Dynamic Response Of Timoshenko Beams On Fractional-Order Viscoelastic Foundations

In engineering practice,beam is an important structural element.The interaction between the foundation and the beam is actually the interaction between the soil and the structure.Compared with elastic foundation,viscoelastic foundation is closer to engineering practice.Therefore,the study of beam vibration on viscoelastic foundation is of great help to engineering practice and provides a theoretical basis for engineering application.In order to reveal the forced vibration characteristics of the beam,this thesis focuses on the analysis of the dynamic responses of Timoshenko beams on viscoelastic and fractional viscoelastic foundations under various loads.(1)Based on the classical Timoshenko beam theory,the modal superposition principle is used to analyze the dynamic responses of two fixed Timoshenko beams without foundation under different loads(harmonic load,moving concentrated load,moving harmonic load and impact load),and the influence of related parameters is analyzed.(2)The dynamic response of a Timoshenko beam placed on a Pasternak foundation is considered.The action of Pasternak foundation reaction force is analyzed,and the governing equation of beam on elastic foundation is obtained by taking the force information of beam element as an example.The natural frequency of the beam on elastic foundation is calculated,and the analytical formula of the deflection of the beam on elastic foundation is obtained by means of mode superposition method.The critical velocity and critical frequency of the load are obtained,and the influences of shear coefficient,load velocity and load frequency on the response amplitude and phase Angle of the beam are analyzed.(3)The dynamic response of Timoshenko beam on viscoelastic Pasternak foundation with integer order under different loads is analyzed.The governing equation of Timoshenko beam on viscoelastic Pasternak foundation is obtained,and the complex natural frequency and mode function with viscous dissipation information are solved.On this basis,the displacement response of the beam under different loads is analyzed by means of mode mode superposition method.The dynamic response of the beam under different foundation viscosity coefficient,load frequency and moving speed is given,and the influence law of the viscoelastic foundation on the dynamic response of the beam is discussed.(4)The integer order viscoelastic foundation model is extended to fractional order viscoelastic model,and the free vibration and dynamic response of Timoshenko beam on fractional order viscoelastic Pasternak foundation are studied.The governing equation of Timoshenko beam on fractional-order viscoelastic Pasternak foundation is obtained,and the complex natural frequency and mode function are solved.On this basis,the displacement response of the beam under different loads is analyzed by mode mode superposition method.The dynamic response of the beam under different fractional derivatives,foundation viscosity coefficient and load moving speed is given,and the influence law of the relevant parameters on the dynamic response of the beam is discussed.