Vibration characteristics of composite/sandwich laminates with piezoelectric layers using a refined hybrid plate model

The free vibration characteristics of laminated composite and sandwich plates with embedded and/or surface-bonded piezoelectric layers is studied, where a hybrid plate theory is proposed for modelling the structural system. It involves a problem of coupled electro-mechanical field. The variation of mechanical/structural displacements across the thickness are modelled by an efficient plate theory, which ensures inter-laminar shear stress continuity as well as stress free condition at the plate top and bottom surfaces. At the same time, this plate model has the distinct advantage of involving unknowns at the reference plane (plate mid-plane) only. For the electrical potential, the through thickness variation is modelled by the layer-wise theory, where the unknowns are taken at all the interfaces including top and bottom surfaces of the plate. However, the degrees of freedom for the electric potential are finally eliminated from the element matrices through condensation. In order to have generality in analysis, the finite element technique is used to approximate the in-plane variation of displacement parameters at the reference plane and electric potential at the different interfaces. For this purpose, an attempt has been made to develop a simple and efficient rectangular element, which satisfies C1 continuity of transverse displacement at the inter-element boundaries. To validate the proposed model, some numerical examples are solved and the results obtained are compared to the published results. As the number of such published results is not sufficient, new examples covering various features are solved to study different aspects of the proposed model.