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Mohammadamir Najafgholipour
PhD, Assistant Professor, Department of Civil and Environmental Engineering, Shiraz University of Technology, Shiraz,
Civil Engineering, Building, Construction & Architecture

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Journal : Civil Engineering Journal

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Modified Differential Transform Method for Solving Vibration Equations of MDOF Systems Mohammadamir Najafgholipour; Navid Soodbakhsh
Civil Engineering Journal Vol 2, No 4 (2016): April
Publisher : Salehan Institute of Higher Education

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1141.659 KB) | DOI: 10.28991/cej-2016-00000019

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.
Co-Authors Navid Soodbakhsh