A three-dimensional theoretical model of free vibration for multifunctional sandwich plates with honeycomb-corrugated hybrid cores

Combining honeycomb and corrugation to construct a multifunctional hybrid core for all-metallic sandwich construction can significantly enhance not only its stiffness and strength but also energy absorption and sound absorption relative to its honeycomb or corrugated sandwich counterpart of equal mass. However, how hybridization affects its vibration characteristics remains poorly understood, especially from a theoretical point of view. To address this deficiency, this study develops a theoretical model based on three-dimensional (3D) elasticity such that the free vibration of a hybrid-cored sandwich plate with arbitrary boundary conditions can be systematically evaluated. Based on micromechanics analysis of the representative volume element, the effect of honeycomb-corrugated coupling is duly accounted and the incorrectly expressed equivalent constitutive of hexagonal honeycombs in previous studies are modified. The model is validated against 3D finite element simulations. The natural frequencies of a honeycomb-corrugated sandwich construction are consistently higher than its honeycomb or corrugated sandwich counterparts, due mainly to mechanisms: honeycomb filling suppresses local vibration of face sheets and corrugated members, and mutual constraint of honeycomb and corrugation enhance the flexural rigidity of hybrid core. The proposed theoretical model can be easily extended to analyze other cases, such as sound radiation and sound insulation of hybrid sandwiches.