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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Articles in this Issue were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence. Articles are hosted by MDPI on as a courtesy and upon agreement with the previous journal publisher.
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Math. Comput. Appl. 1997, 2(3), 141-154;

A Generalized Approach to Coupled Nonlinear Vibrations of Continuous Systems

Department of Mechanical Engineering, Celal Bayar University 45140 Muradiye-Manisa, Turkey
Authors to whom correspondence should be addressed.
Published: 1 December 1997
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A mathematical model covering many practical vibration problems of continuous systems has been proposed. The equations of motion consist of two nonlinearly coupled partial differential equations. The quadratic and cubic nonlinearities as well as the linear part of the equations are represented by arbitrary operators. A perturbation approach (method of multiple time scales) has been applied directly to the partial differential equations. The responses as well as the amplitude and phase modulation equations are found for the case of primary resonances of the external excitation and one-to-one internal resonances between the natural frequencies of the equations. The coefficients of the amplitude and phase modulation equations are calculated in their most general form. Results are then applied to a nonlinear cable vibration problem having small sag-to span ratios.
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Pakdemirli, M.; Boyacı, H. A Generalized Approach to Coupled Nonlinear Vibrations of Continuous Systems. Math. Comput. Appl. 1997, 2, 141-154.

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