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Dynamic Vibration Analysis for Non-linear Partial Differential Equation of the Beam-Columns with Shear Deformation and Rotary Inertia by AGM

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In this study, nonlinear partial differential equations governing vibrating beam-columns with variable cross-section of the new method is applied to solve. Our purpose is to enhance the ability of solving the mentioned nonlinear differential equation with a simple and innovative approach which was named Akbari-Ganji's Method or AGM. Comparisons are made between AGM and Numerical Method (Runge-Kutte 4th). The results reveal that this method is very effective and simple, and can be applied for other nonlinear problems. It is necessary to mention that there are some valuable advantages in this way of solving nonlinear differential equations and also most of the sets of differential equations can be answered in this manner which in the other methods they have not had acceptable solutions up to now. We can solve equation(s) and consequently there is no need to utilize similarity solutions which makes the solution procedure a time-consuming task. According to the afore-mentioned assertions which will be proved in this case study, the process of solving nonlinear equation(s) will be very easy and convenient in comparison with the other methods. According to the explanations given about the capabilities of this method (AGM), non-linear partial differential equations governing the vibration of the beam-column are investigated for dynamic systems.

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