Relationship between nonlinear free vibration behavior and nonlinear forced vibration behavior of viscoelastic plates

In this paper, the relationship between nonlinear free vibration behavior and non-linear forced vibration behavior of viscoelastic plates is studied based on Reddy higher order shear deformation theory and von Karman geometric nonlinearity assumption. Kelvin-Voigt viscoelastic model is adopted to describe the viscoelasticity of the plate. According to the geometric equations and constitutive equations, the elastic potential energy, kinetic energy and virtual work done by the external force and viscous damping force are obtained. Furthermore, the nonlinear governing differential equations of the system are achieved by using Hamilton's principle. On the basis of the harmonic balance method and Runge-Kutta method, the nonlinear free vibration responses and nonlinear forced vibration responses of the system are presented, respectively. The major innovation of the manuscript is that the nonlinear frequency ratio derived from the nonlinear free vibration of the system, is in good agreement with the resonant frequency ratio obtained from the nonlinear forced vibration of the system. Also, the viscous damping coefficient has a little effect on the nonlinear frequency ratio.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This paper investigates the relationship between the nonlinear free vibration behavior and nonlinear forced vibration behavior of viscoelastic plates based on Reddy higher order shear deformation theory and von Karman geometric nonlinearity assumption. The Kelvin-Voigt viscoelastic model is used to describe the viscoelasticity of the plate. The elastic potential energy, kinetic energy, and virtual work done by external force and viscous damping force are obtained based on the geometric equations and constitutive equations. The nonlinear governing differential equations of the system are derived using Hamilton's principle. The nonlinear free vibration responses and nonlinear forced vibration responses of the system are presented using the harmonic balance method and Runge-Kutta method. The major finding of this study is that the nonlinear frequency ratio derived from the nonlinear free vibration is in good agreement with the resonant frequency ratio obtained from the nonlinear forced vibration, and the viscous damping coefficient has little effect on the nonlinear frequency ratio.