APPROXIMATE THEORY AND ANALYTICAL SOLUTION FOR DYNAMIC CALCULATION OF VISCOELASTIC LAYERED PERIODIC PLATE

Rail transit loading and viscoelastic of material are mostly ignored in the previous dynamic calculations of the periodic vibration isolation structures. Approximate theory and analytical solution for viscoelastic layered periodic plate subjected to vertical moving harmonic loading is established, and the viscoelastic of material and the transverse shear deformation are considered. In this theory, Reissner-Mindlin assumption and additional equation of shear deformation are introduced, and the relation between the normal rotation and the shear stress of neutral plane is obtained on the assumption that the transverse shear deformation of the plate's neutral plane is the overall shear deformation of the cross section. Vibration governing equation of viscoelastic layered periodic plate is proposed according to equilibrium equations and stress continuity conditions, and vertical displacement in Fourier series is derived as well. The model is validated by the good agreement with solution of the classical laminate model and the finite element method (FEM).The results show that:(1) Vibration response at the natural frequency of plate can be significantly reduced by substituting viscoelastic layered periodic plate for homogeneous one, but vibration amplification in local low frequency band is aroused as well. (2) The vertical displacement of the plate increases with the increment of the loading velocity, and increase trend slows down once velocity above 300 km/h. (3) Shear modulus of viscoelastic layer can be designed to achieve the optimal vibration isolation characteristic. (4) Vibration response is not susceptible to damping characteristic in low frequency band. (5) It's appropriate to increase the plate length, within the engineering requirement, to improve the vibration isolation performance.