Three dimensional wave propagation in axially loaded pressurized FG cylindrical shells using Frobenius power series and Rayleigh-Ritz methods

In the present study, the behavior of vibratory cylindrical shells composed of functionally graded material (FGM) containing copper and tungsten under internal pressure and axial compression loads is investigated. An exact solution of free harmonic wave propagation using the theory of three dimensional elasticity is extracted. Then, the dispersion equation is analyzed in conjunction with a Frobenius power series method and natural frequency (eigenvalue) of the shell is obtained using Rayleigh-Ritz method. Furthermore, the present analysis is validated by comparing results with those available in the literature

Dynamic Analysis and critical speed of rotating laminated conical shells with orthogonal stiffeners using generalized differential quadrature method

This paper presents effects of boundary conditions and axial loading on frequency characteristics of rotating laminated conical shells with meridional and circumferential stiffeners, i.e., stringers and rings, using Generalized Differential Quadrature Method (GDQM). Hamilton's principle is applied when the stiffeners are treated as discrete elements. The conical shells are stiffened at uniform intervals and it is assumed that the stiffeners have similar material and geometric properties. Equations of motion as well as equations of the boundary condition are transformed into a set of algebraic equations by applying the GDQM. Obtained results discuss the effects of parameters such as rotating velocities, depth to width ratios of the stiffeners, number of stiffeners, cone angles, and boundary conditions on natural frequency of the shell. The results will then be compared with those of other published works particularly with a non-stiffened conical shell and a special case where angle of the stiffened conical shell approaches zero, i.e. a stiffened cylindrical shell. In addition, another comparison is made with present FE method for a non-rotating stiffened conical shell. These comparisons confirm reliability of the present work as a measure to approximate solutions to the problem of rotating stiffened conical shells