Nonlinear dynamic responses of sandwich functionally graded porous cylindrical shells embedded in elastic media under 1:1 internal resonance. (English) Zbl 1480.74117
Summary: In this article, the nonlinear dynamic responses of sandwich functionally graded (FG) porous cylindrical shell embedded in elastic media are investigated. The shell studied here consists of three layers, of which the outer and inner skins are made of solid metal, while the core is FG porous metal foam. Partial differential equations are derived by utilizing the improved Donnell’s nonlinear shell theory and Hamilton’s principle. Afterwards, the Galerkin method is used to transform the governing equations into nonlinear ordinary differential equations, and an approximate analytical solution is obtained by using the multiple scales method. The effects of various system parameters, specifically, the radial load, core thickness, foam type, foam coefficient, structure damping, and Winkler-Pasternak foundation parameters on nonlinear internal resonance of the sandwich FG porous thin shells are evaluated.
MSC:
| 74H45 | Vibrations in dynamical problems in solid mechanics |
| 74K25 | Shells |
| 74E30 | Composite and mixture properties |
| 74E05 | Inhomogeneity in solid mechanics |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 74H15 | Numerical approximation of solutions of dynamical problems in solid mechanics |
Keywords:
internal resonance; sandwich functionally graded porous shell; refined Donnell shell theory; multiple scales method; Galerkin methodReferences:
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