Abstract: The vibration isolation of piles on plane SH waves is simplified to a two-dimensional (2-D) plane problem of elastic wave scattering. Based on the periodic characteristics of the infinite structure in 2-D full-space, an analytical solution for isolation effect of plane SH waves by periodically distributed piles is presented. In the solution, the wave function expansion method together with Graf addition theorem are utilized. Only one periodic element is selected by using the characteristic that the scattering wave field of adjacent periodic elements is one phase different in the frequency domain. Assembling the contribution of the incident wave field and all scattering wave fields, the whole wave fields are obtained by introducing the boundary conditions to determine the unknown coefficients. The analytical solution can accurately solve the scattering problem of infinite periodic distributed piles, and analyze the vibration isolation law when the number of periodic distributed piles is large. It makes up for the shortage that is difficult to solve when there are many piles in the previous theoretical analysis. In this paper, the influences of pile number, pile stiffness, pile spacing and pile type on the vibration isolation effect are discussed. The results show that: 1) The method significantly reduce the amount of storage and calculation in the solving process. The finite period model converges to the infinite period model with the increase of the number of piles, which reflects the correctness of the method. 2) In general, the increase of pile stiffness is beneficial to improve the isolation effect, but it can’t improve vibration isolation effect infinitely. When the shear wave velocity of pile is five times of soil, the isolation effect is enough. 3) The pile spacing has a direct impact on the isolation effect, and reducing the spacing can increase the low frequency band gap width. 4) The type of pile has a significant impact on the isolation effect, the solid pile as a whole has a good isolation effect, and the pipe pile with flexible inner filling has a better isolation effect in the low-frequency segment.

Key words: vibration isolation of piles, periodic distribution, wave function expansion method, Graf addition theorem, plane SH waves