Conical-Shaped Shells of Non-Uniform Thickness Vibration Analysis Using Higher-Order Shear Deformation Theory

Abstract

The aim of this research is to investigate the frequency of conical-shaped shells, consisting of different materials, based on higher-order shear deformation theory (HSDT). The shells are of non-uniform thickness, consisting of two to six symmetric cross-ply layers. Simply supported boundary conditions were used to analyse the frequency of conical-shaped shells. The differential equations, consisting of displacement and rotational functions, were approximated using spline approximation. A generalised eigenvalue problem was obtained and solved numerically for an eigenfrequency parameter and associated eigenvector of spline coefficients. The frequency of shells was analysed by varying the geometric parameters such as length of shell, cone angle, node number in circumference direction and number of layers, as well as three thickness variations such as linear, sinusoidal and exponential. It was also evident that by varying geometrical parameters, the mechanical parameters such as stress, moment and shear resultants were affected. Research results concluded that for three different thickness variations, as the number of layers of conical shells increases, the frequency values decrease. Moreover, by varying length ratios and cone angles, shells with variable thickness had lower frequency values compared to shells of constant thickness. The numerical results obtained were verified through the already existing literature. It is evident that the present results are very close to the already existing literature.

Keywords

• analysis
• vibration
• variable thickness
• eigenfrequency
• higher-order theory