A multiscale “Trefftz” computational method for medium-frequency vibrations of assemblies of heterogeneous plates with uncertainties

Abstract

A new approach, called the “Variational Theory of Complex Rays”, is being developed for the calculation of the vibrations of slightly damped elastic plates in the medium-frequency range. In this approach, the resolution of a small system of equations which does not result from a refined spatial discretization of the structure leads to the evaluation of effective quantities (deformation energy, vibration amplitude, …). This theory has already been validated for assemblies of homogeneous substructures and extended to the case of heterogeneous substructures. In this paper, we propose some improvements to deal with sensitivity analysis. The objective is to evaluate the influence of discontinuities with uncertain positions, sizes or directions on the structural response. A specific partial inversion of the constrained system of equations enables multiple resolutions for combinations of the parameters defining the possible shapes of the discontinuity to be carried out at low cost.