APPLICABILITY OF THE MDTM TO OBTAIN THE PERIODIC SOLUTION OF THE DUFFING TYPE EQUATIONS OF MOTION
J. PETER PRAVEEN *
Department of Mathematics, Koneru Lakshmaiah University, Vaddeswaram, Guntur-522502, India.
B. NAGESWARA RAO
Department of Mechanical Engineering, Koneru Lakshmaiah University, Vaddeswaram, Guntur-522502, India.
*Author to whom correspondence should be addressed.
Several researchers have utilized the modified differential transform method (MDTM), which is claimed to be an efficient method for obtaining periodic solution of the non-linear oscillatory systems. This paper examines the Duffing type equation of motion having an odd restoring force function. The behavior of oscillations is expected to have the same magnitude of positive and negative amplitudes. The solution of the Duffing equation obtained using the MDTM is unable to show the realistic trend in the phase diagram. The method of harmonic balance provides the required periodic solution and gives a clue for further improvement in the MDTM to capture the realistic trend in the phase diagram.
Keywords: Duffing equation, harmonic balance method, modified differential transform method, phase diagram, periodic solution