A hybrid finite element-statistical energy analysis approach for the dynamic response of built-up systems with nonlinear joints

Abstract

The present article deals with the development and validation of a hybrid finite element-statistical energy analysis (FE-SEA) formulation employed to obtain the ensemble-average of the time-averaged vibrational energy response of dynamic systems with nonlinear joints. The proposed FE-SEA formulation is validated via a nonlinear stochastic benchmark model. The theoretical formulation related to the latter, is entirely derived by employing a variational approach. The weak-form of the governing equations, for each of the sample in the ensemble, is based on Kirchhoff’s thin-plate assumptions and is restricted to the out-of-plane motion only. The classical Lagrange-Rayleigh-Ritz method (LRRM), combined with the Monte Carlo simulation (MCS), is used as solution technique. An appropriate degree of uncertainty is introduced into the model in order to break the system symmetries ensuring transition from an exponential to a Rayleigh distribution of the modal spacing. Both in the hybrid FE-SEA and in the LRRM+MCS the localised nonlinearities are linearised by means of the method of harmonic balance. Various built-up plate systems, consisting of rectangular isotropic, homogeneous and linear elastic plates, elastically coupled by virtue of nonlinear translational and/or torsional springs and subjected to harmonic point loads are investigated.