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 (RZT 3, 2 (m) ). The RZT 3, 2 (m) 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 C 0 -continuity requirement in the mixed governing functional, a simple two-node beam finite element (FE) is formulated, i. e. , the 2 B − RZT 3, 2 (m) element. The analytical and FE performances of the proposed RZT 3, 2 (m) 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 RZT 3, 2 (m) 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 2 B − RZT 3, 2 (m) element formulation demonstrates its accuracy and computational advantages in the dynamic analysis of thick sandwich beams.