A modal strategy devoted to the hidden state variables method with large interfaces

Abstract

In many mechanical engineering applications, the interactions of a structure through its boundary is modelled by a dynamic boundary stiffness matrix. Nevertheless, it is well known that the solution of such computational model is very sensitive to the modelling uncertainties on the dynamic boundary stiffness matrix. In a recent work, the hidden state variables method is used to identify mass, stiffness and damping matrices associated with a given deterministic dynamic boundary stiffness matrix which can be constructed by using experimental measurements. Such an identification allows the construction of the probabilistic model of a random boundary stiffness matrix by substituting those identified mass, stiffness and damping matrices by random matrices. Nevertheless, the numerical cost of the hidden state variables method increases drastically with the dimension (number of degrees of freedom) of the interface. We then propose an enhanced approach which consists in a truncated spectral representation of the displacements on the boundary and with a partition of the frequency band of analysis. A collection of mass, stiffness and damping matrices is then identified for each sub-frequency band of analysis. A probabilistic model is constructed in substituting each of those matrices by random matrices. A numerical application is proposed.