Modified Differential Transform Method for Solving Vibration Equations of MDOF Systems
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
Author: Mohammadamir
Najafgholipour, Navid Soodbakhsh
Journal Code: jptsipilgg160027
