Stochastic forced vibration analysis of a tapered beam with performance deterioration

Abstract

This paper’s purpose is to investigate the stochastic dynamic behavior of a tapered cantilever beam, taking into account the deterioration of its performance during the working process. The equation of motion of the tapered beam is established by using Lagrange’s equation. By applying the assumed mode method, the equation of motion of the beam is discretized into a series of coupled linear time-varying ordinary differential equations. To describe the deterioration of the performance of the tapered cantilever beam, the mass and stiffness deteriorations of the beam are modeled by two independent Gamma processes. Based on the stochastic perturbation method, the response of the linear continuous system with stochastic parameters is investigated by superimposing the discretized modes. In the numerical simulation, the validity of the present study is confirmed, the effects of the cone angle (tapered ratio) of the tapered beam and the frequency of the external force on the response of the tapered cantilever beam are investigated, and the influences of the parameters of the two Gamma processes on the variance of the response are also discussed.