Two-scale homogenisation-Chebyshev method for stochastic vibration analysis of heterogeneous core sandwich beams

Porous heterogeneous structures have attracted much attention due to their unique mechanical properties. In particular, lightweight sandwich beams composed of upper and lower skins bonded to a heterogeneous core layer have significant application value in aerospace, marine, and rail transit engineering. To address the issue of random dynamic loads encountered in these fields, this paper proposes a dual-scale homogenisation-Chebyshev method to study their random vibration characteristics. Firstly, the asymptotic homogenisation method in dual-scale analysis is used to obtain the effective material properties of the heterogeneous core layer. Secondly, based on three-dimensional linear elasticity theory, the kinetic energy, strain energy, interlaminar coupling potential energy, and external excitation work are established, and the boundary potential energy is constructed using the virtual spring technique, thereby obtaining the overall Lagrangian energy functional. Finally, Chebyshev polynomials are used to represent each displacement component and substituted into the functional for variation to obtain the vibration equations of the sandwich beam. Comparison with literature, finite element, and experimental results verifies the applicability and accuracy of the proposed method, and the influence of the geometric parameters of the core structure on the random vibration characteristics is further investigated.