Analytical solutions using a higher order refined computational model with 12 degrees of freedom for the free vibration analysis of antisymmetric angle-ply plates

Analytical formulations and solutions to the natural frequency analysis of simply supported antisymmetric angle-ply composite and sandwich plates hitherto not reported in the literature based on a higher order refined computational model with 12 degrees of freedom 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, another higher order computational model with five degrees of freedom already available in the literature is also considered for comparison. The equations of motion are obtained using Hamilton's principle. Solutions are obtained in closed-form using Navier's technique by solving the eigenvalue equation. Plates with varying slenderness ratios, number of layers, degrees of anisotropy, edge ratios and thickness of core to thickness of face sheet ratios are considered for analysis. Numerical results with real properties using above two computational models are presented and compared for the free vibration analysis of multilayer antisymmetric angle-ply composite and sandwich plates, which will serve as a benchmark for future investigations.