2nd Edition
Nonlinear Random Vibration Analytical Techniques and Applications
1 Introduction
2 Markovian And Non-Markovian Solutions Of Stochastic Nonlinear Differential Equations
Introduction
Markovian Solution Of Stochastic Nonlinear Differential Equations
Non-Markovian Solution Of Stochastic Nonlinear Differential Equations
3 Exact Solution Of The Fokker-Planck-Kolmogorov Equation
Introduction
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
Introduction
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
Introduction
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
Introduction
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
Introduction
Truncated Hierarchy Techniques
Perturbation Techniques
Functional Series Techniques
Biography
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
