Attenuation zones of periodic pile barriers with initial stress

Periodic pile barriers exhibit unique dynamic property, i.e., the frequency attenuation zones. When wave frequencies fall in the attenuation zones, the amplitude of the elastic waves could be reduced by the periodic pile barriers. In the present paper, out-of-plane waves propagating in two-dimensional periodic pile barriers are investigated. A novel numerical approach based on the weak form quadrature element method (WFQEM) is developed to study the effect of initial stress on the attenuation zones of the pile barriers. The proposed method is verified to be with significant advantages in both accuracy and convergence with regard to the lumped-mass method (LMM) in particular cases. The theoretical results show that the initial stress significantly alters the position and width of the attenuation zones, however, it does not affect the maximum attenuation coefficient. In addition, elastic waves propagating in periodic pile barriers with finite number of unit cells is simulated at the end of this paper. The results obtained in the present paper are very useful for the design and application of periodic pile barriers in ambient vibration reduction.