In this paper, vibration characteristics of rotating functionally graded cylindrical shell resting on Winkler and Pasternak elastic foundations have been investigated. These shells are fabricated from functionally graded materials. Shell dynamical equations are derived by using the Hamilton variational principle and the Langrangian functional framed from the shell strain and kinetic energy expressions. Elastic foundations, namely Winkler and Pasternak moduli are inducted in the tangential direction of the shell. The rotational motions of the shells are due to the Coriolis and centrifugal acceleration as well as the hoop tension produced in the rotating case. The wave propagation approach in standard eigenvalue form has been employed in order to derive the characteristic frequency equation describing the natural frequencies of vibration in rotating functionally graded cylindrical shell. The complex exponential functions, with the axial modal numbers that depend on the boundary conditions stated at edges of a cylindrical shell, have been used to compute the axial modal dependence. In our new investigation, frequency spectra are obtained for circumferential wave number, length-to-radius ratio, height-to-radius ratio with simply supported–simply supported and clamped–clamped boundary conditions without elastic foundation. Also, the effect of elastic foundation on the rotating cylindrical shells is examined with the simply supported–simply supported edge. To check the validity of the present method, the fundamental natural frequencies of non-rotating isotropic and functionally graded cylindrical shells are compared with the open literature. Also, a comparison is made for infinitely long rotating with the earlier published paper.
The stability problem of a circular cylindrical shell composed of functionally graded materials with elasticity modulus varying continuously in the thickness direction under combined external pressure and axial compression loads is studied in this paper. The formulation is based on the first-order shear deformation theory. A load interaction parameter is defined to express the combination of applied axial compression and external pressure. The stability equations are derived by the adjacent equilibrium criterion method. These equations are employed to analyze the buckling behavior and obtain the critical buckling loads. A detailed numerical study is carried out to bring out the effects of the power law index of functionally graded material, load interaction parameter, thickness ratio, and aspect ratio on the critical buckling loads. The validity of the present analysis was checked by comparing the present results with those results available in literature.
This paper presents a study on the vibration of a supported thick-walled cylindrical shell made of functionally graded material (FGM) subjected to pressure loading. The FGM shell is developed in accordance to the volume fraction law from two constituents, namely stainless steel and nickel. For the power law exponent distribution the top surface of the structure is steel/nickel-rich, whereas the bottom surface is nickel/steel-rich. The FGM properties are graded along the thickness direction of the shell. The supported FGM thick shell equations with one ring and pressure loading are established based on first-order shear deformation theory. The governing equations of motion were employed, using energy function and by applying the Ritz method. The boundary conditions represented by the end conditions of the FGM thick shell are simply supported–simply supported, clamped–clamped, free–free, clamped–free, clamped–simply supported, free–simply supported, sliding–free and sliding–clamped. The effects of the volume fraction law exponent, pressure loading, ring position and different boundary conditions on natural frequency characteristics are studied. The results obtained are compared with those available in the literature.
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