THEORY OF RESPONSE ANALYSIS FOR CONTINUOUS FUZZY STOCHASTIC DYNAMICAL-SYSTEMS - I - NORMAL-MODE METHOD

Most real-life structural/mechanical systems have complex geometrical and material properties and operate under complex fuzzy environmental conditions. These systems are certainly subjected to fuzzy random exci tations induced by the environment. For an analytical treatment of suc h a system subjected to fuzzy random excitations, it becomes necessary to establish the general theory of dynamic response of a system to fu zzy random excitations. In the first paper of a series of reports on t he continuous fuzzy stochastic dynamical systems, we extend the work p ublished in References 18-21, and discuss the response of 1-dimensiona l systems whose response is described by a single fuzzy displacement c omponent (X) under tilde(s, t), and give the normal mode method for th e response of 1-dimensional systems. Systems for which normal modes ex ist, the normal mode method provides a simple analytical framework for determining the dynamic response of continuous fuzzy stochastic dynam ical systems. The theory of the response, fuzzy mean response and fuzz y covariance response of continuous systems to fuzzy random excitation s in the time domain and frequency domain is put forward. One example is considered in order to demonstrate the rationality and validity of the theory.