Interval and random analysis for structure-acoustic systems with large uncertain-but-bounded parameters

For the response analysis of the structure-acoustic system with uncertain-but-bounded parameters, three bounded uncertain models are introduced. One is the bounded random model in which all of the uncertain-but-bounded parameters are described as bounded random variables with well defined probability distribution. The second one is the interval model in which all of the uncertain-but-bounded parameters are described as interval variables due to the limited information. The third one is the bounded hybrid uncertain model in which the interval variables and the bounded random variables exist simultaneously. Based on the parametric Gegenbauer polynomial, which is formulated for bounded random model recently, the Gegenbauer Series Expansion Method (GSEM) is developed for the response prediction of the structure-acoustic system under these three bounded uncertain models. Within GSEM, the response of these three bounded uncertain models of the structure-acoustic system can be approximated by the unified Gegenbauer Series with different values of polynomial parameter. Then, the interval and random analysis for these three bounded uncertain models of the structure-acoustic system are conducted on the basis of Gegenbauer series. Owing to the orthogonal property of Gegenbauer polynomial, the analytical solution of the expectation and variance of Gegenbauer series with respect to the bounded random variables can be readily obtained. The bounds of Gegenbauer series with respect to the interval variables are determined by the Monte Carlo simulation. The GSEM is applied to solve a shell structure-acoustic system under these three bounded uncertain models. Inspired by the convergence behavior of GSEM, the relative improvement criterion is established to estimate the required retained order of Gegenbauer Series for large uncertain problems. The results on numerical examples show that GSEM with the estimated retained order can achieve a prescribed accuracy and good efficiency for structure-acoustic systems with large uncertain-but-bounded parameters.