Study On Thermodynamic Coupling Problems Of Viscoelastic Body Described By Fractional Differential Calculus

Aiming at the mechanics properties of viscoelastic materials can't be described accurately by classical constitutive model,and considering the properties of viscoelastic materials are affected by heat,fractional derivative viscoelastic constitutive model is adopted to describe the constitutive relations of viscoelastic materials in this paper.The coupling problems of fractional derivative thermoviscoelastic objects are studied here.The thermodynamic behaviors of thermoviscoelastic pole,which is described by fractional constitutive model in the dynamic coupling effect,is mainly studied.The thermodynamic behaviors of thermo-viscoelastic poles, which are described by calssical constitutive model and fractional constitutive model separately, are studied mainly,and their thermodynamic behaviors are compared.Moreover,the difference format of governing differential equations of fractional derivative viscoelastic object is studied in the thermodynamic coupling effect.Finally,thermodynamic behaviors of axis-symmetry columniform viscoelastic damper are analyzed under three kinds of intial value conditions.The main results and conclusions are following:(1) Under the conditions of thermodynamic coupling,with the increase of coupling coefficient,viscosity coefficient and elasticity modul,the coupling effect become weaker.So the thermoviscoelastic damp effect become weaker,the speed of vibration decaying become slower.(2) The fractional rank is greater,the speed of vibration decaying become slower and the coupling effect become weaker.Comparing to the classical thermodynamic coupling problems, the physics quantities,decribed by fractional constitutive model,suffer geater coupling effect, the peak value of vibration produced are greater.(3) The velocity is effected the most by the damp effect of system.The difference in temperatuer is effect great to displacement,the gradient of stress and velocity.Comparing to matrials' damp,the thermoviscoelastic damp produced by coupling effect plays more important role in the course of thermodynamic coupling.The study about thermodynamic coupling problems of viscoelastic body described by fractional differential calculus in this dissertation is still very rare at least in the domestic.So the research has provided a solid foundation for further study to the fractional thermo-dynamic coupling problems.