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STUDY ON PRIMARY RESONANCE OF A PARAMETRICALLY EXCITED THIN RECTANGULAR PLATE ON WINKLER FOUNDATION CONSIDERING MATERIAL NONLINEARITY

Han Yan-bin

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Abstract

Primary resonance of a parametrically excited thin rectangular plate on Winkler foundation considering material nonlinearity is studied. Applying the elastic theory, its nonlinear dynamic equations are established. From them its nonlinear oscillation equation is obtained based on Galerkin's method. By means of the method of multiple scales for nonlinear oscillations, the first approximate primary parametric resonance of the system is acquired. The stability of the steady state solutions of the system is investigated. The bifurcation diagrams of the parameter plane and the response equation are obtained. Numerical analysis for influences of excitation, detuning, damping, nonlinear parameter and geometric parameters on the system is carried out.

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Primary resonance of a parametrically excited thin rectangular plate on Winkler foundation considering material nonlinearity is studied. Applying the elastic theory, its nonlinear dynamic equations are established. From them its nonlinear oscillation equation is obtained based on Galerkin's method. By means of the method of multiple scales for nonlinear oscillations, the first approximate primary parametric resonance of the system is acquired. The stability of the steady state solutions of the system is investigated. The bifurcation diagrams of the parameter plane and the response equation are obtained. Numerical analysis for influences of excitation, detuning, damping, nonlinear parameter and geometric parameters on the system is carried out.

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Available abstract

Primary resonance of a parametrically excited thin rectangular plate on Winkler foundation considering material nonlinearity is studied. Applying the elastic theory, its nonlinear dynamic equations are established. From them its nonlinear oscillation equation is obtained based on Galerkin's method. By means of the method of multiple scales for nonlinear oscillations, the first approximate primary parametric resonance of the system is acquired. The stability of the steady state solutions of the system is investigated. The bifurcation diagrams of the parameter plane and the response equation are obtained. Numerical analysis for influences of excitation, detuning, damping, nonlinear parameter and geometric parameters on the system is carried out.

Key concepts: Galerkin method, Nonlinear system, Multiple-scale analysis, Nonlinear resonance, Parametric statistics, Resonance (particle physics), Oscillation (cell signaling), Bifurcation

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STUDY ON PRIMARY RESONANCE OF A PARAMETRICALLY EXCITED THIN RECTANGULAR PLATE ON WINKLER FOUNDATION CONSIDERING MATERIAL NONLINEARITY — Research Paper | ScholarLens