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

Abstract

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 (${\text{RZT}}_{\left\{3,2\right\}}^{\left(m\right)}$). The ${\text{RZT}}_{\left\{3,2\right\}}^{\left(m\right)}$ 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, while the latter is derived through the integration of Cauchy's equations. The equations of motion 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, i.e., the $2B-{\text{RZT}}_{\left\{3,2\right\}}^{\left(m\right)}$ element. The analytical and FE performances of the proposed ${\text{RZT}}_{\left\{3,2\right\}}^{\left(m\right)}$ 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 (LDV) 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 ${\text{RZT}}_{\left\{3,2\right\}}^{\left(m\right)}$ 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 experimental uncertainties. In general, the $2B-{\text{RZT}}_{\left\{3,2\right\}}^{\left(m\right)}$ element formulation demonstrates its accuracy and computational advantages in the dynamic analysis of thick sandwich beams.