Model reduction and perturbation analysis of wave finite element formulations for computing the forced response of coupled elastic systems involving junctions with uncertain eigenfrequencies

The wave finite element method is investigated for computing the low- and mid-frequency forced response of coupled elastic systems involving straight structures with junctions. The relevance of the method is discussed when a component mode synthesis procedure is used for modeling the junctions. A norm-wise selection criterion is proposed so as to reduce efficiently the number of junction modes retained in the wave-based formulations. Component-wise perturbation bounds of the wave-based displacement/force solutions are also derived to address slight uncertainties for the junction eigenfrequencies. Numerical comparisons with standard finite element solutions as well as Monte Carlo simulations highlight the relevance of the formulation.