An equivalent single-layer approach for free vibration analysis of smart laminated thick composite plates

An equivalent single-layer model for the free vibration analysis of smart laminated plates is presented. The electric and magnetic fields are assumed to be quasi-static, and third order in-plane kinematics is employed to adequately take the shear influence into account when the plate thickness increases. The model governing equations are the plate equations of motion written in terms of mechanical primary variables and effective stiffness coefficients, which take the multi-field coupling effects into account. The model shows that the surface magneto-electric boundary conditions enter the definitions of the laminate forces and moment resultants. Moreover, it reveals that new stiffness terms, which are related to the derivatives of the transverse displacement component and are exclusively associated with the piezoelectric and piezomagnetic couplings, are involved. Free vibration solutions for simply supported plates are presented to validate the model by comparing the present results with benchmark 3D solutions. Comparison of the results obtained by lower order models, namely zero and first order shear deformation theories, is presented and discussed, focusing on the adequateness of the obtained models with respect to the plate thickness. Some characteristic features of smart laminate behavior have also been addressed. (paper)