On the behaviour of structures with many nonlinear elements

Abstract

One of the most powerful methods currently available for the analysis of structural dynamics at high frequencies is Statistical Energy Analysis (SEA). The fundamental idea behind the method is that, at higher frequencies, so many modes are present in the response of the structure that individual modes cease to be resolvable and a simplified statistical order emerges in the response. Although the details of the context are very different to SEA, the current paper is motivated by it and provides a preliminary investigation into what happens when very many nonlinear elements are present in a structure under random vibration; the question being, does a simplified statistical order emerge as the influence of the nonlinearities increases? A number of case studies are provided based on computer simulation, arguing the case that order does indeed appear to emerge and a parallel with the SEA case is thus drawn.