VIBRATION ANALYSIS OF A NANOTUBE SUPPLIED WITH FLUID IN SOME DIFFERENT BOUNDARY

vibration modeling of carbon nanotubes comes with nonlinear equations which are difficult to solve exactly and analytically with any existing general analytical method. However, in many cases of developing symbolic solutions for the nonlinear equations, recourse is made to approximate analytical methods in which their accuracies largely depend on the number of terms included in the solutions. In this work, analytical solutions are presented using differential transformation method with after-treatment technique for nonlinear analysis of vibration and flow-induced vibration of fluid-conveying carbon nanotube resting on Winkler and Pasternak foundations. The developed analytical solutions are used to investigate the effects of nonlocal parameter, Knudsen number, temperature, foundation parameters and boundary conditions on the dynamic behaviour of the single-walled nanotube. Also, the developed analytical solutions are verified with the numerical solutions and validated with experimental results. Good agreements are established between the results of the analytical solutions and the numerical solutions, and also between the results of the analytical solutions and the experimental results. The analytical solutions as presented in this work can serve as benchmarks for other methods of solutions of the problem. They can also provide a starting point for a better understanding of the relationship between the physical quantities of the problems.