The Chaos Analysis Of Large Deflection Rectangular Sheet Under Magnetic-Elastic-Thermal Coupling

Thin plate is one kind of common project components,they are usually installated incoupled fields,such as the mechanical field, electromagnetic field and temperature fieldand so on, the dynamic properties of the system have a significant impact on the structuralsafety. Therefore, study of many fields coupled dynamics of magneto-elastic thin plate areessential in both theory aspect and practical aspect.Based on the theory of plates and shells and magnetic elastic mechanics,according tothe large deflection rectangular sheet,the chaotic characteristic of system under coupledaction of mechanical load,electromagnetic field and temperature field is investigated inthis paper.Introduced the related subject research status at home and abroad,and the expressionof electromagnetic force,deduced the nonlinear magneto-elastic vibration equation of thinplate.Introduces the classical Duffing Equation,including expressions,equation classificati-on. And then use Melnikov function method,the chaotic motion condition of the hard andsoft spring Duffing system under the meaning of Smale horseshoe transformation arederived respectively.Considering the influence of temperature field, the nonlinear magneto-elasticcoupling vibration equation of large deflection rectangular thin plate at four kinds ofboundary conditions such as simply supported at each edge, one edge free and otherssimply supported, clamped at each edge and two opposite side simply supported andothers clamped under the action of mechanic field and steady transverse magnetic field arederived,studied many fields coupled dynamics of chaotic characteristic.Use specificexample, and through the numerical simulation of the system,the maximum lyapunovexponent diagram,the bifurcation diagram,the wave diagram of displacement, the phasediagram and the poincare map of this system are obtained.The influences of the parametervariation of mechanical load,electromagnetic field and temperature field to the chaoticmotion of this system are discussed. The results show that structural components which installated in several coupledphysical fields like mechanical field,electromagnetic field,temperature field,etc. contains afairly rich and complex dynamic behavior.The results also can be used for reliabilitydesigning of relevant electromagnetic structure.