Abstract
The present paper proposes a linearised hybrid finite element-statistical energy analysis (FE-SEA) formulation for built-up systems with nonlinear joints and excited by random, as well as harmonic, loadings. The new formulation was validated via an ad-hoc developed stochastic benchmark model. The latter was derived through the combination of the Lagrange-Rayleigh-Ritz method (LRRM) and the Monte Carlo simulation (MCS). Within the build-up plate systems, each plate component was modelled by using the classical Kirchhoff’s thin-plate theory. The linearisation processes were carried out according to the loading-type. In the case of random loading, the statistical linearisation (SL) was employed, while, in the case of harmonic loading, the method of harmonic balance (MHB) was used. To demonstrate the effectiveness of the proposed hybrid FE-SEA formulation, three different case studies, made-up of built-up systems with localized cubic nonlinearities, were considered. Both translational and torsional springs, as joint components, were employed. Four different types of loadings were taken into account: harmonic/random point and distributed loadings. The response of the dynamic systems was investigated in terms of ensemble average of the time-averaged energy.
Highlights
Manufacture uncertainties are widespread in various industrial applications, e.g., aerospace, civil, mechanical, and marine engineering
K where q is the general displacement vector of FE parts under the frequency of ω; f represents the external forces vector exerted to the FE components; frkev is the forces vector resulting from the reverberant field in k-th subsystem; Dd corresponds to the dynamic stiffness matrix of the deterministic components; and Dkdir is the the dynamic stiffness matrix arising from k-th direct field
The average energy of Lagrange-Rayleigh-Ritz method (LRRM)+Monte Carlo simulation (MCS) analysis fluctuates dramatically in lower-frequency range but tends to keep stable and close to the response obtained by using the hybrid finite element-statistical energy analysis (FE-statistical energy analysis (SEA)) formulation in higher-frequency range
Summary
Manufacture uncertainties are widespread in various industrial applications, e.g., aerospace, civil, mechanical, and marine engineering. To realize the response prediction on the overall frequency range, hybrid finite element-statistical energy analysis (FE-SEA) models based on either modal approach or wave approach were proposed by Langley [4,5]. The traditional SEA assumes that the external input is the rain-on-the-roof type, which is a both spatial- and tempo-uncorrelated distributed loading This assumption is consistent with many engineering applications, e.g., those which involve fluid-structure interaction loading-type affected by randomness. Vibration 2020, 3 on the energy response of nonlinear dynamic systems subjected to random loading. Nonlinear dynamic systems with localized cubic nonlinearities introduced by translational and torsional springs, as joint components, are taken into account Both harmonic and random loading-types are considered, and both point or distributed loadings are applied. The response of the dynamic systems was examined in terms of ensemble average of the time-averaged energy
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