EIGENFREQUENCY ANALYSIS OF COMPLETELY FREE MULTILAYERED RECTANGULAR-PLATES USING A HIGHER-ORDER MODEL AND RITZ TECHNIQUE

A numerical model for the analysis of the free vibration of multilayer ed, fully free rectangular plates with arbitrary layups is proposed. T he model is eased on a displacement field that assumes a nonlinear dis tribution of the in-plane displacements with respect to the thickness coordinate and a transverse displacement that is constant through the plate thickness. The displacement field accounts for a parabolic distr ibution of the transverse shear strains and satisfies Be condition of zero transverse shear stresses on the top and bottom surfaces of the p late. The mathematical problem is solved by the Ritz technique, which relies on the minimization of the maximum Lagrangian functional; using a displacement field defined by beam functions in the form of finite series with undetermined parameters. The required mathematical operati ons for the development of the eigenvalue problem are carried out by s ymbolic manipulation By deleting the higher-order terms of Reddy's dis placement field or assuming the Love-Kirchhoff hypothesis, the first-o rder shear deformation and the classical plate theory models, respecti vely are also obtained These models are used to analyze several lamina ted composite plate problems, and the eigenfrequency results are compa red among them and with alternative solutions.