2nd Edition

Nonlinear Random Vibration Analytical Techniques and Applications

By Cho W.S. To Copyright 2012
    312 Pages
    by CRC Press

    312 Pages
    by CRC Press

    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.

    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


    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.

    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