Linear and nonlinear torsional free vibration of functionally graded micro/nano-tubes based on modified couple stress theory

doi:10.1007/s10483-016-2085-6

摘要/Abstract

摘要：

The linear and nonlinear torsional free vibration analyses of functionally graded micro/nano-tubes (FGMTs) are analytically investigated based on the couple stress theory. The employed non-classical continuum theory contains one material length scale parameter, which can capture the small scale effect. The FGMT model accounts for the through-radius power-law variation of a two-constituent material. Hamilton's principle is used to develop the non-classical nonlinear governing equation. To study the effect of the boundary conditions, two types of end conditions, i.e., fixed-fixed and fixed-free, are considered. The derived boundary value governing equation is of the fourthorder, and is solved by the homotopy analysis method (HAM). This method is based on the Taylor series with an embedded parameter, and is capable of providing very good approximations by means of only a few terms, if the initial guess and the auxiliary linear operator are properly selected. The analytical expressions are developed for the linear and nonlinear natural frequencies, which can be conveniently used to investigate the effects of the dimensionless length scale parameter, the material gradient index, and the vibration amplitude on the natural frequencies of FGMTs.

关键词: functionally graded material (FGM), couple stress theory, micro/nano-tube, size effect, torsional vibration, nonlinear vibration

Abstract:

Key words: size effect, nonlinear vibration, torsional vibration, functionally graded material (FGM), couple stress theory, micro/nano-tube

中图分类号:

74B10
74B20

A. R. SETOODEH, M. REZAEI, M. R. ZENDEHDEL SHAHRI. Linear and nonlinear torsional free vibration of functionally graded micro/nano-tubes based on modified couple stress theory[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(6): 725-740.

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