Nonlinear Random Vibration: Analytical Techniques and Applications, 2nd Edition (Paperback) book cover

Nonlinear Random Vibration

Analytical Techniques and Applications, 2nd Edition

By Cho W.S. To

CRC Press

296 pages

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This second edition of the book, Nonlinear Random Vibration: Analytical Techniques and Applications, expands on the original edition with additional detailed steps in various places in the text. It is a first systematic presentation on the subject. Its features include:

• a concise treatment of Markovian and non- Markovian solutions of nonlinear stochastic differential equations,

• exact solutions of Fokker-Planck-Kolmogorov equations,

• methods of statistical linearization,

• statistical nonlinearization techniques,

• methods of stochastic averaging,

• truncated hierarchy techniques, and

• an appendix on probability theory.

A special feature is its incorporation of detailed steps in many examples of engineering applications.

Targeted audience: Graduates, research scientists and engineers in mechanical, aerospace, civil and environmental (earthquake, wind and transportation), automobile, naval, architectural, and mining engineering.


In summary, the technical material in Prof. To’s 2012 second edition of Nonlinear Random Vibration: Analytical Techniques and Applications is well presented, of sufficient depth, detail, and quality, and supported by a good number of solved example problems.

Robert M. Koch

Naval Undersea Warfare Center, Newport, RI, USA

In: Noise Control Engr. J. 61 (2), March-April 2013, pp 251-252

Table of Contents

1 Introduction

2 Markovian And Non-Markovian Solutions Of Stochastic Nonlinear Differential Equations


Markovian Solution Of Stochastic Nonlinear Differential Equations

Non-Markovian Solution Of Stochastic Nonlinear Differential Equations

3 Exact Solution Of The Fokker-Planck-Kolmogorov Equation


Solution Of A General Single-Degree-Of-Freedom System

Applications To Engineering Systems

Solution Of A Multi-Degree-Of-Freedom System

Stochastically Excited Hamiltonian Systems

4 Methods Of Statistical Linearization


Statistical Linearization For Single-Degree-Of-Freedom Nonlinear Systems

Statistical Linearization For Multi-Degree-Of-Freedom Nonlinear Systems

Applications To Engineering Systems

Uniqueness And Accuracy Of Solutions By Statistical Linearization Techniques

5 Statistical Nonlinearization Techniques


Statistical Nonlinearization Techniques Based On Least Mean Square Of Deficiency

Statistical Nonlinearization Technique Based On Equivalent Nonlinear Damping Coefficient

Statistical Nonlinearization Technique For Multi-Degree-Of-Freedom Systems

Accuracy Of Statistical Nonlinearization Techniques

6 Methods Of Stochastic Averaging


Classical Stochastic Averaging Method

Stochastic Averaging Method Of Energy Envelope

Other Stochastic Averaging Techniques

Accuracy Of Stochastic Averaging Techniques

7 Truncated Hierarchy And Other Techniques


Truncated Hierarchy Techniques

Perturbation Techniques

Functional Series Techniques

About the Author

Dr. To joined the Department of Mechanical Engineering, University of Nebraska in 1996. Prior to joining UNL, he was a professor at the University of Western Ontario and an associate professor at the University of Calgary. He was a Reseach Fellow of the Natural Sciences and Engineering Research Council of Canada from 1982-1992, and a Research Fellow at the Institute of Sound and Vibration Research (ISVR), University of Southampton. He is a member of the American Society of Mechanical Engineers (ASME), the American Academy of Mechanics (AAM), the Society of Industrial and Applied Mathematics (SIAM), and a founder Fellow of the Institution of Diagnostics Engineers, U.K. He served as chair of the ASME Finite Element Techniques and Computational Technologies Technical Committee. Dr. To currently serves as the department graduate chair.

About the Series

Advances in Engineering Series

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