Response of a parametrically excited system with quadratic and cubic nonlinearities.
type: Item
instance of: scholarly article
title: Response of a parametrically excited system with quadratic and cubic nonlinearities.
zbMATH Open document ID: 1179.70011
author: Yanyan Li
published in: Mathematical \& Computational Applications
publication date: 2002-11-13T00:00:00Z
review text: Summary: An investigation is presented of the response of a three-degree-of-freedom system with quadratic and cubic nonlinearities under parametric excitations. We consider the problem of suppressing the vibration of a structure that is subjected to combined parametric excitation, where the vibration amplitudes resulting from such resonance cannot be controlled. The fixed points of the three equations are obtained, and their stability is determined. Numerical solutions are conducted to obtain the response of the three modes and their stability. We also examine the effects of different parameters on response and stability of the system.
Mathematics Subject Classification ID: 70K28
Mathematics Subject Classification ID: 70K20
Mathematics Subject Classification ID: 70Q05
zbMATH DE Number: 1827815
zbMATH Keywords: resonance
zbMATH Keywords: stability
zbMATH Keywords: multi-excitation force
MaRDI profile type: Publication
full work available at URL: mca7030263
OpenAlex ID: W2332154195
DOI: 10.3390/MCA7030263
Recommended article: The response of two-degree-of-freedom systems with quadratic and cubic non-linearities to multifrequency parametric excitations
Recommended article: The response of a single-degree-of-freedom system with quadratic and cubic non-linearities to a fundamental parametric resonance
Recommended article: The response of a single-degree-of-freedom system with quadratic and cubic non-linearities to a principal parametric resonance
Recommended article: The response of single degree of freedom systems with quadratic and cubic non-linearities to a subharmonic excitation
Recommended article: The response of multidegree-of-freedom systems with quadratic non-linearities to a harmonic parametric resonance
Recommended article: Nonlinear response of a parametrically excited system using higher-order method of multiple scales
Recommended article: The response of two-degree-of-freedom systems with quadratic non-linearities to a combination parametric resonance
Recommended article: Perturbation analysis in parametrically excited two-degree-of-freedom systems with quadratic and cubic nonlinearities
Recommended article: Parametric Excitation of a Nonlinear System
Recommended article: Resonance of multiple frequency excitated systems with quadratic, cubic and quartic nonlinearity
description: scientific article; zbMATH DE number 1827815