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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 mdpi.com as a courtesy and upon agreement with the previous journal publisher.
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Math. Comput. Appl. 2002, 7(3), 263-274; https://doi.org/10.3390/mca7030263

Response of a Parametrically Excited System with Quadratic and Cubic Non-Linearities

1
Dep. of Eng. Math., Faculty of Electronic Engineering, Menouf 32952, Egypt
2
Department of Mathematics, Faculty of Science, Zagazig, Egypt
*
Author to whom correspondence should be addressed.
Published: 1 December 2002
PDF [777 KB, uploaded 1 April 2016]

Abstract

An investigation is presented of the response of a three-degree-of-freedom system with quadratic and cubic non-linearities under parametric excitations. The problem of suppressing the vibration of a structure that is subjected to combination parametric excitation is considered, where the vibration amplitudes resulting from such resonance can not be controlled. The fixed points of the three equations are obtained and their stability are determined. Numerical solutions are conducted to obtain the response of the three modes and their stability. Effects of the different parameters on both response and stability of the system are also investigated.
Keywords: Resonance; Power series; Stability; System response; Multi excitation force Resonance; Power series; Stability; System response; Multi excitation force
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Eissa, M.; EI-Serafi, S.A.; Kamel, M.M.; Rageb, M.Z.; Amer, Y.A. Response of a Parametrically Excited System with Quadratic and Cubic Non-Linearities. Math. Comput. Appl. 2002, 7, 263-274.

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