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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Format: | Article |
Language: | English |
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Wiley
2012-01-01
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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. |
format | Article |
id | doaj-art-859883721f8843df9ec50b66fffba6de |
institution | Kabale University |
issn | 1070-9622 1875-9203 |
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 |
work_keys_str_mv | AT hdoumiriganji analysisofnonlinearstructuraldynamicsandresonanceintrees AT ssganji analysisofnonlinearstructuraldynamicsandresonanceintrees AT ddganji analysisofnonlinearstructuraldynamicsandresonanceintrees AT fvaseghi analysisofnonlinearstructuraldynamicsandresonanceintrees |