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 a uthor and already reported in the literature are presented. The theoretical model presented herein incorporates laminate deformations which account fo r the effects of transverse shear deformation, transverse normal strain/str ess and a nonlinear variation of in-plane displacements with respect to the thickness coordinate - thus modelling the warping of transverse cross-sect ions more accurately and eliminating the need for shear correction coeffici ents. In addition, few higher-order theories and the first-order theory dev eloped by other investigators and already available in the literature are a lso considered for the evaluation. The equations of motion are obtained usi ng Hamilton's principle. Solutions are obtained in closed form using Navier 's technique and by solving the eigenvalue equation. The comparison of the present results with the available elasticity solutions and the results com puted independently using the first-order and the other higher-order theori es 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 result s for composite plates, new results for sandwich laminates using all the th eories considered in this paper are also presented which may serve as a ben chmark for future investigations. (C) 2001 Elsevier Science Ltd. All rights reserved.