Analysis of Nonlinear Structural Dynamics and Resonance in Trees

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 dyn...

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Main Authors: H. Doumiri Ganji, S.S. Ganji, D.D. Ganji, F. Vaseghi
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Shock and Vibration
Online Access:http://dx.doi.org/10.3233/SAV-2011-0654
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author H. Doumiri Ganji
S.S. Ganji
D.D. Ganji
F. Vaseghi
author_facet H. Doumiri Ganji
S.S. Ganji
D.D. Ganji
F. Vaseghi
author_sort H. Doumiri Ganji
collection DOAJ
description 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.
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institution Kabale University
issn 1070-9622
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language English
publishDate 2012-01-01
publisher Wiley
record_format Article
series Shock and Vibration
spelling doaj-art-859883721f8843df9ec50b66fffba6de2025-02-03T01:09:29ZengWileyShock and Vibration1070-96221875-92032012-01-0119460961710.3233/SAV-2011-0654Analysis of Nonlinear Structural Dynamics and Resonance in TreesH. Doumiri Ganji0S.S. Ganji1D.D. Ganji2F. Vaseghi3Young Researchers Club, Science and Research Branch, Islamic Azad University, Tehran, IranYoung Researchers Club, Science and Research Branch, Islamic Azad University, Tehran, IranDepartment of Mechanical Engineering, Babol University of Technology, Babol, IranDepartment of Industerial Engineering, Iran University of Science and Technology, Tehran, IranWind 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.http://dx.doi.org/10.3233/SAV-2011-0654
spellingShingle H. Doumiri Ganji
S.S. Ganji
D.D. Ganji
F. Vaseghi
Analysis of Nonlinear Structural Dynamics and Resonance in Trees
Shock and Vibration
title Analysis of Nonlinear Structural Dynamics and Resonance in Trees
title_full Analysis of Nonlinear Structural Dynamics and Resonance in Trees
title_fullStr Analysis of Nonlinear Structural Dynamics and Resonance in Trees
title_full_unstemmed Analysis of Nonlinear Structural Dynamics and Resonance in Trees
title_short Analysis of Nonlinear Structural Dynamics and Resonance in Trees
title_sort analysis of nonlinear structural dynamics and resonance in trees
url http://dx.doi.org/10.3233/SAV-2011-0654
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