Free vibration analysis of functionally graded porous elliptical microshells using modified couple stress theory

Abstract

In this study, the free vibration analysis of functionally graded porous (FGP) elliptical microshells was studied for the first time. The microshell was modeled based on Donnell's shell theory along with modified coupled stress theory (MCST). The set of the governing equations were derived using Hamilton's principle and were solved via the Galerkin's method. The accuracy of the presented model was confirmed and the effects on the natural frequencies of the microshell are investigated such as porosity parameter, porosity distribution pattern, length scale parameter, geometrical parameters of the microshell, and the circumferential wave number (n). Numerical results show that for n = 1, the length scale parameter has no considerable effect on the natural frequencies, but for n > 1, the natural frequencies grow by increasing the length scale parameter. Also, it is shown that the effect of length scale parameter on the natural frequencies grows the higher values of elliptical ratio (large-to-small radii ratio).