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

• Published in: Mechanical systems and signal processing Vol. 115; pp. 524 - 544
• Main Authors: Chen, Ning, Xia, Siyuan, Yu, Dejie, Liu, Jian, Beer, Michael
• Format: Journal Article
• Language: English
• Published: Berlin Elsevier Ltd 15-01-2019; Elsevier BV
• Subjects: Acoustics; Bounded hybrid uncertain model; Composite materials; Finite element method; Gegenbauer polynomials; Homogenization; Homogenization method; Hybrid systems; Mathematical models; Multiscale analysis; Parameter uncertainty; Periodical composites; Perturbation methods; Polynomials; Random variables; Series expansion; Sound pressure; Structural-acoustic system; Taylor series; Uncertainty; Structural-acoustic system; Homogenization method; Gegenbauer polynomials; Bounded hybrid uncertain model; Periodical composites
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2018.06.016

•Multi-scale uncertainties in the composite structural-acoustic system are considered.•The HHSIPM and HGPEM for the composite structural-acoustic system with multi-scale bounded hybrid uncertain parameters is developed.•The accuracy of the HHSIPM and HGPEM are compared.
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.