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Oscillator with non-integer order nonlinearity and time variable parameters

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Abstract

In this paper, the vibrations of the oscillator with nonlinearity of integer or non-integer order and with mass variable parameters are considered. New appreciative analytical procedures are developed: first, based on the generating solution that is the exact analytic solution of the system with constant parameters and the second, based on the approximate solution in the form of a trigonometric function with exact period of vibration of the system with constant parameters. For the both methods, the assumed trial solutions represent the perturbed versions of the solutions of the equations with constant parameters, where the amplitude and phase of vibration are supposed to be time variable. The amplitude and phase functions are determined using the averaging procedure over the period of vibration. The obtained approximate analytic solutions are compared with numerical ones. It is shown that the developed methods are accurate for the monotone slow time variable systems. The example of mass variable oscillator is considered. The influence of mass variation, small linear viscous damping and of the reactive force is investigated, too.

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  1. Faculty of Technical Sciences, Trg D. Obradovica 6, 21000, Novi Sad, Serbia

    L. Cveticanin

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  1. L. Cveticanin
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Cveticanin, L. Oscillator with non-integer order nonlinearity and time variable parameters. Acta Mech 223, 1417–1429 (2012). https://doi.org/10.1007/s00707-012-0665-5

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  • DOI: https://doi.org/10.1007/s00707-012-0665-5

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