Frequency response functions of discretized structural systems with uncertain parameters

A procedure for deriving in explicit approximate form the frequency response function (FRF) of linear discretized structures with uncertain stiffness properties is presented. The proposed procedure is based on the following main steps: i) to perform the spectral decomposition of the deviation of the stiffness matrix (with respect to its nominal value) so as to obtain a sum of rank-one matrices, each one associated to a single uncertain parameter; ii) to project the equations of motion in the modal subspace; iii) to introduce a novel series expansion of the FRF in the modal subspace which provides an approximate, but explicit, expression of the FRF of structural systems with uncertain parameters. The potential of the proposed series expansion are demonstrated in the context of the so-called improved interval analysis by determining the range of the modulus of the FRF of structures with uncertain-but-bounded parameters.