The general theory for response analysis of fuzzy stochastic dynamical systems

Abstract

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 excitations induced by the environment. For an analytical treatment of such a system subjected to fuzzy random excitations, it becomes necessary to establish the general theory of fuzzy stochastic dynamical systems. In the first part of this paper on the dynamic response of fuzzy stochastic systems, we construct the mathematical models of fuzzy random algebraic equation dynamic systems, nth-order fuzzy random differential equation dynamic systems and a system of first-order fuzzy random differential equations. The theory of the response, fuzzy mean response and fuzzy covariance response of fuzzy random algebraic equation dynamic systems in time domain and frequency domain is brought forward. In the second part, the theory of the response, fuzzy mean response and fuzzy covariance response of the nth-order fuzzy random differential equation dynamic systems in time domain and frequency domain is put forward. The theory of the response analysis of a system to both stationary and nonstationary fuzzy random excitations is established. The method of the response analysis of a system to nonstationary fuzzy random excitation with evolutionary spectra is brought forward, and two examples are considered. In the third part, the theory of the response, fuzzy mean response and fuzzy covariance response of a system of the first-order fuzzy random differential equations with constant coefficients and variable coefficients in time domain and frequency domain is put forward. An example is given to show the rationality and validity of the theory.