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 nonlinear forced vibration behavior of viscoelastic plates is studied based on Reddy higher-order shear deformation theory and von Kármán 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 obtained 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. Several numerical examples are provided to reveal the relationship between the nonlinear free vibration behavior and the nonlinear forced vibration behavior of the viscoelastic rectangular plate. The analytical solution of nonlinear free vibration responses of the system for a simply supported viscoelastic plate is presented. The authors claim `good agreement' between the present results and the available results. The reviewer does not like the use of the term `good agreement'.
Reddy higher-order shear deformation theory
scientific article; zbMATH DE number 7634565
scientific article