Vibration Theory, Vol. 4: advanced methods in stochastic dynamics of non-linear systems

This text is based on the lecture notes for the courses on advanced methods in stochastic dynamics of non-linear systems taught in November 1994, February 1995 and December 1997 for Ph.D. students at the Department of Building Technology and Structural Engineering at Aalborg University and in 1999 for postgraduate students and academic staff members at the school of Mechanical Engineering of the University of the Witwatersrand, Johannesburg. The book covers, in authors belief, the most important methods for the analyse of non-linear mechanical, or structural, systems. A large part of the methods covered in the book, especially of those relevant to random pulses, have been developed by the authors. The main idea is to present the methods of Markov processes in the widest possible context. Therefore different stochastic processes with independent increments, leading to the Markov processes problems, are introduced. Moreover some non-Markov problems are discussed, which can be exactly converted into Markov problem. A key point for all the techniques devised subsequently is the general integro-differential Chapman-Kolmogorov equation, known in physics as the master equation.