Nonlinear vibrations of fluid-filled functionally graded cylindrical shell considering a time-dependent lateral load and static preload

Abstract

In the recent years, functionally gradient materials (FGMs) have gained considerable attention with possible applications in several engineering fields, especially in a high-temperature or hazardous environment. In this work, the nonlinear vibrations of a simply supported fluid-filled functionally graded cylindrical shell subjected to a lateral time-dependent load and axial static preload are analyzed. To model the shell, the Donnell nonlinear shell theory is used. The fluid is assumed to be incompressible, nonviscous, and irrotational. A new function to describe the variation in the volume fraction of the constituent material through the shell thickness is proposed, extending the concept of sandwich structures to a functionally graded material. Material properties are graded along the shell thickness according to the proposed volume fraction power law distribution. A consistent reduced order model derived from a perturbation technique is used to describe the displacements of the shell and, the Galerkin method is applied to derive a set of coupled nonlinear ordinary differential equations of motion. Results show the influence of the variation of the two constituent materials along the shell thickness, internal fluid, static preload, and shell geometry on the natural frequencies, nonlinear frequencyamplitude relation, resonance curves, and bifurcation scenario of the FG cylindrical shell.

Dynamic Stability of Bi-Directional Functionally Graded Porous Cylindrical Shells Embedded in an Elastic Foundation

“…where the symbol δ denotes the variation of the energy quantities. By combination of Equations (8)- (10) and Equation 11, after integration by parts, we get the following governing equations of motion, under the assumption of a null value for u 0 , v 0 , w 0 , ϕ x , and ϕ y .…”

“…Beni et al [9] presented a novel formulation based on a modified couple stress theory to study simply supported FG circular cylindrical shells in the framework of thin shell structures, whereby the vibration behavior based on a classical continuum was found to be quite unaffected by the length scale parameters. Da Silva et al [10] studied the nonlinear vibrations of a simply supported fluid-filled FG cylindrical shell subjected to a lateral time-dependent load and an axial static preloading condition. Bich and Nguyen [11] applied the displacement method to study the nonlinear vibration of FG circular cylindrical shells subjected to an axial and transverse mechanical loading.…”

Nonlinear dynamic buckling of full-filled fluid sandwich FGM circular cylinder shells

“…Wave propagation approach was employed to calculate. Silva et al [17] studied nonlinear responses of fluid-filled FG circular cylinder shell under mechanical load. Recently, Hong-Liang Dai et al [18] analyzed thermos electro elastic behaviors of a fluid-filled functionally graded piezoelectric material cylindrical thin-shell under the combination of mechanical, thermal and electrical loads.…”