In the current paper a frequency analysis is performed for functionally graded material (FGM) circular cylindrical shells. A comparative study of shell frequencies is given for algebraic polynomial, exponential, and trigonometric volume fraction laws. An FGM shell considered here is structured from two materials. Love's thin shell theory is utilized for strain-displacement and curvature-displacement relations. The Rayleigh-Ritz method is employed to derive the frequency equation in the form of eigenvalue problem. Natural frequencies are evaluated for a shell with simply supported edge conditions. The axial modal dependence is approximated by circular trigonometric functions. Theoretical results are compared with those available in the literature for the validity of the present methodology.

No abstract

In the present study, a vibration frequency analysis of a bi-layered cylindrical shell composed of two independent functionally graded layers is presented. The thickness of the shell layers is assumed to be equal and constant. Material properties of the constituents of bi-layered functionally graded cylindrical shell are assumed to vary smoothly and continuously through the thickness of the layers of the shell and are controlled by volume fraction power law distribution. The expressions for strain-displacement and curvature-displacement relationships are utilized from Love's first approximation linear thin shell theory. The versatile Rayleigh-Ritz approach is employed to formulate the frequency equations in the form of eigenvalue problem. Influence of material distribution in the two functionally graded layers of the cylindrical shells is investigated on shell natural frequencies for various shell parameters with simply supported end conditions. To check the validity, accuracy and efficiency of the present methodology, results obtained are compared with those available in the literature.

In this article vibration frequencies of functionally graded circular cylindrical shells are analysed and studied using the Ritz formulation. Since closed-form solutions are limited to simple cases, an approximate method is employed to solve the shell problem, and numerical evaluation is carried out using a direct variational method. Axial modal dependence is chosen in terms of Ritz polynomials to ascertain a rapid convergence of the method. Sanders and Budiansky's thin shell theory is utilized for strain-displacement and curvature-displacement relations. Functionally graded material characteristics for the constituent materials are distributed in accordance with a volume fraction law. Influence of boundary conditions and volume fraction exponents on the vibration frequency spectra is analysed. The present results are compared with some previous works and excellent agreement is found.

The vibration characteristics of a functionally graded material circular cylindrical shell filled with fluid are examined with a wave propagation approach. The shell is filled with an incompressible non-viscous fluid. Axial modal dependence is approximated by exponential functions. A theoretical study of shell vibration frequencies is analyzed for simply supported-simply supported, clamped-simply supported, and clamped-clamped boundary conditions with the fluid effect. The validity and the accuracy of the present method are confirmed by comparing the present results with those available in the literature. Good agreement is observed between the two sets of results.