Analytical solutions for free vibration of laminated composite and sandwich plates based on a higher-order refined theory

Analytical formulations and solutions to the natural frequency analysis of simply supported composite and sandwich plates hitherto not reported in the literature based on a higher-order refined theory developed by the first author and already reported in the literature are presented. The theoretical model presented herein incorporates laminate deformations which account for the effects of transverse shear deformation, transverse normal strain/stress and a nonlinear variation of in-plane displacements with respect to the thickness coordinate ¯ thus modelling the warping of transverse cross-sections more accurately and eliminating the need for shear correction coefficients. In addition, few higher-order theories and the first-order theory developed by other investigators and already available in the literature are also considered for the evaluation. The equations of motion are obtained using Hamiltonʹs principle. Solutions are obtained in closed form using Navierʹs technique and by solving the eigenvalue equation. The comparison of the present results with the available elasticity solutions and the results computed independently using the first-order and the other higher-order theories available in the literature shows that this refined theory predicts the fundamental and higher frequencies more accurately than all other theories considered in this paper. After establishing the accuracy of present results for composite plates, new results for sandwich laminates using all the theories considered in this paper are also presented which may serve as a benchmark for future investigations.