Solving Vibration Equations of MDOF Systems by Modified Differential Transform Method
Publish place: سومین کنفرانس بین المللی علوم و مهندسی
Publish Year: 1395
نوع سند: مقاله کنفرانسی
زبان: English
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شناسه ملی سند علمی:
ICESCON03_273
تاریخ نمایه سازی: 16 شهریور 1395
Abstract:
Vibration equations of discrete multi-degrees-of-freedom (MDOF) structural systems is system of differential equations. In linear systems, the differential equations are also linear. Various analytical and numerical methods are available for solving the vibration equations in structural dynamics. In this paper modified differential transform method (MDTM) as a semi-analytical approach is generalized for the system of differential equations and is utilized for solving the vibration equations of MDOF systems. The MDTM is a recursive method which is a hybrid of Differential Transform Method (DTM), Pade' approximant and Laplace Transformation. A series of examples including forced and free vibration of MDOF systems with classical and non-classical damping are also solved by this method. Comparison of the results obtained by MDTM with exact solutions shows good accuracy of the proposed method; so that in some cases the solutions of the vibration equation that found by MDTM are the exact solutions. Also, MDTM is less expensive in computational cost and simpler with compare to the other available approaches
Keywords:
Modified Differential Transform Method , Multi-Degrees-of-Freedom Systems , Pade' Approximant , Vibration Equation
Authors
M. A Najafgholipour
Ph.D., Faculty of Department of Civil and Environmental Engineering, Shiraz University of Technology, Shiraz, Iran
Navid Soodbakhsh
M.Sc., Graduated in Applied Mathematics, Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran
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