{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,17]],"date-time":"2025-11-17T02:07:22Z","timestamp":1763345242338,"version":"3.45.0"},"reference-count":69,"publisher":"Tech Science Press","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["CMC"],"published-print":{"date-parts":[[2025]]},"DOI":"10.32604\/cmc.2025.067761","type":"journal-article","created":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T11:14:57Z","timestamp":1753269297000},"page":"557-580","source":"Crossref","is-referenced-by-count":0,"title":["An Optimization-Driven Design Scheme of Lightweight Acoustic Metamaterials for Additive Manufacturing"],"prefix":"10.32604","volume":"85","author":[{"given":"Ying","family":"Zhou","sequence":"first","affiliation":[]},{"given":"Jiayang","family":"Yuan","sequence":"additional","affiliation":[]},{"given":"Zhengtao","family":"Shu","sequence":"additional","affiliation":[]},{"given":"Mengli","family":"Ye","sequence":"additional","affiliation":[]},{"given":"Liang","family":"Gao","sequence":"additional","affiliation":[]},{"given":"Qiong","family":"Wang","sequence":"additional","affiliation":[]}],"member":"17807","published-online":{"date-parts":[[2025]]},"reference":[{"key":"ref1","doi-asserted-by":"crossref","first-page":"e2305232","DOI":"10.1002\/advs.202305232","article-title":"3D-printed lattice structures for sound absorption: current progress, mechanisms and models, structural-property relationships, and future outlook","volume":"11","author":"Li","year":"2024","journal-title":"Adv Sci"},{"key":"ref2","doi-asserted-by":"crossref","first-page":"e2435562","DOI":"10.1080\/17452759.2024.2435562","article-title":"Additively manufactured metamaterials for acoustic absorption: a review","volume":"19","author":"Sekar","year":"2024","journal-title":"Virtual Phys Prototyp"},{"key":"ref3","doi-asserted-by":"crossref","first-page":"nwab171","DOI":"10.1093\/nsr\/nwab171","article-title":"Broadband impedance modulation via non-local acoustic metamaterials","volume":"9","author":"Zhou","year":"2022","journal-title":"Natl Sci Rev"},{"key":"ref4","doi-asserted-by":"crossref","first-page":"104601","DOI":"10.1016\/j.mechmat.2023.104601","article-title":"Soil-expended seismic metamaterial with ultralow and wide bandgap","volume":"180","author":"Bai","year":"2023","journal-title":"Mech Mater"},{"key":"ref5","doi-asserted-by":"crossref","first-page":"2210160","DOI":"10.1002\/adfm.202210160","article-title":"Multi-level bioinspired microlattice with broadband sound-absorption capabilities and deformation-tolerant compressive response","volume":"33","author":"Li","year":"2023","journal-title":"Adv Funct Mater"},{"key":"ref6","doi-asserted-by":"crossref","first-page":"109016","DOI":"10.1016\/j.apacoust.2022.109016","article-title":"Acoustic properties of honeycomb like sandwich acoustic metamaterials","volume":"199","author":"Gai","year":"2022","journal-title":"Appl Acoust"},{"key":"ref7","doi-asserted-by":"crossref","first-page":"1334","DOI":"10.1016\/j.physleta.2016.01.041","article-title":"Pentamodal property and acoustic band gaps of pentamode metamaterials with different cross-section shapes","volume":"380","author":"Huang","year":"2016","journal-title":"Phys Lett A"},{"key":"ref8","doi-asserted-by":"crossref","first-page":"1300","DOI":"10.1002\/nme.5616","article-title":"Optimum design of an acoustic metamaterial with negative bulk modulus in an acoustic-elastic coupled system using a level set-based topology optimization method","volume":"113","author":"Noguchi","year":"2018","journal-title":"Numer Meth Eng"},{"key":"ref9","doi-asserted-by":"crossref","first-page":"1861","DOI":"10.1038\/s41598-018-19374-2","article-title":"Design of an acoustic superlens using single-phase metamaterials with a star-shaped lattice structure","volume":"8","author":"Chen","year":"2018","journal-title":"Sci Rep"},{"key":"ref10","doi-asserted-by":"crossref","first-page":"105638","DOI":"10.1016\/j.ijmecsci.2020.105638","article-title":"Evolutionary topology optimization for mechanical metamaterials with auxetic property","volume":"179","author":"Zheng","year":"2020","journal-title":"Int J Mech Sci"},{"key":"ref11","doi-asserted-by":"crossref","first-page":"2399","DOI":"10.1007\/s00158-020-02819-6","article-title":"Design of one-dimensional acoustic metamaterials using machine learning and cell concatenation","volume":"63","author":"Wu","year":"2021","journal-title":"Struct Multidiscip Optim"},{"key":"ref12","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/0021-9991(88)90002-2","article-title":"Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations","volume":"79","author":"Osher","year":"1988","journal-title":"J Comput Phys"},{"key":"ref13","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1006\/jcph.2000.6581","article-title":"Structural boundary design via level set and immersed interface methods","volume":"163","author":"Sethian","year":"2000","journal-title":"J Comput Phys"},{"key":"ref14","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/S0045-7825(02)00559-5","article-title":"A level set method for structural topology optimization","volume":"192","author":"Wang","year":"2003","journal-title":"Comput Meth Appl Mech Eng"},{"key":"ref15","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/0045-7825(91)90046-9","article-title":"The COC algorithm, part II: topological, geometrical and generalized shape optimization","volume":"89","author":"Zhou","year":"1991","journal-title":"Comput Meth Appl Mech Eng"},{"key":"ref16","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1007\/s004190050248","article-title":"Material interpolation schemes in topology optimization","volume":"69","author":"Bends\u00f8e","year":"1999","journal-title":"Arch Appl Mech"},{"key":"ref17","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1007\/s001580050176","article-title":"A 99 line topology optimization code written in Matlab","volume":"21","author":"Sigmund","year":"2001","journal-title":"Struct Multidiscip Optim"},{"key":"ref18","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/0045-7825(88)90086-2","article-title":"Generating optimal topologies in structural design using a homogenization method","volume":"71","author":"Bends\u00f8e","year":"1988","journal-title":"Comput Meth Appl Mech Eng"},{"key":"ref19","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1016\/0045-7949(93)90035-C","article-title":"A simple evolutionary procedure for structural optimization","volume":"49","author":"Xie","year":"1993","journal-title":"Comput Struct"},{"key":"ref20","doi-asserted-by":"crossref","first-page":"081009","DOI":"10.1115\/1.4027609","article-title":"Doing topology optimization explicitly and geometrically\u2014a new moving morphable components based framework","volume":"81","author":"Guo","year":"2014","journal-title":"J Appl Mech"},{"key":"ref21","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1016\/j.cma.2015.05.005","article-title":"A geometry projection method for continuum-based topology optimization with discrete elements","volume":"293","author":"Norato","year":"2015","journal-title":"Comput Meth Appl Mech Eng"},{"key":"ref22","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1016\/j.apm.2021.05.005","article-title":"Topology optimization of acoustic metasurfaces by using a two-scale homogenization method","volume":"98","author":"Noguchi","year":"2021","journal-title":"Appl Math Model"},{"key":"ref23","doi-asserted-by":"crossref","first-page":"103606","DOI":"10.1016\/j.finel.2021.103606","article-title":"Level set-based topology optimization for graded acoustic metasurfaces using two-scale homogenization","volume":"196","author":"Noguchi","year":"2021","journal-title":"Finite Elem Anal Des"},{"key":"ref24","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/s00158-009-0477-y","article-title":"Topological design of vibrating structures with respect to optimum sound pressure characteristics in a surrounding acoustic medium","volume":"42","author":"Du","year":"2010","journal-title":"Struct Multidiscip Optim"},{"key":"ref25","doi-asserted-by":"crossref","first-page":"110832","DOI":"10.1016\/j.matdes.2022.110832","article-title":"Level set-based topology optimization for the design of labyrinthine acoustic metamaterials","volume":"219","author":"Noguchi","year":"2022","journal-title":"Mater Des"},{"key":"ref26","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1016\/j.cma.2018.02.031","article-title":"Topology optimization for hyperbolic acoustic metamaterials using a high-frequency homogenization method","volume":"335","author":"Noguchi","year":"2018","journal-title":"Comput Meth Appl Mech Eng"},{"key":"ref27","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1007\/s00158-016-1424-3","article-title":"Evolutionary topological design for phononic band gap crystals","volume":"54","author":"Li","year":"2016","journal-title":"Struct Multidiscip Optim"},{"key":"ref28","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.jsv.2017.08.015","article-title":"Topological design of phononic crystals for unidirectional acoustic transmission","volume":"410","author":"Chen","year":"2017","journal-title":"J Sound Vib"},{"key":"ref29","doi-asserted-by":"crossref","first-page":"101126","DOI":"10.1016\/j.eml.2020.101126","article-title":"Realization of full and directional band gap design by non-gradient topology optimization in acoustic metamaterials","volume":"42","author":"Zhang","year":"2021","journal-title":"Extrem Mech Lett"},{"key":"ref30","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1039\/D2MH00977C","article-title":"Multifunctional sound-absorbing and mechanical metamaterials via a decoupled mechanism design approach","volume":"10","author":"Li","year":"2023","journal-title":"Mater Horiz"},{"key":"ref31","doi-asserted-by":"crossref","first-page":"9940","DOI":"10.1021\/acsami.2c19456","article-title":"New class of multifunctional bioinspired microlattice with excellent sound absorption, damage tolerance, and high specific strength","volume":"15","author":"Li","year":"2023","journal-title":"ACS Appl Mater Interfaces"},{"key":"ref32","doi-asserted-by":"crossref","first-page":"063502","DOI":"10.1063\/1.4941338","article-title":"Acoustic metasurface-based perfect absorber with deep subwavelength thickness","volume":"108","author":"Li","year":"2016","journal-title":"Appl Phys Lett"},{"key":"ref33","doi-asserted-by":"crossref","first-page":"108942","DOI":"10.1016\/j.apacoust.2022.108942","article-title":"Thickness-designable acoustic metamaterial for passive phased arrays","volume":"198","author":"Li","year":"2022","journal-title":"Appl Acoust"},{"key":"ref34","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1016\/j.cma.2016.05.039","article-title":"An isogeometric indirect boundary element method for solving acoustic problems in open-boundary domains","volume":"316","author":"Coox","year":"2017","journal-title":"Comput Meth Appl Mech Eng"},{"key":"ref35","doi-asserted-by":"crossref","first-page":"245","DOI":"10.3390\/en13010245","article-title":"Acoustic noise computation of electrical motors using the boundary element method","volume":"13","author":"Sathyan","year":"2020","journal-title":"Energies"},{"key":"ref36","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.advengsoft.2016.09.001","article-title":"GTApprox: surrogate modeling for industrial design","volume":"102","author":"Belyaev","year":"2016","journal-title":"Adv Eng Softw"},{"key":"ref37","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00158-001-0160-4","article-title":"Comparative studies of metamodelling techniques under multiple modelling criteria","volume":"23","author":"Jin","year":"2001","journal-title":"Struct Multidiscip Optim"},{"key":"ref38","doi-asserted-by":"crossref","first-page":"107307","DOI":"10.1016\/j.ijmecsci.2022.107307","article-title":"Graded infill design within free-form surfaces by conformal mapping","volume":"224","author":"Zhou","year":"2022","journal-title":"Int J Mech Sci"},{"key":"ref39","doi-asserted-by":"crossref","first-page":"13709","DOI":"10.1007\/s00500-022-07362-8","article-title":"Recent advances and applications of surrogate models for finite element method computations: a review","volume":"26","author":"Kudela","year":"2022","journal-title":"Soft Comput"},{"key":"ref40","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1016\/j.advengsoft.2017.09.011","article-title":"An integrated beam-plate structure multi-level optimal design framework based on bi-directional evolutionary structural optimization and surrogate model","volume":"115","author":"Li","year":"2018","journal-title":"Adv Eng Softw"},{"key":"ref41","doi-asserted-by":"crossref","first-page":"994","DOI":"10.1108\/AEAT-06-2018-0157","article-title":"A novel improvement of Kriging surrogate model","volume":"91","author":"He","year":"2019","journal-title":"Aircr Eng Aerosp Technol"},{"key":"ref42","doi-asserted-by":"crossref","first-page":"108858","DOI":"10.1016\/j.ress.2022.108858","article-title":"An efficient multi-fidelity Kriging surrogate model-based method for global sensitivity analysis","volume":"229","author":"Shang","year":"2023","journal-title":"Reliab Eng Syst Saf"},{"key":"ref43","doi-asserted-by":"crossref","first-page":"113257","DOI":"10.1016\/j.compstruct.2020.113257","article-title":"Sound insulation performance of membrane-type metamaterials combined with pyramidal truss core sandwich structure","volume":"260","author":"Wang","year":"2021","journal-title":"Compos Struct"},{"key":"ref44","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/s00158-002-0213-3","article-title":"Efficient optimization of a noise transfer function by modification of a shell structure geometry\u2014part I: theory","volume":"24","author":"Marburg","year":"2002","journal-title":"Struct Multidiscip Optim"},{"key":"ref45","doi-asserted-by":"crossref","first-page":"A92","DOI":"10.1121\/10.0004613","article-title":"A tutorial on the finite and boundary element methods in acoustics","volume":"149","author":"Hargreaves","year":"2021","journal-title":"J Acoust Soc Am"},{"key":"ref46","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1006\/jsvi.2001.4037","article-title":"Experimental verification of structural-acoustic modelling and design optimization","volume":"252","author":"Marburg","year":"2002","journal-title":"J Sound Vib"},{"key":"ref47","first-page":"83","article-title":"On analysis and optimization in structural acoustics: part I: problem formulation and solution techniques","volume":"16","author":"Christensen","year":"1998","journal-title":"Struct Optim"},{"key":"ref48","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1016\/j.cma.2016.06.012","article-title":"Integrated design of cellular composites using a level-set topology optimization method","volume":"309","author":"Li","year":"2016","journal-title":"Comput Meth Appl Mech Eng"},{"key":"ref49","doi-asserted-by":"crossref","first-page":"404","DOI":"10.1002\/nme.6055","article-title":"Topology optimization of exterior acoustic-structure interaction systems using the coupled FEM-BEM method","volume":"119","author":"Zhao","year":"2019","journal-title":"Int J Numer Meth Eng"},{"key":"ref50","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1007\/s00158-010-0562-2","article-title":"Heaviside projection based topology optimization by a PDE-filtered scalar function","volume":"44","author":"Kawamoto","year":"2011","journal-title":"Struct Multidiscip Optim"},{"key":"ref51","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/s00158-018-2064-6","article-title":"Topology optimization of shell-infill structures using a distance regularized parametric level-set method","volume":"59","author":"Fu","year":"2019","journal-title":"Struct Multidiscip Optim"},{"key":"ref52","doi-asserted-by":"crossref","first-page":"113354","DOI":"10.1016\/j.cma.2020.113354","article-title":"Spatial-varying multi-phase infill design using density-based topology optimization","volume":"372","author":"Li","year":"2020","journal-title":"Comput Meth Appl Mech Eng"},{"key":"ref53","doi-asserted-by":"crossref","first-page":"3574","DOI":"10.1121\/1.4987600","article-title":"Design of broadband acoustic metamaterials for low-frequency noise insulation","volume":"141","author":"Liu","year":"2017","journal-title":"J Acoust Soc Am"},{"key":"ref54","doi-asserted-by":"crossref","first-page":"6253428","DOI":"10.1155\/2017\/6253428","article-title":"A structure design method for reduction of MRI acoustic noise","volume":"2017","author":"Nan","year":"2017","journal-title":"Comput Math Methods Med"},{"key":"ref55","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.jsv.2017.05.040","article-title":"A level set-based topology optimization method for simultaneous design of elastic structure and coupled acoustic cavity using a two-phase material model","volume":"404","author":"Noguchi","year":"2017","journal-title":"J Sound Vib"},{"key":"ref56","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1016\/j.cma.2017.06.015","article-title":"Topology optimization of continuum structures subjected to filtered white noise stochastic excitations","volume":"324","author":"Yang","year":"2017","journal-title":"Comput Meth Appl Mech Eng"},{"key":"ref57","doi-asserted-by":"crossref","first-page":"1583","DOI":"10.2514\/2.2111","article-title":"Particle swarm optimization","volume":"41","author":"Venter","year":"2003","journal-title":"AIAA J"},{"key":"ref58","doi-asserted-by":"crossref","first-page":"4460","DOI":"10.1016\/j.ins.2010.05.025","article-title":"Cellular particle swarm optimization","volume":"181","author":"Shi","year":"2011","journal-title":"Inf Sci"},{"key":"ref59","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/S0951-8320(03)00058-9","article-title":"Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems","volume":"81","author":"Helton","year":"2003","journal-title":"Reliab Eng Syst Saf"},{"key":"ref60","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/S0167-4730(02)00039-5","article-title":"On Latin hypercube sampling for structural reliability analysis","volume":"25","author":"Olsson","year":"2003","journal-title":"Struct Saf"},{"key":"ref61","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1002\/nme.2750","article-title":"An algorithm for fast optimal Latin hypercube design of experiments","volume":"82","author":"Viana","year":"2010","journal-title":"Numer Meth Eng"},{"key":"ref62","first-page":"3107","article-title":"Reliability-based design optimization using inherited Latin hypercube sampling and local kriging approximation","volume":"24","author":"Li","year":"2018","journal-title":"Comput Integr Manuf Syst"},{"key":"ref63","doi-asserted-by":"crossref","first-page":"2664","DOI":"10.1109\/TCYB.2017.2710978","article-title":"Committee-based active learning for surrogate-assisted particle swarm optimization of expensive problems","volume":"47","author":"Wang","year":"2017","journal-title":"IEEE Trans Cybern"},{"key":"ref64","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.knosys.2018.08.010","article-title":"A generation-based optimal restart strategy for surrogate-assisted social learning particle swarm optimization","volume":"163","author":"Yu","year":"2019","journal-title":"Knowl Based Syst"},{"key":"ref65","doi-asserted-by":"crossref","first-page":"2424","DOI":"10.2514\/1.J055649","article-title":"Adaptive radial-basis-function-based multifidelity metamodeling for expensive black-box problems","volume":"55","author":"Cai","year":"2017","journal-title":"AIAA J"},{"key":"ref66","doi-asserted-by":"crossref","first-page":"1439","DOI":"10.1016\/j.cma.2008.12.008","article-title":"Topology design of multi-material soundproof structures including poroelastic media to minimize sound pressure levels","volume":"198","author":"Yamamoto","year":"2009","journal-title":"Comput Meth Appl Mech Eng"},{"key":"ref67","doi-asserted-by":"crossref","first-page":"111199","DOI":"10.1016\/j.compstruct.2019.111199","article-title":"Study on mechanical properties of honeycomb pentamode structures fabricated by laser additive manufacturing: numerical simulation and experimental verification","volume":"226","author":"Zhang","year":"2019","journal-title":"Compos Struct"},{"key":"ref68","doi-asserted-by":"crossref","first-page":"1517","DOI":"10.1007\/s00366-023-01880-1","article-title":"A ready-to-manufacture optimization design of 3D chiral auxetics for additive manufacturing","volume":"40","author":"Zhou","year":"2024","journal-title":"Eng Comput"},{"key":"ref69","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/j.matdes.2018.08.032","article-title":"On two-step design of microstructure with desired Poisson\u2019s ratio for AM","volume":"159","author":"Zong","year":"2018","journal-title":"Mater Des"}],"container-title":["Computers, Materials & Continua"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/cdn.techscience.cn\/files\/cmc\/2025\/TSP_CMC-85-1\/TSP_CMC_67761\/TSP_CMC_67761.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,17]],"date-time":"2025-11-17T02:02:59Z","timestamp":1763344979000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.techscience.com\/cmc\/v85n1\/63571"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"references-count":69,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025]]},"published-print":{"date-parts":[[2025]]}},"URL":"https:\/\/doi.org\/10.32604\/cmc.2025.067761","relation":{},"ISSN":["1546-2226"],"issn-type":[{"type":"electronic","value":"1546-2226"}],"subject":[],"published":{"date-parts":[[2025]]}}}