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Vibration of Mechanical Systems - Alok Sinha

Vibration of Mechanical Systems

Hardcover

Published: 18th October 2010
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This is a textbook for a first course in mechanical vibrations. There are many books in this area that try to include everything, thus they have become exhaustive compendiums overwhelming for the undergraduate. In this book, all the basic concepts in mechanical vibrations are clearly identified and presented in a concise and simple manner with illustrative and practical examples. Vibration concepts include a review of selected topics in mechanics; a description of single-degree-of-freedom (SDOF) systems in terms of equivalent mass, equivalent stiffness, and equivalent damping; a unified treatment of various forced response problems (base excitation and rotating balance); an introduction to systems thinking, highlighting the fact that SDOF analysis is a building block for multi-degree-of-freedom (MDOF) and continuous system analyses via modal analysis; and a simple introduction to finite element analysis to connect continuous system and MDOF analyses. There are more than 60 exercise problems, and a complete solutions manual. The use of MATLAB(R) software is emphasized.

Prefacep. xiii
Equivalent Single-Degree-of-Freedom System and Free Vibrationp. 1
Degrees of Freedomp. 3
Elements of a Vibratory Systemp. 5
Mass and/or Mass-Moment of Inertiap. 5
Pure Translational Motionp. 5
Pure Rotational Motionp. 6
Planar Motion (Combined Rotation and Translation) of a Rigid Bodyp. 6
Special Case: Pure Rotation about a Fixed Pointp. 8
Springp. 8
Pure Translational Motionp. 8
Pure Rotational Motionp. 9
Damperp. 10
Pure Translational Motionp. 10
Pure Rotational Motionp. 11
Equivalent Mass, Equivalent Stiffness, and Equivalent Damping Constant for an SDOF Systemp. 12
A Rotor-Shaft Systemp. 13
Equivalent Mass of a Springp. 14
Springs in Series and Parallelp. 16
Springs in Seriesp. 16
Springs in Parallelp. 17
An SDOF System with Two Springs and Combined Rotational and Translational Motionp. 19
Viscous Dampers in Series and Parallelp. 22
Dampers in Seriesp. 22
Dampers in Parallelp. 23
Free Vibration of an Undamped SDOF Systemp. 25
Differential Equation of Motionp. 25
Energy Approachp. 27
Solution of the Differential Equation of Motion Governing Free Vibration of an Undamped Spring-Mass Systemp. 34
Free Vibration of a Viscously Damped SDOF Systemp. 40
Differential Equation of Motionp. 40
Solution of the Differential Equation of Motion Governing Free Vibration of a Damped Spring-Mass Systemp. 41
Underdamped (0 < < 1 or 0 < Ceq < cc)p. 42
Critically Damped ( = 1 or Ceq = Cc)p. 45
Overdamped ( > 1 or Ceq > Cc)p. 46
Logarithmic Decrement: Identification of Damping Ratio from Free Response of an Underdamped System (0 < <1)p. 51
Solutionp. 55
Stability of an SDOF Spring-Mass-Damper Systemp. 58
Exercise Problemsp. 63
Vibration of a Single-Degree-of-Freedom System Under Constant and Purely Harmonic Excitationp. 72
Responses of Undamped and Damped SDOF Systems to a Constant Forcep. 72
Undamped ( = 0) and Underdamped (0 < <1)p. 74
Critically Damped ( > 1 or Ceq = Cc)p. 75
Overdamped ( > 1 or Ceq > Cc)p. 76
Response of an Undamped SDOF System to a Harmonic Excitationp. 82
np. 83
= n (Resonance)p. 84
np. 87
= np. 87
Response of a Damped SDOF System to a Harmonic Excitationp. 88
Particular Solutionp. 89
Underdamped (0 < < 1 or 0 < Ceq < Cc)p. 92
Critically Damped ( = 1 or Ceq = Cc)p. 92
Overdamped ( > 1 or Ceq > Cc)p. 94
Steady State Responsep. 95
Force Transmissibilityp. 101
Quality Factor and Bandwidthp. 106
Quality Factorp. 106
Bandwidthp. 107
Rotating Unbalancep. 109
Base Excitationp. 116
Vibration Measuring Instrumentsp. 121
Vibrometerp. 123
Accelerometerp. 126
Equivalent Viscous Damping for Nonviscous Energy Dissipationp. 128
Exercise Problemsp. 132
Responses of an SDOF Spring-Mass-Damper System to Periodic and Arbitrary Forcesp. 138
Response of an SDOF System to a Periodic Forcep. 138
Periodic Function and its Fourier Series Expansionp. 139
Even and Odd Periodic Functionsp. 142
Fourier Coefficients for Even Periodic Functionsp. 143
Fourier Coefficients for Odd Periodic Functionsp. 145
Fourier Series Expansion of a Function with a Finite Durationp. 147
Particular Integral (Steady-State Response with Damping) Under Periodic Excitationp. 151
Response to an Excitation with Arbitrary Naturep. 154
Unit Impulse Function (t - a)p. 155
Unit Impulse Response of an SDOF System with Zero Initial Conditionsp. 156
Undamped and Underdamped System (0 ≤ < 1)p. 158
Critically Damped ( = 1 or Ceq = Cc)p. 158
Overdamped ( > 1 or Ceq > Cc)p. 159
Convolution Integral: Response to an Arbitrary Excitation with Zero Initial Conditionsp. 160
Convolution Integral: Response to an Arbitrary Excitation with Nonzero Initial Conditionsp. 165
Undamped and Underdamped (0 ≤ < 1 or 0 ≤ Ceq < Cc)p. 166
Critically Damped ( = 1 or Ceq = Cc)p. 166
Overdamped ( > 1 or Ceq > Cc)p. 166
Laplace Transformationp. 168
Properties of Laplace Transformationp. 169
Response of an SDOF System via Laplace Transformationp. 170
Transfer Function and Frequency Response Functionp. 173
Significance of Transfer Functionp. 175
Poles and Zeros of Transfer Functionp. 175
Frequency Response Functionp. 176
Exercise Problemsp. 179
Vibration of Two-Degree-of-Freedom-Systemsp. 186
Mass, Stiffness, and Damping Matricesp. 187
Natural Frequencies and Mode Shapesp. 192
Eigenvalue/Eigenvector Interpretationp. 197
Free Response of an Undamped 2DOF System Solutionp. 200
Forced Response of an Undamped 2DOF System Under Sinusoidal Excitationp. 201
Free Vibration of a Damped 2DOF Systemp. 203
Steady-State Response of a Damped 2DOF System Under Sinusoidal Excitationp. 209
Vibration Absorberp. 212
Undamped Vibration Absorberp. 212
Damped Vibration Absorberp. 220
Tuned Case (f = 1 or 22 = 11)p. 224
No restriction on f (Absorber not tuned to main system)p. 224
Modal Decomposition of Responsep. 227
Undamped System (C = 0)p. 228
Damped System (C ≠ 0)p. 228
Exercise Problemsp. 231
Finite and Infinite (Continuous) Dimensional Systemsp. 237
Multi-Degree-of-Freedom Systemsp. 237
Natural Frequencies and Modal Vectors (Mode Shapes)p. 239
Orthogonality of Eigenvectors for Symmetric Mass and Symmetric Stiffness Matricesp. 242
Modal Decompositionp. 245
Undamped System (C = 0)p. 246
Proportional or Rayleigh Dampingp. 249
Continuous Systems Governed by Wave Equationsp. 250
Transverse Vibration of a Stringp. 250
Natural Frequencies and Mode Shapesp. 251
Computation of Responsep. 255
Longitudinal Vibration of a Barp. 258
Torsional Vibration of a Circular Shaftp. 261
Continuous Systems: Transverse Vibration of a Beamp. 265
Governing Partical Differential Equation of Motionp. 265
Natural Frequencies and Mode Shapesp. 267
Simply Supported Beamp. 269
Cantilever Beamp. 271
Computation of Responsep. 273
Finite Element Analysisp. 279
Longitudinal Vibration of a Barp. 279
Total Kinetic and Potential Energies of the Barp. 283
Transverse Vibration of a Beamp. 286
Total Kinetic and Potential Energies of the Beamp. 291
Exercise Problemsp. 295
Equivalent Stiffnesses (Spring Constants) of Beams, Torsional Shaft, and Longitudinal Barp. 299
Some Mathematical Formulaep. 302
Laplace Transform Tablep. 304
Referencesp. 305
Indexp. 307
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9780521518734
ISBN-10: 0521518733
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 328
Published: 18th October 2010
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 23.6 x 15.9  x 2.4
Weight (kg): 0.63