`Shock and VibrationVolume 19, Issue 4, Pages 609-617http://dx.doi.org/10.3233/SAV-2011-0654`

## Analysis of Nonlinear Structural Dynamics and Resonance in Trees

H. Doumiri Ganji,1 S.S. Ganji,1 D.D. Ganji,2 and F. Vaseghi3

1Young Researchers Club, Science and Research Branch, Islamic Azad University, Tehran, Iran
2Department of Mechanical Engineering, Babol University of Technology, Babol, Iran
3Department of Industerial Engineering, Iran University of Science and Technology, Tehran, Iran

Received 23 January 2011; Revised 17 August 2011

Copyright © 2012 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Wind and gravity both impact trees in storms, but wind loads greatly exceed gravity loads in most situations. Complex behavior of trees in windstorms is gradually turning into a controversial concern among ecological engineers. To better understand the effects of nonlinear behavior of trees, the dynamic forces on tree structures during periods of high winds have been examined as a mass-spring system. In fact, the simulated dynamic forces created by strong winds are studied in order to determine the responses of the trees to such dynamic loads. Many of such nonlinear differential equations are complicated to solve. Therefore, this paper focuses on an accurate and simple solution, Differential Transformation Method (DTM), to solve the derived equation. In this regard, the concept of differential transformation is briefly introduced. The approximate solution to this equation is calculated in the form of a series with easily computable terms. Then, the method has been employed to achieve an acceptable solution to the presented nonlinear differential equation. To verify the accuracy of the proposed method, the obtained results from DTM are compared with those from the numerical solution. The results reveal that this method gives successive approximations of high accuracy solution.