Modified Differential Transform Method for Solving Vibration Equations of MDOF Systems
محل انتشار: ژورنال مهندسی عمران، دوره: 2، شماره: 4
سال انتشار: 1395
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 638
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شناسه ملی سند علمی:
JR_CEJ-2-4_005
تاریخ نمایه سازی: 16 شهریور 1395
چکیده مقاله:
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 forsolving the vibration equations in structural dynamics. In this paper modified differential transform method (MDTM) asa semi-analytical approach is generalized for the system of differential equations and is utilized for solving the vibrationequations 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.
کلیدواژه ها:
Modified Differential Transform Method ، Multi-Degrees-of-Freedom Systems ، Pade' Approximant ، Vibration Equation
نویسندگان
M. A. Najafgholipour
Faculty 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