RECENT RESULTS IN RANDOM VIBRATIONS OF NONLINEAR MECHANICAL SYSTEMS

The influence of random vibration on the design of mechanical componen ts has been considered within the framework of the linear theory of sm all oscillations. However in some important cases this theory is inade quate and fails to predict some complex response characteristics that have been observed experimentally and which can only be predicted by n onlinear analyses. This paper describes some recent developments in th e theory of nonlinear random vibration based on Markov methods and rel ated problems in the design of dynamical systems. Research efforts hav e been focused on stability/bifurcation conditions, response statistic s and reliability problems. Significant progress has been made in deve loping new analytical methods and conducting experimental testing. The se developments have helped to resolve some controversies, and to enha nce our understanding of difficult issues. Experimental and numerical simulations have revealed new phenomena that were not predicted analyt ically. These include on-off intermittency, snap-through phenomena, an d the dependence of the response bandwidth on the excitation level. Th e main results of studying the responses of nonlinear single- and two- degree-of-freedom systems to random excitations obtained by the author and others are discussed in this paper.