Study About Thermoviscoelastic Coupling Problem Of Pole Described By Fractional Calculus Constitutive Law

The polymer damping materials are used widely. The property of such materials is affected mostly by temperature, frequency etc. The temperature's change does not only modifies materials' physical property but also produces heat stress. And because of the polymer damping's energy dissipation, it translates the machine energy into heat,so it will change materials' temperature. Obviously, both of them are coupled.So,the study about the polymer damping materials' heat spread and the mechanics problem caused by this is very necessary.Many references indicate that comparing with classical viscoelastic models, fractional derivative models describe not only the constitutive of viscoelastic material and the related mechanics properties accurately in wide range, but also need less model parameters. So this paper used the two kinds of constitutive models to discuss the materials's heat viscoelastic coupling problem.First,this paper introduce the knowledge about heat distortion , the heat viscoelastic basic function and the method how to get these funcitons. Then we can get the math model of the two kind of constitutive models' heat-mechanics coupling problem by using the balance equation,the heat exchange equation and the constitutive equation. And then deduced the two model's temperature field differential equation ,stess field differential equation and displacement field differential equation.In the process of no-dimension ,we gets some usefull physics quantum, such as the coupling coefficient ,elasticity wave etc. Moreover, we obtain some usefull conclusion by comparing the two group of differential equations. The conlusion which is got by comparing the two constitutive's coupling problem and uncoupling problem is helpful for us to understand more about the physics nature of the coupling domino offect. Because it is hard to get resolving solution of this problem,the paper solves the differential equation by using difference method.The paper established difference format of the two kind of constitutive models' heat-mechanics coupling problem and programed MATLAB programme to solve temperature field. The result indicated: coupling domino effect has block effect for temperature conduction;coupling coefficient...