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Math. Comput. Appl. 2011, 16(4), 879-889; doi:10.3390/mca16040879

Forced Vibrations of Strongly Nonlinear Systems with Multiple Scales Lindstedt Poincaré Method

Department of Mechanical Engineering Celal Bayar University, Muradiye 45140 Manisa, Turkey
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Published: 1 December 2011
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Abstract

Forced vibrations of duffing equation with damping is considered. Recently developed Multiple Scales Lindstedt-Poincare (MSLP) technique for free vibrations is applied for the first time to the forced vibration problem in search of approximate solutions. For the case of weak and strong nonlinearities, approximate solutions of the new method are contrasted with the usual Multiple Scales (MS) method and numerical simulations. For weakly nonlinear systems, frequency response curves of both perturbation methods and numerical solutions are in good agreement. For strongly nonlinear systems however, results of MS deviate much from the MSLP method and numerical simulations, the latter two being in good agreement.
Keywords: Perturbation Methods; Lindstedt Poincare method; Multiple Scales method; Numerical Solutions; Forced Vibrations; Strongly Nonlinear Systems Perturbation Methods; Lindstedt Poincare method; Multiple Scales method; Numerical Solutions; Forced Vibrations; Strongly Nonlinear Systems
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Pakdemirli, M.; Karahan, M.M.F.; Boyacı, H. Forced Vibrations of Strongly Nonlinear Systems with Multiple Scales Lindstedt Poincaré Method. Math. Comput. Appl. 2011, 16, 879-889.

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Math. Comput. Appl. EISSN 2297-8747 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
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