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Math. Comput. Appl. 2002, 7(3), 263-274; doi: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
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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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MDPI and ACS Style

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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Math. Comput. Appl. EISSN 2297-8747 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
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