Virtual Experiments in Mechanical Vibrations: Structural Dynamics and Signal Processing

Cover
Title Page
Copyright
Contents
Preface
List of Abbreviations
List of Symbols
About the Companion Website
Chapter 1 Introduction
	1.1 Introduction
	1.2 Typical Laboratory‐Based Vibration Tests
	1.3 Relationship Between the Input and Output for a SISO System
	1.4 A Virtual Vibration Test
	1.5 Some Notes on the Book
	References
Chapter 2 Fundamentals of Vibration
	2.1 Introduction
	2.2 Basic Concepts – Mass, Stiffness, and Damping
	2.3 Single Degree‐of‐Freedom System
	2.4 Free Vibration
	2.5 Impulse Response Function (IRF)
	Results
	Comments
	2.6 Determination of Damping from Free Vibration
	Results
	Comments
	2.7 Harmonic Excitation
	2.8 Frequency Response Function (FRF)
	Results
	Comments
	2.9 Other Features of the Receptance FRF
	2.10 Determination of Damping from an FRF
	Results
	Comments
	2.11 Reciprocal FRF
	Results
	Comments
	2.12 Summary
	References
Chapter 3 Fourier Analysis
	3.1 Introduction
	3.2 The Fourier Transform (FT)
		3.2.1 Example – SDOF system
	3.3 The Discrete Time Fourier Transform (DTFT)
	3.4 The Discrete Fourier Transform (DFT)
	Results
	Comments:
	3.5 Inverse Fourier Transforms
	Results
	Comments:
	3.6 Summary
	References
Chapter 4 Numerical Computation of the FRFs and IRFs of an SDOF System
	4.1 Introduction
	4.2 Effect of Sampling on the FRFs
		4.2.1 Receptance
	Results
	Comments
		4.2.2 Mobility
	Results
	Comments
		4.2.3 Accelerance
	Results
	Comments
	4.3 Effect of Data Truncation
	Results
	Comments
	Results
	Comments
	4.4 Effects of Sampling on the IRFs Calculated Using the IDFT
	Results
	Comments
	4.5 Summary
	References
Chapter 5 Vibration Excitation
	5.1 Introduction
	5.2 Vibration Excitation Devices
		5.2.1 Electrodynamic Shaker
		5.2.2 Instrumented Impact Hammer
	5.3 Vibration Excitation Signals
		5.3.1 Excitation at a Single Frequency
	Results
	Comments
		5.3.2 Excitation Using a Random Signal
	Results
	Comments
		5.3.3 Excitation Using a Chirp or Swept Sine
	Results
	Comments
		5.3.4 Excitation Using a Half‐Sine Pulse
	Results
	Comments
	5.4 Summary
	References
Chapter 6 Determination of the Vibration Response of a System
	6.1 Introduction
	6.2 Determination of the Vibration Response
		6.2.1 Convolution in the Time Domain
		6.2.2 Calculation of the Response via the Frequency Domain
		6.2.3 Numerical Integration of the Equation of Motion
	6.3 Calculation of the Vibration Response of an SDOF System
		6.3.1 Impulsive Force
		6.3.2 Half‐sine Force Impulse
		6.3.3 Chirp (Swept Sine) Force Input
		6.3.4 Random Force Input
	Results
		6.3.4 Example 6.1a
		6.3.4 Example 6.1b
		6.3.4 Example 6.1c
		6.3.4 Example 6.1d
	Comments:
	6.4 Summary
	References
Chapter 7 Frequency Response Function (FRF) Estimation
	7.1 Introduction
	7.2 Transient Excitation
		7.2.1 H1 and H2 Estimators
		7.2.2 Coherence Function
		7.2.3 Examples
	Results
	Comments:
	7.3 Random Excitation
	Results
	Comments:
	7.4 Comparison of Excitation Methods and Effects of Shaker–Structure Interaction
	Results
	Comments:
	7.5 Virtual Experiment – Vibration Isolation
		7.5.1 The Physics of Vibration Isolation
		7.5.2 Experimental Determination of the Stiffness and Damping of a Vibration Isolator
	Results
	Comments:
		7.5.3 Experiment to Investigate the Trade‐off Between Decreasing the Response at the Resonance Frequency and Improving Vibration Isolation
	Results
	Comments:
	7.6 Summary
	References
Chapter 8 Multi‐Degree‐of‐Freedom (MDOF) Systems: Dynamic Behaviour
	8.1 Introduction
	8.2 Lumped Parameter MDOF System
		8.2.1 Example – 3DOF System
	Results
	Comments:
		8.2.2 Free Vibration
	Results
	Comment:
		8.2.3 Resonance and Anti‐resonance Frequencies
	Results
	Comments:
		8.2.4 Modal Decomposition
	Results
	Comments:
		8.2.5 Impulse Response Function (IRF)
	Results
	Comments:
	8.3 Continuous Systems
		8.3.1 Rod
			8.3.1.1 Natural Frequencies and Mode Shapes
			8.3.1.2 Impulse Response Function (IRF)
	Results
	Comments:
		8.3.2 Beam
			8.3.2.1 Natural Frequencies and Mode Shapes
			8.3.2.2 Impulse Response Function (IRF)
	Results
	Comments:
	8.4 Summary
	References
Chapter 9 Multi‐Degree‐of‐Freedom (MDOF) Systems: Virtual Experiments
	9.1 Introduction
	9.2 Two Degree‐of‐Freedom System: FRF Estimation
	Results
	Comments:
		9.2.1 Determination of a Modal Model
	Results
	Comments:
	9.3 Beam: FRF Estimation
	Results
	Comments:
		9.3.1 Determination of a Modal Model
	Results
	Comments:
	9.4 The Vibration Absorber as a Vibration Control Device
		9.4.1 Theory
		9.4.2 Effect of a Vibration Absorber on an SDOF System
		9.4.3 Vibration Absorber Attached to an SDOF System – Virtual Experiment
	Results
	Comments:
	Results
	Comments:
	Results
	Comments:
		9.4.4 Vibration Absorber Attached to a Cantilever Beam – Virtual Experiment
	Results
	Comments:
	9.5 Summary
	References
Appendix A Numerical Differentiation and Integration
	A.1 Differentiation in the Time Domain
	A.2 Integration in the Time Domain
	Results
	Comments:
	A.3 Differentiation and Integration in the Frequency Domain
	Reference
Appendix B The Hilbert Transform
Appendix C The Decibel: A Brief Description
Appendix D Numerical Integration of Equations of Motion
	D.1 Euler's Method
	D.2 The Runge–Kutta Method
	Results
	Comments
	References
Appendix E The Delta Function
	E.1 Properties of the Delta Function
	E.2 Fourier Series Representation of a Train of Delta Functions
	Reference
Appendix F Aliasing
Appendix G Convolution
	Results
	Comments:
	G.1 Relationship Between Convolution and Multiplication
	Results
	Comments:
	G.2 Circular Convolution
	Results
	Comments:
	References
Appendix H Some Influential Scientists in Topics Related to This Book
Index
EULA