THEORY OF RESPONSE ANALYSIS FOR CONTINUOUS FUZZY STOCHASTIC DYNAMICAL SYSTEMS II. INFLUENCE FUNCTION METHOD∗

Abstract

Every structural/mechanical system has a continuous distribution of mass, stiffness, and damping. While discrete models can be used to describe the dynamical behavior of such a system, continuous models are often more convenient; and being closer to the actual physical condition, they are more realistic. Continuous models are usually constructed by treating a structural/mechanical system as an assemblage of idealized elements (strings, bars, beams, plates, shells and so forth). The mathematical models of such a system are represented by systems of partial fuzzy random differential equations. In the second paper of a series of reports on the continuous fuzzy stochastic dynamical systems, we continue the work in References 22, and extend the work published in References 18-21, and discuss the response of 1-dimensional systems, and give the influence function method for the response of 1-dimensional systems, and establish the relation of the normal mode and the influence function methods. In the present paper, the influence function method will provide a general method for determining the response of continuous fuzzy stochastic dynamic systems both in the time and frequency domains. This approach can be used even in cases where the normal mode approach is not applicable. One example is considered in order to demonstrate the rationality and validity of the theory.

Keywords:

• Fuzzy stochastic dynamic system
• fuzzy random excitation
• dynamic response
• continuous system
• fuzzy stochastic process

Notes

∗This research was supported by National Key Projects on Basic Research and Applied Research: Applied Research on Safety and Durability of Major Construction Projects.