EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 85(99), pp. 119–130 (2009)

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Livija Cveticanin

Department of Mechanics, Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia

Abstract: Oscillations of a system with strong quadratic damping are considered. For the exact analytical form of the energy-displacement function the explicit form of the maximal amplitudes of vibration are obtained by introducing the Lambert-w function. Comparing the neighbor maximal amplitudes and the corresponding energies the conclusions about the energy dissipation is given. The approximate solution for a strong nonlinear differential equation which describes the motion of the oscillator with quadratic damping is calculated applying the elliptic-harmonic-balance method. The accuracy of the solution is affirmed by comparing the maximal displacements obtained using the approximate method with the exact one obtained by energy method.

Classification (MSC2000): 34C15

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Electronic fulltext finalized on: 23 Apr 2009. This page was last modified: 22 Oct 2009.

© 2009 Mathematical Institute of the Serbian Academy of Science and Arts
© 2009 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition