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Article

A Generalized Approach to Coupled Nonlinear Vibrations of Continuous Systems

Department of Mechanical Engineering, Celal Bayar University 45140 Muradiye-Manisa, Turkey
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Authors to whom correspondence should be addressed.
Math. Comput. Appl. 1997, 2(3), 141-154; https://doi.org/10.3390/mca2030141
Published: 1 December 1997

Abstract

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.

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MDPI and ACS Style

Pakdemirli, M.; Boyacı, H. A Generalized Approach to Coupled Nonlinear Vibrations of Continuous Systems. Math. Comput. Appl. 1997, 2, 141-154. https://doi.org/10.3390/mca2030141

AMA Style

Pakdemirli M, Boyacı H. A Generalized Approach to Coupled Nonlinear Vibrations of Continuous Systems. Mathematical and Computational Applications. 1997; 2(3):141-154. https://doi.org/10.3390/mca2030141

Chicago/Turabian Style

Pakdemirli, M., and H. Boyacı. 1997. "A Generalized Approach to Coupled Nonlinear Vibrations of Continuous Systems" Mathematical and Computational Applications 2, no. 3: 141-154. https://doi.org/10.3390/mca2030141

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