Chaotic Analysis Of The Magneto-Elastic And Fluid-Elastic Interaction For Shell And Plate

Coupled mechanical problems is to study the interaction of two or more physical fields of mechanical problems. The problems contain the magneto-elastic problem, fluid-solid interaction problem, thermal-elastic problem and so on. The magneto-elastic coupling means the electromagnetic field with the deformation field problem. Fluid-solid coupling of solid mechanics and fluid mechanics is the formation of a mechanical branch of cross.Chaos is a nonlinear system-specific form of a movement is generated in the deterministic system, sensitive dependence on initial conditions of the steady-state non-periodic movement back and forth, with long-term unpredictability is a new discipline in recent years.Thin plate and shell is one kind of common project components, and they are usually installated in coupled fields, such as the mechanical field, electromagnetic field and temperature field and so on, the dynamic properties of the system have a significant impact on the structural safety. Therefore, study of many fields coupled dynamics of magneto-elastic thin plate is of great theoretical and practical significance.In this paper, the nonlinear elastic bifurcation and chaos of the thin plates and shell which in the electromagnetic fields, mechanical force and fluid field are studied. Based on the theory of shell and plate mechanics, magnetoelastic mechanics and fluid elastic mechanics , the nonlinear system dynamics coupled model is founded. The main work can be outlined as follow:The problem of bifurcation and chaos under the different boundary condition thin circular plate under the electromagnetic fields and mechanic fields is studied. Base on nonlinear electro-magneto-elastic equations of the thin circular plate and the expression of electromagnetic forces, the vibration equations of thin circular plate under uniform transverse magnetic field, round current and mechanical loadings are obtained and then solved numerically using the forth order Runge-Kutta method. By some examples, the wave diagram of displacement, phase diagram and Poincare map are derived. The influences of magnetic field and electrical on vibration properties of the system state are analyzed.The chaotic motion problem of a thin cylindrical shell with two sides simply supported under the coupled action of mechanical field and electromagnetic field is studied. The results showed that changes of the magnetic intensity as well as the magnitude and direction of the circumferential current will realize the conversion between chaotic motion and periodic motion of the thin cylindrical shell with two sides simply supported under the action of mechanical loads.The problem of chaos in rotating disk in electromagnetic and mechanical fields is studied. Based on the expression of electromagnetic forces and nonlinear electro-magneto-elastic equations for a rotating disk, vibration equations under the mechanical loading in a steady radial magnetic field together with a circulating electric current are derived. Under certain conditions, the influences of the electromagnetic field and the speed on system vibration properties are analyzed.On the basic motion equations of fluid mechanics and elastic mechanics, the single Lagrangian method is used to form the fluid-solid interaction problem. In the model of cylinder filled with compressible gas and the piston vibration is the harmonic vibration, the problem of chaos in elastic cylinder is studied.On the basic motion equations of fluid mechanics and elastic mechanics, the chaotic motion of the artery are analyzed by changing the momentum of blood viscosity, arterial blood pressure and Poisson ratio.On the basic motion equations of fluid mechanics and elastic mechanics, the chaotic motion of the double-shell cylinder are analyzed.Research projects are coupled nonlinear dynamics in the forefront. This research has a theoretical value and the scholarly significance of the national defense, medical and material.