Study On Wave And Vibration Behavior Of Rectangular Plate On Fractional Viscoelastic Foundation

At present,a large number of studies on foundation plate are based on Kirchhoff plate theory.However,in practical engineering applications,many engineering structures have relatively large thickness and span,which is obviously beyond the scope of application of thin plate theory.Therefore,research on Mindlin medium thick plate is also crucial in engineering.Upper plate on elastic foundation of the free vibration and dynamic response problem of domestic and foreign scholars have done a lot of research,but in the practical engineering,the foundation more show the viscoelastic properties,so the upper fluctuations on a viscoelastic foundation,studies the vibration and dynamic response can provide better supporting role in engineering problems in the processing.Some scholars have found that fractional calculus can better analyze and study viscoelastic materials.Therefore,some scholars thought of using fractional calculus theory to describe the viscoelastic properties of foundation soil.Based on this background,this thesis established fractional viscoelastic Pasternak foundation model to simulate the real situation of foundation soil frequently encountered in engineering.This thesis,based on the elastic Pasternak foundation,continues to take into account the viscosity of the foundation,and the fractional viscoelastic pastoral model is established by the combination of viscoelastic standard foundations and the theory of fractional calculus.The spread of bending waves in Kirchhoff and Mindlin plates on elastic,viscoelastic and fractional viscoelastic foundations,The natural frequencies and modes of free vibration and the stationary reaction of the charged plates are examined.The main research contents and conclusions are as follows:(1)analysis of elasticity and the fluctuation problem of thin plate extent on a viscoelastic foundation Pasternak,with and without damping to wave damping in the foundation types and had significant effect on the propagation characteristics of thin plate on elastic foundation existing in the two opposite direction wave propagation and standing wave propagation in the opposite direction,and the thin plate on viscoelastic foundation there are four kinds of wave attenuation,The viscosity coefficient also has obvious influence on the velocity of these four traveling waves.According to the wave number expression,there are six medium waves in the plate,which can be divided into three groups.The type of the first wave has no relation with the foundation,but only affects the latter two groups of waves.(2)The free vibration of thin plate and medium thick plate on elastic and viscoelastic Pasternak foundation is studied.The first three natural frequencies and modes of plate under different boundary conditions are obtained,and the influence of foundation parameters and viscosity coefficient is analyzed.(3)The waves of thin plate and medium thick plate on fractional viscoelastic Pasternak foundation are studied,and the effects of foundation parameters,fractional order and viscosity coefficient on wave types and propagation characteristics are analyzed.(4)The dynamic response of thin plate and medium thick plate on fractional order viscoelastic Pasternak foundation under uniform distributed load is studied,and the influence of foundation parameters,fractional order and viscosity coefficient on the response time curve of plate center displacement is analyzed.