Solving Vibration Equations of MDOF Systems by Modified Differential Transform Method
Solving Vibration Equations of MDOF Systems by Modified Differential Transform Method
Mohammadamir Najafgholipour1 Navid Soodbakhsh2
1) Ph.D., Faculty of Department of Civil and Environmental Engineering, Shiraz University of Technology, Shiraz, Iran
2) M.Sc., Graduated in Applied Mathematics, Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran
Publication :
3rd international conference of Science and Engineering(3icesconf.com)
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-FreedomÙˆ Systems
Vibration Equation.