This second edition of this 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. It covers 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.
Cho W. S. To
Country of Publication:
2nd New edition
Series: Advances in Engineering Series
10 August 2011
Professional and scholarly
Further / Higher Education
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
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.
Reviews for Nonlinear Random Vibration: Analytical Techniques and Applications
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