Virtual Experiments in Mechanical Vibrations: Structural Dynamics and Signal Processing

✍ Scribed by Bin Tang, Michael J. Brennan

• Publisher: Wiley
• Year: 2022
• Tongue: English
• Leaves: 339
• Category: Library

✦ Synopsis

VIRTUAL EXPERIMENTS in MECHANICAL VIBRATIONS

The first book of its kind to explain fundamental concepts in both vibrations and signal processing using MATLAB virtual experiments

Students and young engineers with a strong grounding in engineering theory often lack the practical skills and knowledge required to carry out experimental work in the laboratory. Fundamental and time-consuming errors can be avoided with the appropriate training and a solid understanding of basic concepts in vibrations and/or signal processing, which are critical to testing new designs.

Virtual Experiments in Mechanical Vibrations: Structural Dynamics and Signal Processing is designed for readers with limited knowledge of vibrations and signal processing. The intention is to help them relate vibration theory to measurements carried out in the laboratory. With a hands-on approach that emphasizes physics rather than mathematics, this practical resource explains fundamental concepts in vibrations and signal processing. It uses the concept of a virtual experiment together with MATLAB to show how the dynamic properties of vibration isolators can be determined, how vibration absorbers can be designed, and how they perform on distributed parameter structures.

Readers will find that this text:

• Allows the concepts of experimental work to be discussed and simulated in the classroom using a physics-based approach
• Presents computational virtual experiments using MATLAB examples to determine the dynamic behaviour of several common dynamic systems
• Explains the rationale of virtual experimentation and describes typical vibration testing setups
• Introduces the signal processing tools needed to determine the frequency response of a system from input and output data
• Includes access to a companion website containing MATLAB code

Virtual Experiments in Mechanical Vibrations: Structural Dynamics and Signal Processing is a must-have resource for researchers, mechanical engineers, and advanced undergraduate and graduate students who are new to the subjects of vibrations, signal processing, and vibration testing. It is also an invaluable tool for universities where the possibilities of doing experimental work are limited.

✦ Table of Contents

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