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

M. Eissa; S. A. EI-Serafi; M. M. Kamel; M. Z. Rageb; Y. A. Amer

doi:10.3390/mca7030263

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Article

1 December 2002

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

and

Dep. of Eng. Math., Faculty of Electronic Engineering, Menouf 32952, Egypt

Department of Mathematics, Faculty of Science, Zagazig, Egypt

Author to whom correspondence should be addressed.

Math. Comput. Appl.2002, 7(3), 263-274;https://doi.org/10.3390/mca7030263

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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

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