Affiliations: Young Researchers Club, Science and Research Branch,
Islamic Azad University, Tehran, Iran | Department of Mechanical Engineering, Babol University
of Technology, Babol, Iran | Department of Industerial Engineering, Iran University
of Science and Technology, Tehran, Iran
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.
