The Study Of Viscoelastic Material Model And Vibration Based On Distributed-order Derivative

Viscoelastic material is a kind of material with both viscous and elastic mechanical properties.It is widely used in the field of vibration reduction and noise reduction.It is necessary to study the constitutive relations of viscoelastic materials because of their excellent properties.The first chapter introduces the research background and research status at home and abroad from the theory and application.The second chapter introduces the preparatory knowledge,including the definition of fractional calculus,the special functions and methods used in solving,and the basic theory of viscoelastic materials.In the third chapter,the six-parameter fractional order constitutive model is studied.The expressions of creep compliance and relaxation modulus with different values of parameters are analyzed,and the energy dissipation diagram is obtained.The complex inverse theory is used to calculate the integral expression and residue theorem to calculate the pole.Finally,it is concluded that the model can describe four types of viscoelasticity.In Chapter 4,the viscoelastic constitutive relation under the distribution order is considered,and the appropriate weight distribution function and integral interval are determined.The expressions of creep compliance and relaxation modulus are obtained,and the corresponding images are drawn.It is concluded that the model describes the elastic type I.In Chapter 5,the steady-state response of viscous damped vibration system is studied.It includes two parts: integer order vibration system and distributed order vibration system.The amplitude frequency response and phase frequency response of the system are studied respectively,and the influence of distribution order on the response is considered,that is,stiffness contribution factor and damping contribution factor appear.The last part is the summary and Prospect of this paper.