Vibration analysis of composite and sandwich plates reinforced with parabolic fibers using an alternative hierarchical finite element method

This paper presents a numerical method for determining natural frequencies and vibration modes of sandwich thick plates reinforced with parabolic fibers. The approach is based on the p-version finite element method with hierarchical trigonometric functions and Reddy’s high order shear deformation theory. The equations of motion of free vibration of thick composite laminated and sandwich plates are obtained based on Hamilton’s principle. A very fast convergence is obtained by increasing the number of hierarchical shape functions. The accuracy of the present method is established by a comparisons made between the present results and published results. The effects of boundary conditions, thickness ratio, material properties, and orientation angle on natural frequencies and normalized cross-sections of mode shape for sandwich plates reinforced with parabolic fibers are studied and investigated.