On the free and forced vibrations of porous GPL reinforced composite conical panels using a Legendre-Ritz method

Abstract

An analysis is conducted in the present investigation to study the free and forced vibration characteristics of composite laminated conical panels. It is assumed that composite panel is reinforced with graphene platelets (GPLs) where the amount of GPLs may be different between the layers which results in a piecewise functionally graded media. In addition, the effect of uniform and non-uniform porosities is also included into the formulation. The elasticity modulus of the media is estimated following the Halpin-Tsai rule while the simple rule of mixtures approach is applied to obtain the mass density and Poisson's ratio on the panel. With the aid of the first order shear deformation theory of shells and Donnell kinematics, definition of strain, kinetic and potential energy of applied loads is given. After that with the general idea of Ritz method suitable for arbitrary types of boundary conditions and Legendre polynomials as the basic functions, the energies are discreted which results in the general form of the equations of motion. While standard eigenvalue solution is applied to obtain the natural frequencies, a Newmark time marching method is implemented to obtain the temporal evolution of displacement of the panel. Results of this study are well-compared with the available data in the open literature and after that novel results on the present study are provided in the form of figures and tables. It is highlighted that type of porosity and graded pattern of GPLs are both important on the frequencies and dynamic deflection of the panel.