Maximizing the decay of anti-plane shear waves in periodic pile barriers by topology optimization and its application in barrier design considering a moving load

Mitigating ambient vibrations using periodic pile barriers has gained significant attention in the past decade. The width of the bandgap and the attenuation coefficient are two important factors that determine the vibration reduction capabilities of periodic pile barriers. In certain situations, significant vertical anti-plane vibrations may occur, such as those generated by subways. Therefore, the focus of this article is to optimize the attenuation coefficients of anti-plane shear waves in periodic pile barriers. Firstly, a single-objective topology optimization framework is developed based on the Genetic Algorithm (GA) to maximize the attenuation coefficient of anti-plane shear waves in periodic pile barriers at a target frequency. The optimization considers the effects of the target frequency, elastic modulus of soil, and wave vector direction. A comparison between the optimized and traditional pile barriers is performed to demonstrate the superiority of the optimized design. Secondly, a multi-objective optimization framework is developed based on the non-dominated sorting GA II (NSGA-II) to investigate the relationship between the attenuation coefficient and the filling fraction, as well as the relationship between the attenuation coefficient and the bandgap width. The results indicate that a higher filling fraction results in a larger attenuation coefficient, while there is a tradeoff between the filling ratio and the bandgap width. Thirdly, an optimization framework is established considering the effect of a moving load, and the coverage rate of the target frequency range is defined to design periodic pile barriers. Finally, numerical simulations are conducted to validate the effectiveness of periodic pile barriers in mitigating vibrations when a finite number of pile rows is used.