# Nonlinear vibration analysis of the fluid-filled single walled carbon nanotube with the shell model based on the nonlocal elacticity theory

P. Soltani, R. Bahramian, J. Saberian

Research output: Contribution to journalArticle

### Abstract

Nonlinear vibration of a fluid-filled single walled carbon nanotube (SWCNT) with simply supported ends is investigated in this paper based on Von-Karman's geometric nonlinearity and the simplified Donnell's shell theory. The effects of the small scales are considered by using the nonlocal theory and the Galerkin's procedure is used to discretize partial differential equations of the governing into the ordinary differential equations of motion. To achieve an analytical solution, the method of averaging is successfully applied to the nonlinear governing equation of motion. The SWCNT is assumed to be filled by the fluid (water) and the fluid is presumed to be an ideal non compression, non rotation and in viscid type. The fluid-structure interaction is described by the linear potential flow theory. An analytical formula was obtained for the nonlinear model and the effects of an internal fluid on the coupling vibration of the SWCNT-fluid system with the different aspect ratios and the different nonlinear parameters are discussed in detail. Furthermore, the influence of the different nonlocal parameters on the nonlinear vibration frequencies is investigated according to the nonlocal Eringen's elasticity theory.

Original language English 5 58-70 13 Journal of Solid Mechanics 7 1 Published - 2015 Yes

### Fingerprint

Vibration analysis
Single-walled carbon nanotubes (SWCN)
Fluids
Equations of motion
Fluid structure interaction
Potential flow
Nonlinear equations
Ordinary differential equations
Partial differential equations
Aspect ratio
Elasticity
Compaction
Water

### Keywords

• Donnell's shell model
• Fluid-filled swcnt
• Nonlinear vibration
• Nonlocal parameter

### ASJC Scopus subject areas

• Mechanics of Materials
• Mechanical Engineering

### Cite this

In: Journal of Solid Mechanics, Vol. 7, No. 1, 5, 2015, p. 58-70.

Research output: Contribution to journalArticle

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N2 - Nonlinear vibration of a fluid-filled single walled carbon nanotube (SWCNT) with simply supported ends is investigated in this paper based on Von-Karman's geometric nonlinearity and the simplified Donnell's shell theory. The effects of the small scales are considered by using the nonlocal theory and the Galerkin's procedure is used to discretize partial differential equations of the governing into the ordinary differential equations of motion. To achieve an analytical solution, the method of averaging is successfully applied to the nonlinear governing equation of motion. The SWCNT is assumed to be filled by the fluid (water) and the fluid is presumed to be an ideal non compression, non rotation and in viscid type. The fluid-structure interaction is described by the linear potential flow theory. An analytical formula was obtained for the nonlinear model and the effects of an internal fluid on the coupling vibration of the SWCNT-fluid system with the different aspect ratios and the different nonlinear parameters are discussed in detail. Furthermore, the influence of the different nonlocal parameters on the nonlinear vibration frequencies is investigated according to the nonlocal Eringen's elasticity theory.

AB - Nonlinear vibration of a fluid-filled single walled carbon nanotube (SWCNT) with simply supported ends is investigated in this paper based on Von-Karman's geometric nonlinearity and the simplified Donnell's shell theory. The effects of the small scales are considered by using the nonlocal theory and the Galerkin's procedure is used to discretize partial differential equations of the governing into the ordinary differential equations of motion. To achieve an analytical solution, the method of averaging is successfully applied to the nonlinear governing equation of motion. The SWCNT is assumed to be filled by the fluid (water) and the fluid is presumed to be an ideal non compression, non rotation and in viscid type. The fluid-structure interaction is described by the linear potential flow theory. An analytical formula was obtained for the nonlinear model and the effects of an internal fluid on the coupling vibration of the SWCNT-fluid system with the different aspect ratios and the different nonlinear parameters are discussed in detail. Furthermore, the influence of the different nonlocal parameters on the nonlinear vibration frequencies is investigated according to the nonlocal Eringen's elasticity theory.

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