Modal testing : a practitioner's guide

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. 3.13.3 Typical Measurement: Frequency Response Function -- 3.13.4 Typical Measurement: Coherence Function -- 3.14 Time and Frequency Relationship Definition -- 3.15 Input-Output Model with Noise -- 3.15.1 H1 Formulation: Output Noise Only -- 3.15.2 H2 Formulation: Output Noise Only -- 3.15.3 H1 Formulation: Input Noise Only -- 3.15.4 H2 Formulation: Input Noise Only -- 3.16 Summary -- Chapter 4 Excitation Techniques -- 4.1 Introduction -- 4.2 Impact Excitation Technique -- 4.2.1 Impact Hammer -- 4.2.2 Hammer Impact Tip Selection -- 4.2.3 Useful Frequency Range for Impact Excitation -- 4.2.4 Force Window for Impact Excitation -- 4.2.5 Pre-trigger Delay -- 4.2.6 Double Impact -- 4.2.7 Response due to Impact -- 4.2.8 Roving Hammer vs Stationary Hammer and Reciprocity -- 4.2.9 Impact Testing: an Example Set of Measurements -- 4.3 Shaker Excitation -- 4.3.1 Modal Shaker Setup -- 4.3.2 Historical Development of Shaker Excitation Techniques -- 4.3.3 Swept Sine Excitation -- 4.3.4 Pure Random Excitation -- 4.3.5 Pure Random Excitation with Windows Applied -- 4.3.6 Pure Random Excitation with Overlap Processing -- 4.3.7 Pseudo-random Excitation -- 4.3.8 Periodic Random Excitation -- 4.3.9 Burst Random Excitation -- 4.3.10 Sine Chirp Excitation -- 4.3.11 Digital Stepped Sine Excitation -- 4.4 Comparison of Different Excitations for a Weldment Structure -- 4.4.1 Random Excitation with No Window -- 4.4.2 Random Excitation with Hanning Window -- 4.4.3 Burst Random Excitation with No Window -- 4.4.4 Sine Chirp Excitation with No Window -- 4.4.5 Comparison of Random, Burst Random and Sine Chirp -- 4.4.6 Comparison of Random and Burst Random at Resonant Peaks -- 4.4.7 Linearity Check Using Sine Chirp -- 4.5 Multiple-input, Multiple-output Measurement -- 4.5.1 Multiple Input vs Single Input Testing -- 4.5.2 Multiple Input vs Single Input for a Weldment Structure 4.5.3 Multiple Input vs Single Input Testing -- 4.5.4 Comparison of Multiple Input and Single Input for Weldment Structure -- 4.5.5 MIMO Measurements on a Multi-component Structure -- 4.6 Summary -- Chapter 5 Modal Parameter Estimation Techniques -- 5.1 Introduction -- 5.2 Experimental Modal Analysis -- 5.2.1 Least Squares Approximation of Data -- 5.2.2 Classification of Modal Parameter Estimation Techniques -- 5.3 Extraction of Modal Parameters -- 5.3.1 Peak Picking Technique -- 5.3.2 Circle Fitting - Kennedy and Pancu -- 5.3.3 SDOF Polynomial -- 5.3.4 Residual Effects of Out of Band Modes -- 5.3.5 MDOF Polynomial -- 5.3.6 Least Squares Complex Exponential -- 5.3.7 Advanced Forms of Time and Frequency Domain Estimators -- 5.3.8 General Time Domain Techniques -- 5.3.9 General Frequency Domain Techniques -- 5.3.10 General Consideration for Time vs Frequency Representation -- 5.3.11 Additional Remarks on Modal Parameter Estimation -- 5.3.12 Two Step Process for Modal Parameter Estimation -- 5.4 Mode Identification Tools -- 5.4.1 Summation Function -- 5.4.2 Mode Indicator Function -- 5.4.3 Complex Mode Indicator Function -- 5.4.4 Stability Diagram -- 5.4.5 PolyMAX -- 5.5 Modal Model Validation Tools -- 5.5.1 Synthesis of Frequency Response Functions using Extracted Parameters -- 5.5.2 Modal Assurance Criterion -- 5.5.3 Mode Participation Factors -- 5.5.4 Mode Overcomplexity -- 5.5.5 Mean Phase Co-linearity and Mean Phase Deviation -- 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 Cover -- Title Page -- Copyright -- Dedication -- Contents -- Preface -- About the CompanionWebsite -- 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? -- 1.2.1 Why is Only One Row or Column of the FRF Matrix Needed? -- 1.3 What's the Difference between a Shaker Test and an Impact Test? -- 1.3.1 What Measurements do we Actually make to Compute the FRF? -- 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 -- 1.8.1 What is Operating Data? -- 1.8.2 So what Good is Modal Data? -- 1.8.3 So Should I Collect Modal Data or Operating Data? -- 1.9 Closing Remarks -- Chapter 2 General Theory of Experimental Modal Analysis -- 2.1 Introduction -- 2.2 Basic Modal Analysis Theory - SDOF -- 2.2.1 Single Degree of Freedom System Equation -- 2.2.2 Single Degree of Freedom System Response due to Harmonic Excitation -- 2.2.3 Damping Estimation for Single Degree of Freedom System -- 2.2.4 Response Assessment with Varying Damping -- 2.2.5 Laplace Domain Approach for Single Degree of Freedom System -- 2.2.6 System Transfer Function -- 2.2.7 Different Forms of the Transfer Function -- 2.2.8 Residue of the SDOF System -- 2.2.9 Frequency Response Function for a Single Degree of Freedom System -- 2.2.10 Transfer Function/Frequency Response Function/S-plane for a Single Degree of Freedom System -- 2.2.11 Frequency Response Function Regions for a Single Degree of Freedom System 2.2.12 Different Forms of the Frequency Response Function -- 2.2.13 Complex Frequency Response Function -- 2.3 Basic Modal Analysis Theory - MDOF -- 2.3.1 Multiple Degree of Freedom System Equations -- 2.3.2 Laplace Domain for Multiple Degree of Freedom System -- 2.3.3 The Frequency Response Function -- 2.3.4 Mode Shapes from Frequency Response Equations -- 2.3.5 Point-to-Point Frequency Response Function -- 2.3.6 Response of Multiple Degree of Freedom System to Harmonic Excitations -- 2.3.7 Example: Cantilever Beam Model with Three Measured DOFs -- 2.3.8 Summary of Time, Frequency, and Modal Domains -- 2.3.9 Response due to Forced Excitation using Mode Superposition -- 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 -- 3.5.1 ADC Underload -- 3.5.2 ADC Overload -- 3.6 AC Coupling -- 3.7 Sampling Theory -- 3.8 Aliasing -- 3.9 What is the Fourier Transform? -- 3.9.1 Fourier Transform and Discrete Fourier Transform -- 3.9.2 FFT: Periodic Signal -- 3.9.3 FFT: Non-periodic Signal -- 3.10 Leakage and Minimization of Leakage -- 3.10.1 Minimization of Leakage -- 3.11 Windows and Leakage -- 3.11.1 Rectangular Window -- 3.11.2 Hanning Window -- 3.11.3 Flat Top Window -- 3.11.4 Comparison of Windows with Worst Leakage Distortion Possible -- 3.11.5 Comparison of Rectangular, Hanning and Flat Top Window -- 3.11.6 Force Window -- 3.11.7 Exponential Window -- 3.11.8 Convolution of the Window in the Frequency Domain -- 3.12 Frequency Response Function Formulation -- 3.13 Typical Measurements -- 3.13.1 Time Signal and Auto-power Functions -- 3.13.2 Typical Measurement: Cross Power Function 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? -- 7.4.1 Skewed Impact Force -- 7.4.2 Inconsistent Impact Force Location -- 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 -- 7.10.1 Academic Structure -- 7.10.2 Large Wind Turbine Blade -- 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 -- 7.14.1 Case 1: Sensitive Accelerometer with Exponential Window -- 7.14.2 Case 2: Sensitive Accelerometer with No Window -- 7.14.3 Case 3: Less Sensitive Accelerometer with No Window -- 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 -- 8.1.1 General Information about Shakers and Amplifiers -- 8.1.2 What is the Difference between the Constant Current and Constant Voltage Settings on the Shaker Amplifier? -- 8.1.3 Some Shakers have a Trunnion: Is it Really Needed and Why Do You Have It? -- 8.1.4 Where is the Best Location to Place a Shaker for a Modal Test? -- 8.1.5 How Should the Shaker be Constrained when Testing? The practical, clear, and concise guide for conducting experimental modal tests Modal Testing: A Practitioner's Guid e 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. Taking a hands-on approach, this practical, clear, and concise guide explores the issues related to conducting a test from start to finish and covers the cornerstones of the basic information needed while summarizing all the pertinent theory rel 8.1.6 What's the Best Way to Support a Shaker for Lateral Vibration When it is Hung?