Analysis Of Chaotic Behavior Of Nonlinear Viscoelastic Structures

The structure like beam,column and pile is the most common engineering structure,which is widely applied into traffic,architecture and machinery.Its dynamic behavior is closely related to the safe capability of structure.Hence the dynamic behavior of the structures is always an important subject of scholars and researchers.The introduction of chaos theory as a new concept brings new vigor and vitality to the study of structural dynamics.In this paper,chaotic motion of the common nonlinear structure under loads in engineerings is studied.Firstly,the ordinary differential equation of the structure is obtained by Differential Quadrature Method;then,by using numerical analysis method and programming with the software Matlab,phase-plane diagram,power spectrum diagram,poincare section diagram and time history curve are figured out,the influence of initial conditions and parameters on the chaotic effect is analyzed,the basic characteristics of chaos effect are also described in detail.Here are the main contents:1.The constitutive relation of the structure obeys the Kelvin model,considering the influence of friction between pile and soil,a mathematical model of nonlinear vibration of viscoelastic pile under axial load is established.The dynamic partial differential equation of the structure is obtained by the analysis of the mechanical model.The differential quadrature method(DQM)is used to discretely simplify the partial differential equations with meshing in spatial domain.An ordinary differential equation model for dynamic vibration of viscoelastic pile foundation is established.By using the software Matlab,the chaotic effect of viscoelastic pile foundationis is simulated.Results suggest that,with the decrease of the elastic modulus of pile and the stiffness coefficient of soil around the pile,the occurrence of chaotic motion can be suppressed.with the soil layer thinner and the damping coefficient of soil smaller,pile foundation is more prone to happen chaos effect.2.Considering the structure of cantilever beam with one end fixed and the other freed,by the Kelvin model,dynamic partial differential equations of viscoelastic cantilever beam under external loads is established.The nonlinear dynamic differential equation of viscoelastic cantilever beam is obtained,by using the software Matlab,the chaotic effect of viscoelastic cantilever beam is analyzed.Results indicate that,the larger the amplitude of the lateral load and the value of the viscoelastic coefficient,the more chaotic effect the cantilever structure is likely to emerge.3.Considering the axially loaded viscoelastic column with one end fixed and the other freed,by the Kelvin model,dynamic partial differential equations of viscoelasticcolumn is established.,by using the software Matlab,the chaotic effect of viscoelastic cantilever column is analyzed.Results show that,the larger the amplitude of the periodic load and the value of the viscoelastic coefficient,the more chaotic effect the cantilever structure is easily to produce.