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.
Math. Comput. Appl. 2002, 7(3), 263-274; https://doi.org/10.3390/mca7030263
Published: 1 December 2002
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
Share and Cite
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. https://doi.org/10.3390/mca7030263
AMA Style
Eissa M, EI-Serafi SA, Kamel MM, Rageb MZ, Amer YA. Response of a Parametrically Excited System with Quadratic and Cubic Non-Linearities. Mathematical and Computational Applications. 2002; 7(3):263-274. https://doi.org/10.3390/mca7030263
Chicago/Turabian StyleEissa, M., S. A. EI-Serafi, M. M. Kamel, M. Z. Rageb, and Y. A. Amer. 2002. "Response of a Parametrically Excited System with Quadratic and Cubic Non-Linearities" Mathematical and Computational Applications 7, no. 3: 263-274. https://doi.org/10.3390/mca7030263
