Nonlinear Analysis of Flow-induced Vibration in Fluid-conveying Structures using Differential Transformation Method with Cosine-Aftertreatment Technique

In this work, analytical solutions are provided to the nonlinear equations arising in thermal and flow-induced vibration in fluid-conveying structures using Galerkin-differential transformation method with cosine aftertreatment technique. From the analysis, it was established that increase of the length and aspect ratio of the fluid-conveying structures result in decrease the nonlinear vibration frequencies of the structure while increase in the fluid-flow velocity causes increase in nonlinear vibration frequencies of the structures. Also, increase in the slip parameter leads to decrease in the frequency of vibration of the structure and the critical velocity of the conveyed fluid while increase in the slip parameter leads to decrease in the dimensionless frequency ratio of vibration of the structure. As the Knudsen number increases, the bending stiffness of the nanotube decreases and in consequent, the critical continuum flow velocity decreases as the curves shift to the lowest frequency zone. Good agreement are established when the results of the differential transformation method are compared with the results of the numerical method and exact analytical method for the non-linear and linear models, respectively.