Gradient-based optimization of seismic metasurfaces for broadband vibration mitigation in layered soil based on power flow

Abstract

This paper presents a gradient-based optimization method to enhance the performance of seismic metasurfaces for broadband vibration mitigation. The metasurface consists of an array of single-degree-of-freedom (SDOF) resonators. A 3D coupled finite element–boundary element method is used to model the interaction of the resonators with the soil. The wave field generated by a point load at the soil’s surface represents environmental ground vibration. The transmitted power is quantified by the power flow through an auxiliary plane behind the metasurface. The integrated power flow over a range of frequencies is minimized in an optimization problem, providing a global metric of the metasurface’s effectiveness. An adjoint formulation is developed to efficiently compute gradients. Initially, each row of resonators is optimized. Subsequently, individual resonators are tuned to explore the trade-off between design complexity and performance. The optimized metasurfaces are benchmarked against a conventional inverse metawedge with graded resonance frequencies and uniform mass. The algorithm yields a non-uniform mass distribution at the total mass limit, achieving enhanced vibration mitigation. The optimization is particularly beneficial in layered soil where the wave propagation pattern is more complex. The performance of both optimized designs is similar, indicating limited benefit from tuning individual resonators. The power-flow-based objective function is shown to be robust with respect to the position and size of the auxiliary plane.