Chaos And Bifurcation Analisys Of The Thermo-Mechanical Coupling Viscoelastic Rectangular Plate

With the extensive application of viscoelastic materials and structures and the widening of the working temperature, the dynamic behaviors of the viscoelastic structures are closely related to thermal effect. So, it is necessary to consider the thermal effect in the study of nonlinear dynamic behaviors of the viscoelastic structures. Namely, the coupling with thermal and mechanical effect should be considered.Three main parts are included in the paper:1) The nonlinear dynamic model of a thermo-mechanical coupling viscoelastic rectangular plate is established. The processes base on the Karman theory for thin plates with large deflection, thermo-viscoelastic constitutive equations which are described by Boltzman's superposition principle, deformation geometry equations, dynamic equilibrium equation, and heat conduction equation. The rectangular plate has thermal expansion, heat conduction, convection effect, and is subjected to both actions of an alternating periodic transverse external excitation and in-plane uniform distributed force. The model may be converted to a nonlinear differential-integral dynamical system by using Galerkin's method. And the simplified models are discussed according to the application conditions.2) The numerical models of nonlinear vibration of thermo-mechanical coupling viscoelastic plate are studied. First, the difference-differential dynamic model is obtained from control equation by difference method. Then, the iteration numerical model is obtained by Newmark method. And difference numerical model is obtained by central difference method. Especially, a special kind of numerical model are obtained by introducing new variables.3) The dynamic behaviors of the thermo-mechanical coupling viscoelastic plate are revealed. The effects of thermal expansion and heat conduction on the nonlinear dynamic behaviors are investigated. The processes use several methods in dynamic systems. The results show that the dynamic properties of the thermo-mechanical coupling viscoelastic plate are abundant, while the plate is subjected to both actions of an alternating periodic transverse external excitation and in-plane uniform distributed force. With the influence of temperature, the model's chaotic property also is stronger. Especially, the motion state of hyperchaos appears. Coefficient of thermo-mechanical coupling and the amplitude of thermo-mechanical coupling system are enlarged by the increasing coefficient of thermal conduction and the decreasing coefficient of heat expansion.