Vibration of Mechanical Systems

ISBN-10: 0521518733

ISBN-13: 9780521518734

Edition: 2010

Authors: Alok Sinha

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Book details

List price: $88.95
Copyright year: 2010
Publisher: Cambridge University Press
Publication date: 10/18/2010
Binding: Hardcover
Pages: 328
Size: 6.25" wide x 9.25" long x 1.00" tall
Weight: 1.694
Language: English

Preface
Equivalent Single-Degree-of-Freedom System and Free Vibration
Degrees of Freedom
Elements of a Vibratory System
Mass and/or Mass-Moment of Inertia
Pure Translational Motion
Pure Rotational Motion
Planar Motion (Combined Rotation and Translation) of a Rigid Body
Special Case: Pure Rotation about a Fixed Point
Spring
Pure Translational Motion
Pure Rotational Motion
Damper
Pure Translational Motion
Pure Rotational Motion
Equivalent Mass, Equivalent Stiffness, and Equivalent Damping Constant for an SDOF System
A Rotor-Shaft System
Equivalent Mass of a Spring
Springs in Series and Parallel
Springs in Series
Springs in Parallel
An SDOF System with Two Springs and Combined Rotational and Translational Motion
Viscous Dampers in Series and Parallel
Dampers in Series
Dampers in Parallel
Free Vibration of an Undamped SDOF System
Differential Equation of Motion
Energy Approach
Solution of the Differential Equation of Motion Governing Free Vibration of an Undamped Spring-Mass System
Free Vibration of a Viscously Damped SDOF System
Differential Equation of Motion
Solution of the Differential Equation of Motion Governing Free Vibration of a Damped Spring-Mass System
Underdamped (0 < � < 1 or 0 < C<sub>eq</sub> < c<sub>c</sub>)
Critically Damped (� = 1 or C<sub>eq</sub> = C<sub>c</sub>)
Overdamped (� > 1 or C<sub>eq</sub> > C<sub>c</sub>)
Logarithmic Decrement: Identification of Damping Ratio from Free Response of an Underdamped System (0 < � <1)
Solution
Stability of an SDOF Spring-Mass-Damper System
Exercise Problems
Vibration of a Single-Degree-of-Freedom System Under Constant and Purely Harmonic Excitation
Responses of Undamped and Damped SDOF Systems to a Constant Force
Undamped (� = 0) and Underdamped (0 <� <1)
Critically Damped (� > 1 or C<sub>eq</sub> = C<sub>c</sub>)
Overdamped (� > 1 or C<sub>eq</sub> > C<sub>c</sub>)
Response of an Undamped SDOF System to a Harmonic Excitation
� &#8800; �<sub>n</sub>
� = �<sub>n</sub> (Resonance)
� &#8800; �<sub>n</sub>
� = �<sub>n</sub>
Response of a Damped SDOF System to a Harmonic Excitation
Particular Solution
Underdamped (0 < � < 1 or 0 < C<sub>eq</sub> < C<sub>c</sub>)
Critically Damped (� = 1 or C<sub>eq</sub> = C<sub>c</sub>)
Overdamped (� > 1 or C<sub>eq</sub> > C<sub>c</sub>)
Steady State Response
Force Transmissibility
Quality Factor and Bandwidth
Quality Factor
Bandwidth
Rotating Unbalance
Base Excitation
Vibration Measuring Instruments
Vibrometer
Accelerometer
Equivalent Viscous Damping for Nonviscous Energy Dissipation
Exercise Problems
Responses of an SDOF Spring-Mass-Damper System to Periodic and Arbitrary Forces
Response of an SDOF System to a Periodic Force
Periodic Function and its Fourier Series Expansion
Even and Odd Periodic Functions
Fourier Coefficients for Even Periodic Functions
Fourier Coefficients for Odd Periodic Functions
Fourier Series Expansion of a Function with a Finite Duration
Particular Integral (Steady-State Response with Damping) Under Periodic Excitation
Response to an Excitation with Arbitrary Nature
Unit Impulse Function �(t - a)
Unit Impulse Response of an SDOF System with Zero Initial Conditions
Undamped and Underdamped System (0 &#8804; � < 1)
Critically Damped (� = 1 or C<sub>eq</sub> = C<sub>c</sub>)
Overdamped (� > 1 or C<sub>eq</sub> > C<sub>c</sub>)
Convolution Integral: Response to an Arbitrary Excitation with Zero Initial Conditions
Convolution Integral: Response to an Arbitrary Excitation with Nonzero Initial Conditions
Undamped and Underdamped (0 &#8804; � < 1 or 0 &#8804; C<sub>eq</sub> < C<sub>c</sub>)
Critically Damped (� = 1 or C<sub>eq</sub> = C<sub>c</sub>)
Overdamped (� > 1 or C<sub>eq</sub> > C<sub>c</sub>)
Laplace Transformation
Properties of Laplace Transformation
Response of an SDOF System via Laplace Transformation
Transfer Function and Frequency Response Function
Significance of Transfer Function
Poles and Zeros of Transfer Function
Frequency Response Function
Exercise Problems
Vibration of Two-Degree-of-Freedom-Systems
Mass, Stiffness, and Damping Matrices
Natural Frequencies and Mode Shapes
Eigenvalue/Eigenvector Interpretation
Free Response of an Undamped 2DOF System Solution
Forced Response of an Undamped 2DOF System Under Sinusoidal Excitation
Free Vibration of a Damped 2DOF System
Steady-State Response of a Damped 2DOF System Under Sinusoidal Excitation
Vibration Absorber
Undamped Vibration Absorber
Damped Vibration Absorber
Tuned Case (f = 1 or �<sub>22</sub> = �<sub>11</sub>)
No restriction on f (Absorber not tuned to main system)
Modal Decomposition of Response
Undamped System (C = 0)
Damped System (C &#8800; 0)
Exercise Problems
Finite and Infinite (Continuous) Dimensional Systems
Multi-Degree-of-Freedom Systems
Natural Frequencies and Modal Vectors (Mode Shapes)
Orthogonality of Eigenvectors for Symmetric Mass and Symmetric Stiffness Matrices
Modal Decomposition
Undamped System (C = 0)
Proportional or Rayleigh Damping
Continuous Systems Governed by Wave Equations
Transverse Vibration of a String
Natural Frequencies and Mode Shapes
Computation of Response
Longitudinal Vibration of a Bar
Torsional Vibration of a Circular Shaft
Continuous Systems: Transverse Vibration of a Beam
Governing Partical Differential Equation of Motion
Natural Frequencies and Mode Shapes
Simply Supported Beam
Cantilever Beam
Computation of Response
Finite Element Analysis
Longitudinal Vibration of a Bar
Total Kinetic and Potential Energies of the Bar
Transverse Vibration of a Beam
Total Kinetic and Potential Energies of the Beam
Exercise Problems
Equivalent Stiffnesses (Spring Constants) of Beams, Torsional Shaft, and Longitudinal Bar
Some Mathematical Formulae
Laplace Transform Table
References
Index
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