Publisher's Synopsis
A presentation of the theoretical foundations of analysis of linear and non-linear systems subject to random loadings. It deals with the three main methods employed for solving non-linear vibration problems using the stochastic approach - ie the Fokker-Planck-Kolmogorov diffusion equation, the small parameter and related correlation method, and the method of linearization.;The first of these methods is considered as strict, provided that the diffusion equation has been exactly solved and is employed for a special type of nonlinearity occurring mainly as non-linear spring forces. The other two methods, assumed to be approximate, are used, like the first, to determine interesting characteristics of vibrating systems. Several examples and applications of the theory are considered.;The problem of stability is discussed in relation to parametric vibration of linear systems for which resonance regions are determined. Nonstationary problems, ie random loadings and changes in parameters, have been left open since so few cases are investigated in relation to linear systems.
