### Analysis of Nonlinear Dynamic Behaviour of Nanobeam resting on Winkler and Pasternak Foundations

#### Abstract

Dynamic modeling of nanobeam under stretching and two-parameter foundation effects result in nonlinear equations that are very difficult to find exact analytical solutions. In this study, variation iteration method is used to develop approximate analytical solutions to nonlinear vibration analysis of nanobeam under the effects of stretching and Winkler and Pasternak foundations. The governing equation of motion for the nanotube was derived based on Euler-Bernoulli beam theory. The developed approximate analytical solutions for the governing equation are validated the results of other methods of analysis, are also used to carry out effects of some model parameters on the dynamic behaviour of the nanobeam. These analytical solutions can serve as a starting point for a better understanding of the relationship between the physical quantities in the problems as it provides clearer insights to understanding the problems in comparison with numerical methods.

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