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Solving Nonlinear Differential Equation Governing on the Rigid Beams on Viscoelastic Foundation by AGM

Journal of Marine Science and Application 2015年第1期14卷 30-38页

作者： M. R. Akbari D. D. Ganji A. K. Rostami M. Nimafar Department of Civil Engineering and Chemical Engineering University of Tehran P.O. Box 11155-4563 Tehran Iran Department of Mechanical Engineering Babol University of Technology P.O. Box 484 Babol Iran Department of Mechanical and Aerospace Engineering Politecnico di Torino 24-10129 Turin Italy

In the present paper a vibrational differential equation governing on a rigid beam on viscoelastic foundation has been investigated. The nonlinear differential equation governing on this vibrating system is solved by a simple and innovative approach, which has been called Akbari-Ganji＇s method （AGM）. AGM is a very suitable computational process and is usable for solving various nonlinear differential equations. Moreover, using AGM which solving a set of algebraic equations, complicated nonlinear equations can easily be solved without any mathematical operations. Also, the damping ratio and energy lost per cycle for three cycles have been investigated. Furthermore, comparisons have been made between the obtained results by numerical method （Runk45） and AGM. Results showed the high accuracy of AGM. The results also showed that by increasing the amount of initial amplitude of vibration （A）, the value of damping ratio will be increased, and the energy lost per cycle decreases by increasing the number of cycle. It is concluded that AGM is a reliable and precise approach for solving differential equations. On the other hand, it is better to say that AGM is able to solve linear and nonlinear differential equations directly in most of the situations. This means that the final solution can be obtained without any dimensionless procedure Therefore, AGM can be considered as a significant progress in nonlinear sciences.

关键词： nonlinear differential equation Akbari-Ganji's method(AGM) rigid beam viscoelastic foundation vibrating system damping ratio energy lost per cycle

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