An analytical framework for broadband dynamic analysis of plate built-up structures with uncertain viscoelastic boundary or connection conditions

Abstract

This paper proposes an analytical stochastic spectral dynamic stiffness method (SSDSM) for free and forced vibration analysis of plate built-up structures subject to uncertain viscoelastic boundary or connection conditions (BCs or CCs). First, a recently developed spectral dynamic stiffness (SDS) theory for broadband vibration analysis of plate built-up structure with arbitrary spatially-varying viscoelastic BCs or CCs is extended to model deterministic viscoelastic BCs or CCs. Then, uncertain viscoelastic BCs or CCs are described by random fields in stiffness and damping, which are discretized by Karhunen–Loève expansion. By using the modified Fourier series as the shape functions for the BCs or CCs, the analytical SSDS matrices of the uncertain viscoelastic BCs or CCs are developed. Then, those SSDS matrices are superposed directly to the SDS matrix of the plate built-up structure. For the solution technique, the extended Wittrick–Williams algorithm is used for stochastic eigenvalue analysis, whereas two different methods are proposed for stochastic response analysis. Representative examples are chosen to validate and demonstrate the superiorities of the proposed method. The proposed method retains all the advantages of the SDS method which is highly efficient and accurate within the whole frequency range. Meanwhile, the proposed method also provides a feasible technique for stochastic broadband dynamic analysis of plate-like structures subject to uncertain boundary or connection conditions.