Analytical and finite element modeling of laminated composite and sandwich plates: An assessment of a new shear deformation theory for free vibration response

Recently developed inverse hyperbolic shear deformation theory by the authors is extended to analyze the free vibration response of laminated composite and sandwich plates. Euler–Lagrange equations are derived employing the principle of virtual work for the dynamic problem. A Navier type and finite element solutions are proposed to obtain the free vibration response of laminated composite and sandwich plates. A C0-continuous isoparametric biquadratic-quadrilateral serendipity element is used for the finite element solution of generalized higher order shear deformation theory so as to ensure its applicability to general laminates subjected to different combinations of boundary conditions. Higher modes of vibration are obtained for laminated cross-ply and angle-ply plates and efficiency of the theory is ensured by comparing the results with the existing results. It is observed that both analytical and finite element solutions with the present theory are capable for accurate prediction of the free vibration response.