Topology optimization of periodic barriers for surface waves

Abstract

Dispersion engineering is always the important topic in the field of artificial periodic structures. In particular, topology optimization of composite structures with expected bandgaps plays a key role. However, most reported studies focused on topology optimization for bulk waves, and the optimization for surface wave bandgaps (SWBGs) is still missing. In this paper, we develop a topology optimization framework based on the genetic algorithm and finite element method to design periodic barriers embedded in semi-infinite space for reducing surface waves on demand. The objective functions for SWBGs are proposed based on the energy distribution properties of surface waves. The numerical results show that the optimization framework has stable convergence for this problem and is effective to optimize SWBGs. Considering large SWBGs and low filling fraction of solids, we investigate single-and multi-objective optimizations, respectively, and obtain novel wave barriers with good performance. The beneficial configuration features and mechanism of broadband SWBGs from the optimized results are explored. The results indicate that for the first-order SWBG, most optimized structures consist of a main scatterer at the center and some subsidiary scatterers near the surface. The rigid body resonance of the main scatterer determines the lower edge of SWBG, and the subsidiary scatterers can regulate the upper edge. Higher-order SWBGs are generated from the interaction of multiple scatterers, whose relative distance has a great influence on the position of SWBGs. The optimized structures can make the surface waves propagate far away from the surface within the frequencies of bandgaps, leading to a strong attenuation of surface vibration. In practice, our topological optimization framework is promising in designing high-performance surface wave devices and novel isolating structures for earthquake or environmental vibration in civil engineering.

Metamaterial approach to mitigate ground‐borne vibrations induced by moving trains

“…However, mitigation results are also affected by buried vertical structure parameters that are periodically arranged between the source and receiver, such as the length of the structure, cross-sectional volume parameters, and the distance between adjacent structures. Similar research methods and results readers can also found in He and colleagues[45][46][47][48][49][50][51][52][53][54][55][56] and references therein.F I G U R E 8 Schematic diagram of metamaterials in the fastener system and track bed[40].F I G U R E 9 Metamaterial-based mitigation measures on the transmission path: (a) Mitigation device based on the phononic crystal concept[23]; (b) the 3D coupled train-track-soil model, where the insets are the seismic metamaterials composed of an array of concrete inclusions[42]; (c) the periodic underground barriers based on the concept of phononic crystals[43]; and (d) vibration generated by the subway and the periodic pile barrier[44]. 3D, three dimensional.In addition, Dijckmans et al [57] investigated the effectiveness of a sheet pile wall in reducing train-induced vibration transmission by utilizing field measurements and numerical simulation.…”

Tailoring Structure‐Borne Sound through Bandgap Engineering in Phononic Crystals and Metamaterials: A Comprehensive Review

“…This has led to inverse‐design based studies that start with the desired BG configuration or functionality and employ optimization approaches to arrive at the geometry and material that is required to achieve them. Most of these efforts largely rely on topology optimization, [ 56,57,411–436 ] genetic algorithms, [ 215,432,437,438 ] or machine learning‐based approaches [ 439–446 ] and have unveiled unusual and hence previously inconceivable geometries that enable materials with enhanced BG characteristics. While these efforts are now burgeoning thanks to modern computational power, one of the earliest fruitful strides in this direction for elastic waves, can be attributed to the works of Sigmund and Søndergaard Jensen [ 411 ] in the early 2000s, who first put forward a theoretical framework showing that phononic BGs could be considerably enlarged by opening the design space of the unit cell geometry, while enforcing the boundary conditions as constraints—in other words, via topology optimization.…”

Topological design of 2D periodic structures for anti-plane waves based on deep learning

“…Some efficient design methods were developed for periodic structures with analytical formulation or tunability (Mehaney and Ahmed, 2020; Wang et al, 2020b), but the problems addressed are limited. Recently, some scholars obtained great achievements in the inverse design of periodic structures using gradient-based or gradient-free algorithms (Chen et al, 2010; Gasparetto and ElSayed, 2021; Li and Li, 2018; Liu et al, 2021; Sigmund and Søndergaard Jensen, 2003). However, gradient-based algorithms need to preset an initial value close to the design target and easily falls into a local optimum (Zhao et al, 2011), and for multiple eigenvalue problems, the sensitivity analysis and the formula derivation process are complicated (Aishima, 2018).…”