Stochastic Nonlinear Vibration of Fluid-Loaded Double-Walled Carbon Nanotubes

Abstract:

This paper investigates the stochastic dynamic behaviors of nonlinear vibration of the fluid-loaded double-walled carbon nanotubes (DWCNTs) by considering the effects of the geometric nonlinearity and the nonlinearity of van der Waals (vdW) force. The nonlinear governing equations of the fluid-conveying DWCNTs are formulated based on the Hamilton’s principle. The Young’s modulus of elasticity of the DWCNTs is assumed as stochastic with respect to the position to actually describe the random material properties of the DWCNTs. By utilizing the perturbation technique, the nonlinear governing equations of the fluid-conveying can be decomposed into two sets of nonlinear differential equations involving the mean value of the displacement and the first variation of the displacement separately. Then we adopt the harmonic balance method in conjunction with Galerkin’s method to solve the nonlinear differential equations successively. Some statistical dynamic response of the DWCNTs such as the mean values and standard deviations of the amplitude of the displacement are computed. It is concluded that the mean value and standard deviation of the amplitude of the displacement increase nonlinearly with the increase of the frequencies.

• Periodical: Applied Mechanics and Materials (Volumes 284-287)
• Pages: 362-366
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.284-287.362
• Online since: January 2013
• Authors: Tai Ping Chang
• Keywords: Fluid-Loaded Double-Walled Carbon Nanotubes, Galerkin’s Method, Nonlinear Vibration, Random Material Properties

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