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2007•Journal of Tangshan CollegeRequires access

1/3 Subharmonic Resonance of a Thin Rectangular Plate on Nonlinear Foundation in Temperature Field

Yang Zhi-an

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Abstract

In order to study 1/3 subharmonic resonance of a thin rectangular plate on nonlinear foundation in temperature field,nonlinear dynamical equation of the system is established with the application of elastic theory.Nonlinear vibration equation is obtained based on Galerkin's method. By means of the method of multiple scales for nonlinear vibrations the approximation solution of 1/3 subharmonic resonance of the system is acquired.Numerical analysis of the influence of temperature,foundation coefficient,damping,geometric parameter,and excitation on the system is carried out.The change laws of response curve with changing parameters are obtained.

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What this paper is about

In order to study 1/3 subharmonic resonance of a thin rectangular plate on nonlinear foundation in temperature field,nonlinear dynamical equation of the system is established with the application of elastic theory.Nonlinear vibration equation is obtained based on Galerkin's method. By means of the method of multiple scales for nonlinear vibrations the approximation solution of 1/3 subharmonic resonance of the system is acquired.Numerical analysis of the influence of temperature,foundation coefficient,damping,geometric parameter,and excitation on the system is carried out.The change laws of response curve with changing parameters are obtained.

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Available abstract

In order to study 1/3 subharmonic resonance of a thin rectangular plate on nonlinear foundation in temperature field,nonlinear dynamical equation of the system is established with the application of elastic theory.Nonlinear vibration equation is obtained based on Galerkin's method. By means of the method of multiple scales for nonlinear vibrations the approximation solution of 1/3 subharmonic resonance of the system is acquired.Numerical analysis of the influence of temperature,foundation coefficient,damping,geometric parameter,and excitation on the system is carried out.The change laws of response curve with changing parameters are obtained.

Key concepts: Galerkin method, Nonlinear system, Vibration, Subharmonic, Resonance (particle physics), Nonlinear resonance, Foundation (evidence), Multiple-scale analysis

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