Vibrations

by Balachandran, Balakumar; Magrab, Edward B.

• ISBN13: 9780534395100
• ISBN10: 0534395104
• Edition: 1st
• Format: Hardcover
• Copyright: 2003-05-05
• Publisher: CL Engineering

Summary

Featuring outstanding coverage of linear and non-linear single degree-of-freedom and multi-degree-of-freedom systems, this book teaches the use of vibration principles in a broad spectrum of applications. In this introduction for undergraduate students, authors Balakumar Balachandran and Edward B. Magrab present vibration principles in a general context and illustrate the use of these principles through carefully chosen examples from different disciplines. Their balanced approach integrates principles of linear and nonlinear vibrations with modeling, analysis, prediction, and measurement so that physical understanding of the vibratory phenomena and their relevance for engineering design can be emphasized. The authors also provide design guidelines that are applicable to a wide range of vibratory systems. MATLAB is thoroughly integrated throughout the text.

Table of Contents

Introduction	xx
Introduction	1	(3)
Preliminaries from Dynamics	4	(12)
Summary	16	(4)
Exercises	16	(4)
Modeling of Vibratory Systems	20	(42)
Introduction	21	(1)
Inertia Elements	22	(4)
Stiffness Elements	26	(19)
Dissipation Elements	45	(5)
Model Construction	50	(5)
Summary	55	(7)
Exercises	56	(6)
Single Degree-of-Freedom Systems: Governing Equations	62	(52)
Introduction	63	(1)
Force-Balance and Moment-Balance Methods	64	(9)
Natural Frequency and Damping Factor	73	(9)
Governing Equations for Different Types of Damping	82	(1)
Governing Equations for Different Types of Applied Forces	83	(4)
Lagrange's Equations	87	(20)
Summary	107	(7)
Exercises	107	(7)
Single Degree-of-Freedom System: Solution for Response and Free-Response Characteristics	114	(56)
Introduction	115	(2)
General Solution	117	(4)
Free Responses of Undamped and Damped Systems	121	(31)
Stability of Single Degree-of-Freedom System	152	(3)
Machine Tool Chatter	155	(3)
Single Degree-of-Freedom Systems with Nonlinear Elements	158	(6)
Summary	164	(6)
Exercises	164	(6)
Single Degree-of-Freedom Systems Subjected to Periodic Excitations	170	(90)
Introduction	171	(2)
Response to Harmonic Excitation	173	(19)
Frequency-Response Function	192	(13)
Systems with Rotating Unbalanced Mass	205	(6)
Systems with Base Excitation	211	(7)
Acceleration Measurement: Accelerometer	218	(3)
Vibration Isolation	221	(3)
Energy Dissipation and Equivalent Damping	224	(8)
Response to Excitation with Harmonic Components	232	(14)
Influence of Nonlinear Stiffness on Forced Response	246	(8)
Summary	254	(6)
Exercises	254	(6)
Single Degree-of-Freedom Systems Subjected to Transient Excitations	260	(48)
Introduction	261	(1)
Response to Impulse Excitation	262	(12)
Response to Step Input	274	(10)
Response to Ramp Input	284	(5)
Spectral Energy of the Response	289	(1)
Response to Rectangular Pulse Excitation	290	(4)
Response to Half-Sine Wave Pulse	294	(11)
Summary	305	(3)
Exercises	305	(3)
Multiple Degree-of-Freedom Systems: Governing Equations and Characteristics of Free Responses	308	(76)
Introduction	309	(1)
Governing Equations	310	(26)
Free Responses	336	(36)
Stability	372	(1)
Summary	372	(12)
Exercises	373	(11)
Multiple Degree-of-Freedom Systems: General Solution for Response and Forced Oscillations	384	(90)
Introduction	385	(2)
Normal-Mode Approach	387	(20)
State-Space Formulation	407	(12)
Laplace Transform Approach	419	(10)
Transfer Functions and Frequency-Response Functions	429	(11)
Vibration Absorbers	440	(20)
Vibration Isolation: Transmissibility Ratio	460	(4)
Systems with Moving Base	464	(5)
Summary	469	(5)
Exercises	469	(5)
Vibrations of Beams	474	(101)
Introduction	475	(1)
Governing Equations of Motion	476	(18)
Free Oscillations	494	(51)
Forced Oscillations	545	(11)
Summary	556	(1)
Appendix
A Laplace Transform Pairs	557	(7)
B Fourier Series	564	(1)
C Decibel Scale	565	(2)
D Direct Methods to Determine Response to Harmonic Excitation	567	(3)
E Matrices	570	(5)
Index	575