Nonlinear Dynamics Research Of Vibration Of Viscoelastic Structures

Due to the viscoelastic properties of materials and various nonlinear factors, viscoelastic structures will represent complex nonlinear dynamical behaviors, when they bechance nonlinear vibration. It is these complicated dynamical behaviors that make the phenomenon of nonlinear vibration for viscoelastic structures become a frontier topics of the key attention. The research on the system not only analyses the dynamical characteristics of vibration of viscoelastic structures from the point of view of nonlinear dynamics, but also promotes the development and improvement of modern nonlinear dynamics theory and methods.Therefore, for the two most basic structures in practical engineering-viscoelastic beams and viscoelastic columns, when they bechance nonlinear vibration under the external excitation, their nonlinear dynamical behaviors are studied by theoretical analysis and numerical simulation methods. The main work and research results of this dissertation are as follows:(1) Based on reviewing and summarizing a large number of relevant literatures about home and abroad, the research methods and significance of nonlinear dynamics are discussed, as well as the engineering background and significance of the study of vibration problems of viscoelastic structures. From different aspects, overseas and domestic research status about nonlinear vibration of viscoelastic beams and viscoelastic columns are summarized roundly.(2) By considering the viscoelastic constitutive relation of differential type, the boundary conditions of simply supported at both ends and the external excitation, this paper respectively establishes the corresponding nonlinear dynamic models of vibration of a viscoelastic beam and a viscoelastic column, which adopts the differential quadrature method. The equations are respectively carried out numerical simulation by writing the fourth order Runge- Kutta algorithm with Matlab program. And some graphics are drawn, which is including phase plane diagrams, the time history curves, power spectrum figures and Poincare section diagrams.Based on fixing a set of initial conditions and parameters, with increasing viscoelastic damping coefficient, the viscoelastic beam gradually shows haploid periodic motion, chaotic motion, chaotic motion, periodic-3 motion and then returns to haploid periodic motion. This reflects the path to chaos- paroxysmal chaotic way. Besides, with increasing external excitation amplitude, the motion states of the viscoelastic beam are changed from haploid periodic motion, quasi-periodic motion to chaotic motion. This also reflects the way of break of quasi-periodic torus.(3) At the same time, by fixing a set of initial conditions and parameters, with the increase of viscosity coefficient, the viscoelastic column gradually shows haploid periodic motion, periodic-2 motion, periodic-6 motion and then returns to periodic-6 motion, periodic-2 motion, haploid periodic motion. Besides, with the increase of external excitation amplitude, the viscoelastic column also appears haploid periodic motion, periodic-6 motion, quasi-periodic motion, and completely enters into chaos motion state. This also reflects the way of break of quasi-periodic torus.(4) The results shows that not only the two types of viscoelastic structure appear alternately periodic motion, fold periodic motion and chaotic motion in a certain range of parameters, but also reflects the difference between chaotic motion and deterministic motion. Finally, based on the same theory and numerical methods, movement forms that they present respectively are not the same because of the different structures.