Modal response uncertainty in structural acoustic systems using generalized polynomial chaos expansion

Abstract

When knowledge of material design parameters is lacking, it is important to understand how this uncertainty effects the system response. Generalized polynomial chaos (gPC) expansions provide a means for quantifying this uncertainty and typically show good agreement with Monte Carlo techniques at a much reduced cost [K. Sepahvand et al. / Applied Acoustics 87 (2015) 23-29]. In this work, we apply gPC expansions to study the effects of design parameter uncertainty on a structure’s modal characteristics—both eigenvalues and eigenfunctions. The gPC expansions permit the propagation of uncertainty from the design parameters to the modes and natural frequencies, which then characterize the vibration response of the system as a function of the random parameters. The response uncertainty can then be described using the solutions of the deterministic system sampled carefully over the parameter space. Uncertainty in the forcing function can also be included in this formulation. Numerical calculations demonstrate these techniques to predict the structural acoustic uncertainty of a vibrating plate with the results validated against Monte Carlo simulations. The effects of uncertain forcing functions will also be discussed.