38(2)
2.2.2 Single Degree of Freedom System Response due to Harmonic Excitation
40(2)
2.2.3 Damping Estimation for Single Degree of Freedom System
42(1)
2.2.4 Response Assessment with Varying Damping
43(3)
2.2.5 Laplace Domain Approach for Single Degree of Freedom System
46(1)
2.2.6 System Transfer Function
47(1)
2.2.7 Different Forms of the Transfer Function
48(1)
2.2.8 Residue of the SDOF System
49(1)
2.2.9 Frequency Response Function for a Single Degree of Freedom System
49(2)
2.2.10 Transfer Function/Frequency Response Function/S-plane for a Single Degree of Freedom System
51(1)
2.2.11 Frequency Response Function Regions for a Single Degree of Freedom System
51(2)
2.2.12 Different Forms of the Frequency Response Function
53(1)
2.2.13 Complex Frequency Response Function
53(3)
2.3 Basic Modal Analysis Theory-MDOF
56(33)
2.3.1 Multiple Degree of Freedom System Equations
57(9)
2.3.2 Laplace Domain for Multiple Degree of Freedom System
66(2)
2.3.3 The Frequency Response Function
68(1)
2.3.4 Mode Shapes from Frequency Response Equations
68(3)
2.3.5 Point-to-Point Frequency Response Function
71(1)
2.3.6 Response of Multiple Degree of Freedom System to Harmonic Excitations
72(3)
2.3.7 Example: Cantilever Beam Model with Three Measured DOFs
75(8)
2.3.8 Summary of Time, Frequency, and Modal Domains
83(4)
2.3.9 Response due to Forced Excitation using Mode Superposition
87(2)
2.4 Summary
89(4)
3 General Signal Processing and Measurements Related to Experimental Modal Analysis
93(38)
3.1 Introduction
93(1)
3.2 Time and Frequency Domain
93(3)
3.3 Some General Information Regarding Data Acquisition
96(1)
3.4 Digitization of Time Signals
97(1)
3.5 Quantization
97(3)
3.5.1 ADC Underload
98(2)
3.5.2 ADC Overload
100(1)
3.6 AC Coupling
100(1)
3.7 Sampling Theory
101(2)
3.8 Aliasing
103(2)
3.9 What is the Fourier Transform?
105(4)
3.9.1 Fourier Transform and Discrete Fourier Transform
107(1)
3.9.2 FFT: Periodic Signal
108(1)
3.9.3 FFT: Non-periodic Signal
108(1)
3.10 Leakage and Minimization of Leakage
109(2)
3.10.1 Minimization of Leakage
111(1)
3.11 Windows and Leakage
111(8)
3.11.1 Rectangular Window
112(4)
3.11.2 Hanning Window
116(1)
3.11.3 Flat Top Window
116(1)
3.11.4 Comparison of Windows with Worst Leakage Distortion Possible
116(3)
3.11.5 Comparison of Rectangular, Hanning and Flat Top Window
119(1)
3.11.6 Force Window
119(1)
3.11.7 Exponential Window
119(1)
3.11.8 Convolution of the Window in the Frequency Domain
119(1)
3.12 Frequency Response Function Formulation
119(4)
3.13 Typical Measurements
123(3)
3.13.1 Time Signal and Auto-power Functions
123(1)
3.13.2 Typical Measurement: Cross Power Function
124(1)
3.13.3 Typical Measurement: Frequency Response Function
124(1)
3.13.4 Typical Measurement: Coherence Function
124(2)
3.14 Time and Frequency Relationship Definition
126(1)
3.15 Input-Output Model with Noise
127(2)
3.15.1 H1 Formulation: Output Noise Only
127(1)
3.15.2 H2 Formulation: Output Noise Only
128(1)
3.15.3 H1 Formulation: Input Noise Only
128(1)
3.15.4 H2 Formulation: Input Noise Only
128(1)
3.16 Summary
129(2)
4 Excitation Techniques
131(58)
4.1 Introduction
131(1)
4.2 Impact Excitation Technique
132(27)
4.2.1 Impact Hammer
132(4)
4.2.2 Hammer Impact Tip Selection
136(1)
4.2.3 Useful Frequency Range for Impact Excitation
137(1)
4.2.4 Force Window for Impact Excitation
137(1)
4.2.5 Pre-trigger Delay
137(3)
4.2.6 Double Impact
140(1)
4.2.7 Response due to Impact
140(3)
4.2.8 Roving Hammer vs Stationary Hammer and Reciprocity
143(4)
4.2.9 Impact Testing: an Example Set of Measurements
147(12)
4.3 Shaker Excitation
159(13)
4.3.1 Modal Shaker Setup
161(1)
4.3.2 Historical Development of Shaker Excitation Techniques
162(1)
4.3.3 Swept Sine Excitation
163(1)
4.3.4 Pure Random Excitation
163(2)
4.3.5 Pure Random Excitation with Windows Applied
165(1)
4.3.6 Pure Random Excitation with Overlap Processing
165(2)
4.3.7 Pseudo-random Excitation
167(1)
4.3.8 Periodic Random Excitation
167(1)
4.3.9 Burst Random Excitation
168(2)
4.3.10 Sine Chirp Excitation
170(1)
4.3.11 Digital Stepped Sine Excitation
170(2)
4.4 Comparison of Different Excitations for a Weldment Structure
172(3)
4.4.1 Random Excitation with No Window
172(1)
4.4.2 Random Excitation with Hanning Window
173(1)
4.4.3 Burst Random Excitation with No Window
173(1)
4.4.4 Sine Chirp Excitation with No Window
174(1)
4.4.5 Comparison of Random, Burst Random and Sine Chirp
175(1)
4.4.6 Comparison of Random and Burst Random at Resonant Peaks
175(1)
4.4.7 Linearity Check Using Sine Chirp
175(1)
4.5 Multiple-Input, Multiple-Output Measurement
175(12)
4.5.1 Multiple Input vs Single Input Testing
177(4)
4.5.2 Multiple Input vs Single Input for a Weldment Structure
181(1)
4.5.3 Multiple Input vs Single Input Testing
181(1)
4.5.4 Comparison of Multiple Input and Single Input for Weldment Structure
182(1)
4.5.5 MIMO Measurements on a Multi-component Structure
182(5)
4.6 Summary
187(2)
5 Modal Parameter Estimation Techniques 1S
S9
5.1 Introduction
189(1)
5.2 Experimental Modal Analysis
190(8)
5.2.1 Least Squares Approximation of Data
190(3)
5.2.2 Classification of Modal Parameter Estimation Techniques
193(5)
5.3 Extraction of Modal Parameters
198(8)
5.3.1 Peak Picking Technique
198(1)
5.3.2 Circle Fitting-Kennedy and Pancu
199(1)
5.3.3 SD OF Polynomial
200(1)
5.3.4 Residual Effects of Out of Band Modes
200(1)
5.3.5 MDOF Polynomial
201(1)
5.3.6 Least Squares Complex Exponential
201(2)
5.3.7 Advanced Forms of Time and Frequency Domain Estimators
203(1)
5.3.8 General Time Domain Techniques
203(1)
5.3.9 General Frequency Domain Techniques
203(1)
5.3.10 General Consideration for Time vs Frequency Representation
204(1)
5.3.11 Additional Remarks on Modal Parameter Estimation
204(1)
5.3.12 Two Step Process for Modal Parameter Estimation
205(1)
5.4 Mode Identification Tools
206(6)
5.4.1 Summation Function
206(1)
5.4.2 Mode Indicator Function
206(1)
5.4.3 Complex Mode Indicator Function
207(1)
5.4.4 Stability Diagram
208(2)
5.4.5 PolyMAX
210(2)
5.5 Modal Model Validation Tools
212(4)
5.5.1 Synthesis of Frequency Response Functions using Extracted Parameters
212(1)
5.5.2 Modal Assurance Criterion
213(2)
5.5.3 Mode Participation Factors
215(1)
5.5.4 Mode Overcomplexity
215(1)
5.5.5 Mean Phase Co-linearity and Mean Phase Deviation
216(1)
5.6 Operating Modal Analysis
216(3)
5.7 Summary
219(2)
Part II: Practical Considerations for Experimental Modal Testing 221(206)
6 Test Setup Considerations
223(24)
6.1 Test Plan?
224(1)
6.2 How Many Modes Required?
225(3)
6.3 Frequency Range of Interest?
228(4)
6.4 Transducer Possibilities?
232(1)
6.5 Test Configurations?
232(3)
6.6 How Many Measurement Points Needed?
235(3)
6.7 Excitation Techniques
238(1)
6.8 Miscellaneous Items to Consider
238(7)
6.9 Summary
245(2)
7 Impact Testing Considerations
247(46)
7.1 Hammer Impact Location
247(1)
7.2 Hammer Tip and Frequency Range
248(1)
7.3 Hammers for Different Size Structures
249(7)
7.4 How Does Impact Skew and Deviation of Input Point Affect the Measurement?
256(1)
7.4.1 Skewed Impact Force
256(1)
7.4.2 Inconsistent Impact Force Location
256(1)
7.5 Impact Hammer Frequency Bandwidth
256(8)
7.6 Accelerometer ICP Considerations for Low Frequency Measurements
264(1)
7.7 Considerations for Reciprocity Measurements
264(3)
7.8 Roving Hammer vs Roving Accelerometer
267(1)
7.9 Picking a Good Reference Location
268(1)
7.10 Multiple Impact Difficulties and Considerations
268(6)
7.10.1 Academic Structure
269(2)
7.10.2 Large Wind Turbine Blade
271(3)
7.11 What is "Filter Ring" during an Impact Measurement?
274(1)
7.12 Test Bandwidth Much Wider than Desired Frequency Range
275(4)
7.13 Why Does the Structure Response Need to Come to Zero at the End of the Sample Time?
279(3)
7.14 Measurements with no Overload but Transducers are Saturated
282(4)
7.14.1 Case 1: Sensitive Accelerometer with Exponential Window
282(1)
7.14.2 Case 2: Sensitive Accelerometer with No Window
283(1)
7.14.3 Case 3: Less Sensitive Accelerometer with No Window
283(3)
7.15 How much Roll Off in the Input Hammer Force Spectrum is Acceptable?
286(3)
7.16 Can the Hammer be Switched in the Middle of a Test to Avoid Double Impacts?
289(3)
7.17 Closing Remarks
292(1)
8 Shaker Testing Considerations
293(34)
8.1 General Hardware Related Issues
293(9)
8.1.1 General Information about Shakers and Amplifiers
293(1)
8.1.2 What is the Difference between the Constant Current and Constant Voltage Settings on the Shaker Amplifier?
294(1)
8.1.3 Some. Shakers have a Trunnion: Is it Really Needed and Why Do You Have It?
294(1)
8.1.4 Where is the Best Location to Place a Shaker for a Modal Test?
295(1)
8.1.5 How Should the Shaker be Constrained when Testing?
296(1)
8.1.6 What's the Best Way to Support a Shaker for Lateral Vibration When it is Hung?
296(1)
8.1.7 What are the Most Common Practical Failures with Shaker Setup?
297(1)
8.1.8 What is the Correct Level of Shaker Excitation for Modal Testing?
297(1)
8.1.9 How many Shakers should I use in my Modal Test?
297(1)
8.1.10 Shaker and Stinger Alignment Issues
297(1)
8.1.11 When should the Shaker be Attached to the Structure?
298(1)
8.1.12 Should I Disconnect the Stingers while not Testing?
298(2)
8.1.13 Force Gage or Impedance Head must be Mounted on Structure Side of Stinger?
300(1)
8.1.14 What's an Impedance Head? Why use it? Where does it go?
301(1)
8.2 Stinger Related Issues
302(12)
8.2.1 Why should Stingers be used?
302(1)
8.2.2 Can a Poorly Designed Shaker/Stinger Setup Produce Incorrect Results?
303(3)
8.2.3 Stingers and their Effect on Measured Frequency Response Functions
306(8)
8.2.3.1 Stinger Location
307(1)
8.2.3.2 Stinger Alignment
307(1)
8.2.3.3 Stinger Length
308(2)
8.2.3.4 Stinger Type
310(1)
8.2.3.5 Sleeved Stingers
310(4)
8.2.3.6 How do Piano Wire Stingers Work? How are they Pretensioned??
314(1)
8.3 Shaker Related Issues
314(11)
8.3.1 Is MIMO needed for Structures with Directional Modes?
314(2)
8.3.2 Shaker Force Levels and SISO vs MIMO Considerations
316(30)
8.3.2.1 High Shaker Force Levels
316(2)
8.3.2.2 High Shaker Force Levels
318(2)
8.3.2.3 Effects of FRF Measurements in the Modal Parameter Estimation Process
320(5)
8.4 Concluding Remarks
325(2)
9 Insight into Modal Parameter Estimation
327(38)
9.1 Introductory Remarks
327(1)
9.2 Mode Indicator Tools Help Identify Modes
328(2)
9.3 SDOF vs MDOF for a Simple System
330(2)
9.4 Local vs Global: MACL Frame
332(2)
9.5 Repeated Root: Composite Spar
334(1)
9.6 Wind Turbine Blade: Same Geometry but Very Different Modes
335(2)
9.7 Stability Diagram Demystified
337(3)
9.8 Curvefitting Demystified
340(3)
9.9 Curvefitting Different Bands for the Poles and Residues
343(1)
9.10 Synthesizing the FRF from Parameters from Several Bands Stitched Together
344(2)
9.11 A Large Multiple Reference Modal Test Parameter Estimation
346(11)
9.11.1 Case 1: Use of All Measured FRFs
346(4)
9.11.2 Case 2: Use of Selected Sets of Measured FRFs
350(2)
9.11.3 Case 3: Use of PolyMAX
352(5)
9.12 Operating Modal Analysis
357(6)
9.13 Concluding Remarks
363(2)
10 General Considerations
365(30)
10.1 An Experimental Modal Test: a Thought Process Divulged
369(8)
10.2 FFT Analyzer Setup
377(2)
10.2.1 General FFT Analyzer Setup
377(1)
10.2.2 Setup for Impact Testing
378(1)
10.2.3 Setup for Shaker Testing
379(1)
10.3 Log Sheets
379(1)
10.4 Practical Considerations: Checklists
379(13)
10.4.1 Checklist for Analyzer Setup
380(2)
10.4.2 Checklist for Impact Testing
382(2)
10.4.3 Checklist for Shaker Testing
384(2)
10.4.4 Checklist for Measurement Adequacy
386(2)
10.4.5 Checklist for Miscellaneous
388(4)
10.5 Summary 391 Appendix: Logbook Forms
392(3)
11 Tips, Tricks, and Other Stuff
395(32)
11.1 Modal Testing Primer
396(4)
11.1.1 Impact Setup
396(1)
11.1.2 Shaker Setup
397(1)
11.1.3 Drive Point Measurements
398(1)
11.1.4 Reciprocity
398(1)
11.1.5 Inappropriate Reference Location
399(1)
11.1.6 Multiple-input, Multiple-output Testing
399(1)
11.1.7 Multiple Reference Testing
400(1)
11.2 Impact Hammer and Impulsive Excitation
400(3)
11.2.1 The Right Hammer for the Test
400(1)
11.2.2 Hammer-Get the Swing of it
401(1)
11.2.3 Hammer Tripod
401(1)
11.2.4 Hammer tip selection
401(1)
11.2.5 No Hammer: Improvise
402(1)
11.2.6 Pete's Hammer Test Impact Ritual
402(1)
11.3 Accelerometer Issues
403(8)
11.3.1 Mass Loading
403(1)
11.3.2 Mass Loading Effects from Tri-axial Accelerometers
404(3)
11.3.3 Accelerometer Sensitivity Selection
407(1)
11.3.4 Tri-axial Accelerometers
408(3)
11.4 Curvefitting Considerations
411(3)
11.4.1 Should all Measurements be used when Curvefitting
412(2)
11.5 Blue Frame with Three Plate Subsystem
414(8)
11.6 Miscellaneous Issues
422(3)
11.6.1 Modal Test Axis Labels
422(1)
11.6.2 Testing Does Not Need to Start at point 1
423(1)
11.6.3 Test to a Wider Frequency Range
423(1)
11.6.4 U1 times Uj; the key to many questions
423(2)
11.7 Summary
425(2)
A Linear Algebra: Basic Operations Needed for Modal Analysis Operations 427(6)
A.1 Define a Matrix
427(1)
A.2 Define a Column Vector
427(1)
A.3 Define a Row Vector
428(1)
A.4 Define a Diagonal Matrix
428(1)
A.5 Define Matrix Addition
428(1)
A.6 Define Matrix Scalar Multiply
428(1)
A.7 Define Matrix Multiply
429(1)
A.8 Matrix Multiplication Rules
429(1)
A.9 Transpose of a Matrix
430(1)
A.10 Transposition Rules
430(1)
A.11 Symmetric Matrix Rules
430(1)
A.12 Define a Matrix Inverse
431(1)
A.13 Matrix Inverse Properties
431(1)
A.14 Define an Eigenvalue Problem
431(1)
A.15 Generalized Inverse
431(1)
A.16 Singular Value Decomposition
432(1)
B Example Using Two Degree of Freedom System: Eigenproblem 433(4)
C Pole, Residue, and FRF Problem for 2-DOF System 437(6)
D Example using Three Degree of Freedom System 443(8)
E DYNSYS Website Materials 451(12)
E.1 Technical Materials Developed
451(2)
E.1.1 Theoretical Aspects of First and Second Order Systems
452(1)
E.1.2 First Order Systems: Modeling Step with ODE and Block Diagram
452(1)
E.1.3 Second Order Systems: Modeling Step, Impulse, IC with ODE and Block Diagram
452(1)
E.1.4 Mathematical Modeling Considerations
452(1)
E.1.5 Simulink and MATLAB Primer Materials
453(1)
E.1.6 Miscellaneous Materials
453(1)
E.2 DYNSYS.UML.EDU Website
453(10)
F Basic Modal Analysis Information 463(4)
F.1 SDOF Definitions
463(3)
F.1.1 Damping Estimates
463(1)
F.1.2 System Transfer Function
464(1)
F.1.3 Different Forms of the System Transfer Function
464(1)
F.1.4 Frequency Response Function
465(1)
F.2 MDOF Definitions
466(1)
Part III: Collection of Sets of Modal Data Collected for Processing 467(52)
G Repeated Root Frame: Boundary Condition Effects
469(10)
G.1 Corner Supports Set #1
470(4)
G.2 Midlength Supports Set #2
474(1)
G.3 Modal Correlation between Set #1 and Set #2
474(5)
H Radarsat Satellite Testing
479(8)
H.1 Data Reduction Set 1: Reference BUS:109:Z, BUS:118:Z, PMS:217:X and PMS:1211:Y
479(1)
H.2 Data Reduction Set 2: Reference PMS:217:X and PMS:1211:Y
479(8)
I Demo Airplane Testing
487(10)
I.1 Impact Testing
487(1)
I.2 SIMO Testing with Skewed Shaker
487(6)
I.3 MIMO Testing with Two Vertical Modal Shakers
493(4)
J Whirlpool Dryer Cabinet Modal Testing
497(4)
K GM MTU Automobile Round Robin Modal Testing
501(4)
L UML Composite Spar Modal Testing
505(4)
M UML BUR Modal Testing
509(6)
N Nomenclature
515(4)
Index 519
PETER AVITABILE is Professor Emeritus at the University of Massachusetts Lowell, the co-director of the Structural Dynamics and Acoustic Systems Laboratory, and the former President for the Society for Experimental Mechanics. In addition, he is the Associate Editor of the Handbook for Experimental Structural Mechanics. He has written hundreds of papers and articles on analytical and experimental modal analysis techniques, including the Modal Space article series published in SEM's Experimental Techniques.
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