Calculation Method and Characteristics of Periodic Pile Arrangement Based on Artificial Spring Model

As a new type of vibration reduction system, periodic row piles achieve vibration suppression and even isolation, which is of great significance in the field of vibration isolation and damping. Periodic row piles in soil exhibit an attenuation domain, which has a significant isolation effect on vibrations within this domain. This study introduces an artificial spring model based on periodic theory and the energy principle to simulate the boundary of periodic elements and the closely connected interface between piles and soil. The boundary constraints are transformed into the elastic potential energy of the spring, overcoming the difficulty of constructing displacement shape functions that satisfy boundary conditions using traditional energy methods. When calculating the attenuation domain by scanning the wave number, only the stiffness matrix corresponding to the elastic potential energy of the periodic boundary contains the wave number term. In contrast, the mass matrix and other stiffness matrices do not include this term, eliminating the need for repeated calculations and significantly reducing the computational workload. The convergence analysis of the number of terms in the shape function and the stiffness of the artificial spring, compared to the finite element method, demonstrates that the proposed method not only provides high accuracy but also improves computational efficiency. When comparing different forms of hexagonal row piles and square row piles with the same filling rate, the attenuation domain width of hexagonal row piles is larger than that of square row piles. When comparing different pile types, such as pipe piles and solid piles, with the same filling rate, the attenuation domain width of pipe piles is also larger than that of solid piles. In addition, analyzing the influence of filled soil on the attenuation domain indicates that the width of the attenuation domain increases with the density of the filled soil, and first increases and then decreases with the increase of the elastic modulus of the filled soil. The maximum width of the attenuation domain is obtained when <italic>E</italic>=16 MPa.