Higher Education

Vibrations, 2nd Edition

  • Balakumar Balachandran University of Maryland
  • Edward B. Magrab University of Maryland
  • ISBN-10: 0534552064  |  ISBN-13: 9780534552060
  • 712 Pages
  • Previous Editions: 2004
  • © 2009 | Published
  • College Bookstore Wholesale Price = $157.00
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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.

Features and Benefits

  • Examples are relevant to theoretical discussions and are drawn from a wide range of applications; biomechanics, electronic circuit boards, machines, machining processes, micromechancical devices and structures.
  • Natural progression from linear to nonlinear systems.
  • Integration of analysis, modellng, prediction and design so students do not develop artificial distictions between these various tools.

Table of Contents

Chapter 1: Introduction
1.1 Introduction
1.2 Preliminaries from Dynamics
1.3 Summary

Chapter 2: Modeling of Vibratory Systems
2.1 Introduction
2.2 Inertia Elements
2.3 Stiffness Elements
2.4 Dissipation Elements
2.5 Model Construction
2.6 Design for Vibration
2.7 Summary

Chapter 3: Single Degree-of-Freedom Systems: Governing Equations
3.1 Introduction
3.2 Force-Balance and Moment-Balance Methods
3.3 Natural Frequency and Damping Factor
3.4 Governing Equations for Different Types of Damping
3.5 Governing Equations for Different Types of Applied Forces
3.6 Lagrange’s Equations
3.7 Summary

Chapter 4: Single Degree-of-Freedom System: Solution for Response and Free-Response Characteristics
4.1 Introduction
4.2 Free Responses of Undamped and Damped Systems
4.3 Stability of Single Degree-of-Freedom System
4.4 Machine Tool Chatter
4.5 Single Degree-of-Freedom Systems with Nonlinear Elements
4.6 Summary

Chapter 5: Single Degree-of-Freedom Systems Subjected to Periodic Excitations
5.1 Introduction
5.2 Response to Harmonic Excitation
5.3 Frequency-Response Function
5.4 Systems with Rotating Unbalanced Mass
5.5 Systems with Base Excitation
5.6 Acceleration Measurement: Accelerometer
5.7 Vibration Isolation
5.8 Energy Dissipation and Equivalent Damping
5.9 Response to Excitation with Harmonic Components
5.10 Influence of Nonlinear Stiffness on Forced Response
5.11 Summary

Chapter 6: Single Degree-of-Freedom Systems Subjected to Transient Excitations
6.1 Introduction
6.2 Response to Impulse Excitation
6.3 Response to Step Input
6.4 Response to Ramp Input
6.5 Spectral Energy of the Response
6.6 Response to Rectangular Pulse Excitation
6.7 Response to Half-Sine Wave Pulse
6.8 Impact Testing
6.9 Summary

Chapter 7: Multiple Degree-of-Freedom Systems: Governing Equations and Natural Frequencies and Mode Shapes
7.1 Introduction
7.2 Governing Equations
7.3 Free Responses
7.4 Rotating Shafts on Flexible Supports
7.5 Stability
7.6 Summary

Chapter 8: Multiple Degree-of-Freedom Systems: General Solution for Response and Forced Oscillations
8.1 Introduction
8.2 Normal-Mode Approach
8.3 State-Space Formulation
8.4 Laplace Transform Approach
8.5 Transfer Functions and Frequency-Response Functions
8.6 Vibration Absorbers
8.7 Vibration Isolation: Transmissibility Ratio
8.8 Systems with Moving Base
8.9 Summary

Chapter 9: Vibrations of Beams
9.1 Introduction
9.2 Governing Equations of Motion
9.3 Free Oscillations: Natural Frequencies and Mode Shapes
9.4 Forced Oscillations
9.5 Summary


A Laplace Transform Pairs
B Fourier Series
C Decibel Scale
D Solutions to Ordinary Differential Equations
E Matrices
F Complex Numbers and Variables
G Natural Frequencies and Mode Shapes of Bars, Shafts, and Strings

Answers to Selected Exercises


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  • International Student Edition

    ISBN-10: 0495411256 | ISBN-13: 9780495411253

    List Price = $254.95  | College Bookstore Wholesale Price = $191.75

Efficacy and Outcomes


This is a solid text as a first course in Mechanical Vibrations and a good follow on from a first course in Applied Mechanics.

— Dr. Leonard Louis Koss

The text provides excellent example problems and an excellent collection of end-of chapter problems.The chapter introduction and summaries are excellent for motivating and recapping the material. Overall, I think the text is very sound.

— Dr. Rob Langlois

This is an excellent text. In my opinion its real strength is that it introduces nonlinear dynamics at an early stage as a natural concept. Too many texts focus just on the linear dynamics, and treat nonlinearity as some anomalous behavior to be considered at the end of the text. Here, the authors give the subject the treatment it deserves and in a non-intimidating manner.

— Reviewer -


All supplements have been updated in coordination with the main title. Select the main title's "About" tab, then select "What's New" for updates specific to title's edition.

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Instructor Supplements

Instructor's Solutions Manual - Vibrations  (ISBN-10: 0495411264 | ISBN-13: 9780495411260)

Meet the Author

Author Bio

Balakumar Balachandran

Dr. Balachandran received his B. Tech (Naval Architecture) from the Indian Institute of Technology, Madras, India, M.S. (Aerospace Engineering) from Virginia Tech, Blacksburg, VA and Ph.D. (Engineering Mechanics) from Virginia Tech. Currently, he is a Professor of Mechanical Engineering at the University of Maryland, where has been since 1993. His research interests include nonlinear phenomena, dynamics and vibrations, and control, and his recent efforts have focused on taking advantage of nonlinear phenomena for the benefit of a system. The publications that he has authored/co-authored include over fifty journal publications and several textbooks. He serves on the editorial board of the Journal of Vibration and Control, is a Deputy Editor of the AIAA Journal, and is an Associate Editor of the ASME Journal of Computational and Nonlinear Dynamics. He is a Fellow of ASME, an Associate Fellow of AIAA, and a member of AAM, ASA, Sigma Xi, and SPIE. He served as the Chair of the ASME Applied Mechanics Division Technical Committee on Dynamics and Control of Structures and Systems from 2005 to 2007, and he currently serves as the Chair of the ASME Design Engineering Division Technical Committee on Multi-Body Systems and Nonlinear Dynamics.

Edward B. Magrab

Dr. Magrab is a Professor of Mechanical Engineering at the University of Maryland, College Park, MD. He has conducted extensive research in the areas of vibrations and acoustics, and recently, his research efforts have focused on the integration of design and manufacturing. He joined the Department of Mechanical Engineering after spending more than twelve years at the National Institute of Standards and Technology (NIST), Gaithersburg, MD, where he held several supervisory positions including Chief of the Sound Section. Prior to going to NIST, he was a Professor of Mechanics at the Catholic University of America, Washington, D. C. He has authored numerous journal publications and six books on subjects including vibrations, noise control, dynamic measurements, integrated design, and MATLAB. Sijthoff and Noordhoff published his graduate level textbook VIBRATIONS OF ELASTIC STRUCTURAL MEMBERS in 1979. Dr. Magrab is a fellow of ASME and a registered Professional Engineer in the State of Maryland.