Free vibration of laminated composite plate and shell structures for constant and variable thickness

Abstract

This study is conducted to analyse the free vibration of rectangular plates, circular plates and conical shells of anti-symmetric angle-ply laminated composite using classical theory, first order shear deformation theory and third order shear deformation theory of constant and variable thickness. The variations of thickness used are in the form of linear, exponential and sinusoidal. Free vibration of conical shells with constant thickness is investigated under classical theory. An extended study has been done by using developed shell theories where shear deformation is included. Free vibration of circular plates of variable thickness is analysed under first order shear deformation theory. Using the same theory, the free vibration analysis of conical shells for variable thickness is conducted. Third order shear deformation theory is adopted to the study of free vibration of rectangular plates for variable thickness. In this study, stress resultants and strain-displacement relations are substituted into the governing equation of structures. The solution is assumed to be separable in the form of displacement and rotational functions to obtain ordinary differential. The displacement and rotational functions are approximated using spline method. The obtained equations together with equations of boundary conditions are reduced to eigenvalue problem. The solutions of the eigenvalue problems are the frequencies of the plates and shells. The effects of boundary conditions, aspect ratio, side-to-thickness ratio, ply angle, number of layers, circumferential node number, variable thickness, cone angle, length ratio and radii ratio on the vibration of structures are investigated. The results show that the frequencies are higher for clamped-clamped boundary conditions than simply-supported and clamped-free boundary conditions. Also, it is found that the geometric parameters affect the vibration of structures.