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Robust-to-Uncertainties Optimal Design of Seismic Metamaterials
Paul-Remo Wagner 1 , Vasilis K. Dertimanis 2 , Eleni N. Chatzi 3 , James L. Beck 4

1  Ph.D. Student, Dept. of Civil, Environmental and Geomatic Engineering, Institution of Structural Engineering, ETH Zürich, Stefano-Franscini-Platz 5, 8093 Zürich, Switzerland
2  Researcher, Dept. of Civil, Environmental and Geomatic Engineering, Institution of Structural Engineering, ETH Zürich, Stefano-Franscini-Platz 5, 8093 Zürich, Switzerland
3  Assistant Professor, Dept. of Civil, Environmental and Geomatic Engineering, Institution of Structural Engineering, ETH Zürich, Stefano-Franscini-Platz 5, 8093 Zürich, Switzerland (corresponding author)
4  Professor, Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125

Published: 01 March 2018 by American Society of Civil Engineers in Journal of Engineering Mechanics
American Society of Civil Engineers, Volume 144; 10.1061/(asce)em.1943-7889.0001404
Abstract: Metamaterials, which draw their origin from a special class of structured (periodic) materials characterized by a dynamic filtering effect, have recently emerged as a prospective means for structural seismic protection. This paper explores such a periodic arrangement in the form of local adaptive resonators buried in the soil, serving as a seismic protection barrier. As a starting point, a simplistic representation is chosen herein that comprises chains of mass-in-mass unit cells. A robust-to-uncertainties optimization of such a chain, addressing uncertainties at the level of the excitation, the system properties and the model structure itself, is conducted. The optimization problem is formulated within the context of reliability assessment, where the objective function is the failure probability of the structure to be protected against seismic input. The problem is solved through adoption of the subset optimization algorithm enhanced through the simultaneous implementation of a stochastic approximation algorithm. It is demonstrated that not all parameters of the chain model require optimization, because the failure probability proves to be a monotonic function of a subset of the parameters. A primary objective herein lies in optimizing the internal unit-cell stiffness properties. It is further demonstrated that the effectiveness of the protection offered by the metamaterial is improved for spatially varying unit-cell properties. The optimization procedure is carried out in the frequency domain, with an example application confirming that a time domain optimization is expected to yield similar optimal configurations. A parametric study using a nonlinear model is also presented, offering a starting point for more refined future investigations.
Keywords: Materials Characterized, metamaterials, model require, seismic protection, stochastic approximation, Uncertainties Optimization, unit cell

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