A stochastic perturbation edge-based smoothed finite element method for the analysis of uncertain structural-acoustics problems with random variables

Abstract

Among the current methods in predicting the response of structural-acoustics problems in mid-frequency regime, some problems such as low accuracy and inability to deal with the uncertainties still need to be solved. To eliminate these issues, a novel stochastic perturbation edge-based smoothed FEM method (SP-ES-FEM) is proposed for the analysis of structural-acoustics problems in this work. The edge-based smoothing technique is applied in the standard FEM approach to soften the over-stiff behavior of structural-acoustics problems aiming to improve the accuracy of deterministic response predictions. Then, this approach, for the first time, intends to introduce the first-order perturbation technique into the edge-based smoothed FEM theory frame especially for the probabilistic analysis of structural-acoustics problems. The response of the coupled systems can be expressed simply as a linear function of all the pre-defined input variables by using the change of variable techniques. Due to the linear relationships of variables and response, the probability density function and cumulative probability density function of the response can be obtained based on the simple mathematical transformation of probability theory. The proposed approach not only improves the numerical accuracy of deterministic output quantities with respect to a given random variable, but also can handle the randomness well in the systems. Two numerical examples for frequency response analysis of random structural-acoustics are presented and verified by Monte Carlo simulation, to demonstrate the effectiveness of the present method.