In this paper, the quantification of uncertainty effects on stochastic responses of interior vibro-acoustic interaction systems with moderate geometry complexities and uncertain design parameters is investigated. A variational-based stochastic model is developed to predict the vibro-acoustic responses submitted to probabilistic parameters, and it is illustrated by application to a built-up system consisting of an irregular acoustic cavity backed up a plate assembly. The model is derived from the combination of the multi-domain Rayleigh–Ritz approach, used to solve the deterministic structural–acoustic equations, together with the generalized polynomial chaos expansion (gPCE) to represent propagation of uncertainty and estimate the statistical characteristics of the responses. Benchmark comparisons are made with the Monte Carlo simulations (MCS) to demonstrate the tremendous computational advantage of the present methodology. Uncertainty analysis is performed to ascertain the influence of random parameters on responses. The results reveal that system uncertainty is significant enough to affect the vibro-acoustic behaviors and hence the consideration of input uncertainties is necessary in analyses and designs to ensure the sustainable system performance.
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