Hybrid interval and random analysis for structural-acoustic systems including periodical composites and multi-scale bounded hybrid uncertain parameters

For the response analysis of periodical composite structural-acoustic systems with multi-scale uncertain-but-bounded parameters, a bounded hybrid uncertain model is introduced, in which the interval variables and the bounded random variables exist simultaneously. In the periodical composite structural-acoustic system, the equivalent macro constitutive matrix and average mass density of the microstructure are calculated through the homogenization method. On the basis of the conventional first-order Taylor series expansion, a homogenization-based hybrid stochastic interval perturbation method (HHSIPM) is developed for the prediction of periodical composite structural-acoustic systems with multi-scale bounded hybrid uncertain parameters. By incorporating the Gegenbauer polynomial approximation theory into the homogenization-based finite element method, a homogenization-based Gegenbauer polynomial expansion method (HGPEM) is also proposed to calculate the bounds of expectation and variance of the sound pressure response. Numerical examples of a hexahedral box and an automobile passenger compartment are given to investigate the effectiveness of the HHSIPM and HGPEM for the prediction of periodical composite structural-acoustic systems with multi-scale bounded hybrid uncertain parameters.