Optimal Meta‐Foundation for Isolating Structures Under Obliquely Incident Seismic Waves

The safety of civil infrastructure during an earthquake is a critical issue. To address this challenge, we explore the potential use of meta‐foundations to shield structures from obliquely incident seismic waves in this article. Both finite periodic and aperiodic arrangement of rubber and geofoam layers placed beneath the conventional concrete foundation are considered. An analytical method is developed to optimize the material properties and geometric placement of materials in the meta‐foundation to achieve maximum attenuation of seismic waves over a broad range of wave frequencies and incidence angle. This analytical approach combines transfer matrix method and nonlinear constrained optimization for the periodic meta‐foundation, and transfer matrix method is coupled with topology optimization for the aperiodic meta‐foundation. Finally, finite element based numerical simulations are conducted to test the efficacy of the analytically obtained foundation designs when some of the approximations are relaxed to simulate more realistic finite‐width meta‐foundations. This comparison shows that the analytically obtained optimized foundation design works effectively in attenuating both shear and surface waves across a broad frequency range for all incident angles considered.