An experimental and numerical dynamic study of thick sandwich beams using a mixed {3,2}-RZT formulation

This work presents some numerical and experimental validations of the free-vibration behaviour of thick sandwich beams using the mixed {3,2}-Refined Zigzag Theory. The formulation enhances the Timoshenko’s kinematics with a piece-wise zigzag cubic distribution of the axial displacement, and a smoothed parabolic variation for the transverse deflection. Simultaneously, an a-priori assumption is made for the transverse normal stress and the transverse shear one: the former is assumed to be a third-order power series expansion of the thickness coordinate, the latter is derived through the integration of the Cauchy’s equations. The equations of motions and consistent boundary conditions for the free-vibration problem are derived through the Hellinger-Reissner (HR) theorem. Taking advantage of the C0-continuity requirement in the mixed governing functional, a simple two-node beam finite element (FE) is formulated. The analytical and FE performances of the proposed model are first addressed by means of a comparison with high-fidelity 3D FE models. Subsequently, an experimental campaign is conducted using LASER Doppler Vibrometry (LVD) to evaluate the modal parameters of a series of thick sandwich beams made of aluminium alloy face-sheets and Rohacell WF110 core. The experimental results concerning the natural frequencies and modal shapes of the thick sandwich beam specimens under free-free boundary conditions are compared with those given by the proposed model and high-fidelity 3D FE models. The numerical-experimental assessment highlights the effect of core and face-sheet thickness on frequency estimations, as well as the complexity of reproducing in the numerical model the real boundary conditions. In general, the element formulation demonstrates its accuracy and computational advantages in the dynamic analysis of thick sandwich beams.