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Summary
Summary
Vibration Testing: Theory and Practice, Second Edition is a step-by-step guide that shows how to obtain meaningful experimental results via the proper use of modern instrumentation, vibration exciters, and signal-processing equipment, with particular emphasis on how different types of signals are processed with a frequency analyzer. Thoroughly updated, this new edition covers all basic concepts and principles underlying dynamic testing, explains how current instruments and methods operate within the dynamic environment, and describes their behavior in a number of commonly encountered field and laboratory test situations.
Author Notes
KENNETH G. McCONNELL, PE , is Professor Emeritus, Aerospace Engineering and Engineering Mechanics, Iowa State University, and has over forty-three years' experience in vibrations and experimental mechanics. He is a Fellow of the Society of Experimental Mechanics, and recipient of SEM's M.M. Frocht Award for "outstanding achievement as an experimental mechanics educator"; SEM's highest award, the William M. Murray Lecturer, for his "outstanding contribution to SEM in the fields of dynamic instrumentation, vibration testing techniques, and fluid structure interaction"; the D.J. DeMichele Award for "promoting the scientific and educational aspects of modal analysis"; and the Brewer Award, "in recognition of his contributions as an outstanding practicing experimental stress analyst." He is the author of Instrumentation for Engineering Measurements , Second Edition (coauthored with James E. Dally and William F Riley and published by Wiley) and other books in the field.
PAULO S. VAROTO is professor on Dynamics and Vibrations at the Mechanical Engineering Department, School of Engineering of São Carlos, University of São Paulo. Professor Varoto earned his BSc and MSc in mechanical engineering from the University of São Paulo and holds a PhD in engineering mechanics from the Department of Aerospace Engineering and Engineering Mechanics, Iowa State University, where he worked under the supervision of Ken McConnell.
Table of Contents
| Chapter 1 An Overview Of Vibration Testing |
| 1.1 Introduction |
| 1.2 Preliminary Considerations |
| 1.3 General Input/Output Relationships in the Frequency Domain |
| 1.4 Overview of Equipment Employed |
| 1.5 Summary |
| Chapter 2 Dynamic Signal Analysis |
| 2.1 Introduction |
| 2.1.1 Signal Classification |
| 2.1.2 Temporal Mean Value |
| 2.1.3 Temporal Mean Square and Temporal Root Mean Square |
| 2.1.4 The Frequency Spectrum |
| 2.1.5 Analysis of a Single Sinusoid |
| 2.2 Phasor Representation of Periodic Functions |
| 2.2.1 The Phasor |
| 2.2.2 The Phasor and Real-Valued Sinusoids |
| 2.3 Periodic Time Histories |
| 2.3.1 Periodic Fourier Series |
| 2.3.2 The Mean, Mean Square, and Parseval's Formula |
| 2.3.3 Analysis of a Square Wave |
| 2.4 Transient Signal Analysis |
| 2.4.1 Difference Between Periodic and Transient Frequency Analysis |
| 2.4.2 The Transient Fourier Transform |
| 2.4.3 Transient Mean, Mean Square, And Parseval's Formula |
| 2.5 Correlation Concepts - A Statistical Point of View |
| 2.6 Correlation Concepts - Periodic Time-Histories |
| 2.6.1 Cross-Correlation |
| 2.6.2 Auto-Correlation |
| 2.7 Correlation Concepts - Transient Time-Histories |
| 2.7.1 Cross-Correlation |
| 2.7.2 Auto-Correlation |
| 2.8 C rrelation Concepts - Random Time Histories |
| 2.8.1 Auto-Correlation and Auto-Spectral Density |
| 2.8.3 Correlation and Spectral Densities of Multiple Random Processes |
| 2.8.4 Statistical Distributions |
| 2.9 Summary |
| 2.10 General References on Signal Analysis.References |
| Chapter 3 Vibration Concepts |
| 3.1 Introduction |
| 3.2 The Single DOF Model |
| 3.2.1 Equation of Motion |
| 3.2.2 Free Undamped Vibration |
| 3.2.3 Free Damped Vibration |
| 3.2.4 Structure Orientation and Natural Frequency |
| 3.3 Single Degree of Freedom Forced Response |
| 3.3.1 The Viscous Damping Case |
| 3.3.2 Common Frfs |
| 3.3.3 Damping Models in Forced Response |
| 3.3.4 The Structural Damping Response |
| 3.3.5 The Bode Diagram |
| 3.3.6 Real & Imaginary Plots and Nyquist Diagrams |
| 3.4 General Input-Output Model for Linear Systems |
| 3.4.1 The Frequency-Domain (Fourier Transform) Approach |
| 3.4.2 The Time-Domain Impulse Response Approach |
| 3.4.3 Receptance Frf Vs Impulse Response Function |
| 3.4.4 Random Input-Output Relationships |
| 3.4.5 Shock Response Spectra |
| 3.5 The Two Degree of Freedom Vibration Model |
| 3.5.1 Equations of Motion |
| 3.5.2 Undamped Natural Frequencies and Mode Shapes |
| 3.5.3 Steady State Forced Vibration Response (Direct Method) |
| 3.5.4 Steady State Forced Response (Modal Method) |
| 3.5.5 Comparison of Direct and Modal Response FRFs |
| 3.6 The Second Order Continuous Vibration Model |
| 3.6.1 The Fundamental Equation of Motion |
| 3.6.2 Separation of Space and Time Variables |
| 3.6.3 Orthogonality Conditions |
| 3.6.4 The Modal Model and Forced Vibrations |
| 3.6.5 The Generalized Excitation Force for Distributed Loads |
| 3.6.6 Continuous Model FRFs |
| 3.7 Fourth Order Continuous Vibration System - The Beam |
| 3.7.1 The Fundamental Equation of Motion |
| 3.7.2 Natural Frequencies and Mode Shapes |
| 3.7.3 Natural Frequencies and Boundary Conditions |
| 3.7.4 The Modal Model |
| 3.7.5 The Beam Under Tension |
| 3.8 Non-Linear Behavior |
| 3.8.1 The Phase Plane |
| 3.8.2 The Simple Pendulum |
| 3.8.3 The Duffing Equation of Forced Vibration |
| 3.8.4 The Van Der Pol Equation and Limit Cycles |
| 3.8.5 The Mathieu Equation |
| 3.8.6 Chaotic Vibration |
| 3.9 Summary.References |
| Chapter 4 Transducer Measurement Considerations |
| 4.1 Introduction |
| 4.2 Fixed Reference Transducers |
| 4.2.1 The Linear Variable Differential Transformer (LVDT) |
