Study On The Wave And Vibration Of Timoshenko Beams On A Fractional-order Viscoelastic Pasternak Foundation

In practical engineering,beam and slab are important load-bearing structural elements.For the interaction between foundation and beam,it is actually an interaction between soil and structure.Compared with elastic foundation,viscoelastic foundation is closer to engineering practice.The research on the wave vibration of beam and slab on viscoelastic foundation can provide a theoretical basis for engineering application,In order to better describe the wave and vibration characteristics of the beam,viscoelastic and fractional viscoelastic foundation models are established in this thesis.The effects of relevant parameters on the wave and vibration of Timoshenko beam and its displacement function under simple harmonic load are analyzed.(1)Based on the classical Timoshenko beam,the modified Timoshenko beam theory is deduced and compared.The derivation of elastic Pasternak foundation model and two viscoelastic foundation models are introduced.The wave motion and vibration of Timoshenko beam on elastic and viscoelastic Pasternak foundation are studied,and the variation laws of wave velocity and natural frequency of the beam under the influence of different foundation reaction coefficient,viscosity coefficient and foundation shear coefficient are discussed.(2)The fractional order standard solid viscoelastic foundation model is derived and substituted into the classical and modified motion control equations of Timoshenko beam.The wave and vibration problems of Timoshenko beam on fractional order standard solid viscoelastic Pasternak foundation are discussed.The effects of different fractional orders,viscosity coefficients and foundation shear coefficients on the complex modulus of fractional order standard solid viscoelastic model,as well as on the wave velocity Influence of attenuation coefficient and natural frequency variation.(3)The forced vibration of classical and modified Timoshenko beams on elastic,viscoelastic and fractional viscoelastic Pasternak foundation under load is discussed.The displacement functions of classical and modified Timoshenko beams on elastic,viscoelastic and fractional viscoelastic Pasternak foundation are obtained by modal superposition method.