{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T17:32:41Z","timestamp":1775583161211,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,6,30]],"date-time":"2022-06-30T00:00:00Z","timestamp":1656547200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China (NNSFC)","award":["12172186"],"award-info":[{"award-number":["12172186"]}]},{"name":"National Natural Science Foundation of China (NNSFC)","award":["11772166"],"award-info":[{"award-number":["11772166"]}]},{"name":"National Natural Science Foundation of China (NNSFC)","award":["11832002"],"award-info":[{"award-number":["11832002"]}]},{"name":"National Natural Science Foundation of China (NNSFC)","award":["11672188"],"award-info":[{"award-number":["11672188"]}]},{"name":"National Natural Science Foundation of China (NNSFC)","award":["11772166"],"award-info":[{"award-number":["11772166"]}]},{"name":"Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (PHRIHLB)","award":["12172186"],"award-info":[{"award-number":["12172186"]}]},{"name":"Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (PHRIHLB)","award":["11772166"],"award-info":[{"award-number":["11772166"]}]},{"name":"Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (PHRIHLB)","award":["11832002"],"award-info":[{"award-number":["11832002"]}]},{"name":"Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (PHRIHLB)","award":["11672188"],"award-info":[{"award-number":["11672188"]}]},{"name":"Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (PHRIHLB)","award":["11772166"],"award-info":[{"award-number":["11772166"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Negative Poisson\u2019s ratio materials are increasingly used in the design of vibration isolation bases due to their unique tensile properties. In this paper, based on the expansion feature of the negative Poisson\u2019s ratio re-entrant structure, the influence of the size of the re-entrant structure within a single structure was analyzed, and a honeycomb base was designed with a negative Poisson\u2019s ratio re-entrant structure. A new modeling method for the honeycomb base is proposed. In the modeling process, the honeycomb base was analyzed according to its symmetry using the Lagrange equation for base modeling and the finite element consistent mass matrix was introduced to simplify the calculation. The vibration isolation performance of the honeycomb base was evaluated by vibration level difference. COMSOL software was used to simulate and analyze the cellular base in order to verify the correctness of the results obtained from numerical modeling. In conclusion, the honeycomb base had a vibration isolation effect on external excitation in the vertical direction of the base. Furthermore, the vibration isolation performance of the base was greatly related to the wall thickness and Poisson\u2019s ratio of the re-entrant structure.<\/jats:p>","DOI":"10.3390\/sym14071356","type":"journal-article","created":{"date-parts":[[2022,7,1]],"date-time":"2022-07-01T01:40:36Z","timestamp":1656639636000},"page":"1356","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Negative Poisson\u2019s Ratio Re-Entrant Base Modeling and Vibration Isolation Performance Analysis"],"prefix":"10.3390","volume":"14","author":[{"given":"Kun","family":"Pan","sequence":"first","affiliation":[{"name":"Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0210-5642","authenticated-orcid":false,"given":"Wei","family":"Zhang","sequence":"additional","affiliation":[{"name":"Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2085-5383","authenticated-orcid":false,"given":"Jieyu","family":"Ding","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,30]]},"reference":[{"key":"ref_1","first-page":"15","article-title":"Reviews on metamaterials manufacturing via 3D printing","volume":"4","author":"Hu","year":"2017","journal-title":"Ind. Technol. Innov."},{"key":"ref_2","unstructured":"Liu, W.W. (2004). Mechanics of Materials I, Higher Education Press."},{"key":"ref_3","first-page":"48","article-title":"Advances in negative Poisson\u2019s ratio materials","volume":"6","author":"Shi","year":"2003","journal-title":"Polym. Bull."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"41101","DOI":"10.1063\/1.4964479","article-title":"Auxetic nanomaterials, precent progress and future development","volume":"3","author":"Jiang","year":"2016","journal-title":"Appl. Phys. Rev."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1963","DOI":"10.1002\/pssb.201248550","article-title":"A review of the manufacture, mechanical properties and potential applications of auxetic foams","volume":"250","author":"Critchley","year":"2013","journal-title":"Phys. Status Solidi"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1049\/esej:20000402","article-title":"Auxetic materials, the positive side of being negative","volume":"9","author":"Evans","year":"2000","journal-title":"Eng. Sci. Educ. J."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"753496","DOI":"10.1155\/2014\/753496","article-title":"Review of Mechanics and Applications of Auxetic Structures","volume":"2014","author":"Mir","year":"2014","journal-title":"Adv. Mater. Sci. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"897","DOI":"10.1177\/1045389X08099605","article-title":"In-plane Tensile Behavior of Shape Memory Alloy Honeycombs with Positive and Negative Poisson\u2019s Ratio","volume":"20","author":"Hassan","year":"2009","journal-title":"J. Intell. Mater. Syst. Struct."},{"key":"ref_9","first-page":"25","article-title":"The Mechanics of two-dimensional cellular materials","volume":"382","author":"Gibson","year":"1982","journal-title":"Proc. R. Soc. A"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2712","DOI":"10.1002\/adfm.201002022","article-title":"Three-dimensional polymer constructs exhibiting a tunable negative Poisson\u2019s ratio","volume":"21","author":"Fozdar","year":"2011","journal-title":"Adv. Funct. Mater."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Gibson, L.J., and Ashby, M.F. (1997). Cellular Solids, Structure and Properties, Cambridge University Press.","DOI":"10.1017\/CBO9781139878326"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1243\/0309324001514152","article-title":"Numerical and experimental uniaxial loading on in-plane auxetic honeycombs","volume":"35","author":"Scarpa","year":"2000","journal-title":"J. Strain Anal. Eng. Des."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1179\/146580102225006495","article-title":"Auxetic polypropylene fibres, Part 1 Manufacture and character isation","volume":"31","author":"Alderson","year":"2013","journal-title":"Plast. Rubber Compos."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1080\/08927020500401139","article-title":"On the potential of connected stars as auxetic systems","volume":"31","author":"Grima","year":"2005","journal-title":"Mol. Simul."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Lim, T.C. (2015). Auxetic Materials and Structures, Springer.","DOI":"10.1007\/978-981-287-275-3"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2091","DOI":"10.1098\/rspa.1999.0394","article-title":"Micropolar theory for two-dimensional stresses in elastic honeycomb","volume":"455","author":"Wang","year":"1999","journal-title":"Proc. R. Soc. A"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1016\/j.proeng.2014.06.079","article-title":"Auxetic materials for sports applications","volume":"72","author":"Sanami","year":"2014","journal-title":"Procedia Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/j.jsv.2004.10.051","article-title":"Free vibration of cellular structures using continuum modes","volume":"287","author":"Banerjee","year":"2005","journal-title":"J. Sound Vib."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1177\/1045389X03035515","article-title":"Control of wave propagation in sandwich beams with auxetic core","volume":"14","author":"Ruzzene","year":"2003","journal-title":"J. Intell. Mater. Syst. Struct."},{"key":"ref_20","first-page":"123","article-title":"Computational modelling of vibrations transmission loss of auxetic lattice structure","volume":"27","author":"Idczak","year":"2016","journal-title":"Vib. Phys. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"084012","DOI":"10.1088\/0964-1726\/22\/8\/084012","article-title":"A nonlinear auxetic structural vibration damper with metal rubber particles","volume":"22","author":"Ma","year":"2013","journal-title":"Smart Mater. Struct."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/j.matdes.2013.04.004","article-title":"Multi-physics modeling of the fabrication and dynamic performance of all-metal auxetic-hexagonal sandwich-structures","volume":"51","author":"Grujicic","year":"2013","journal-title":"Mater. Des."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"51007","DOI":"10.1115\/1.4030007","article-title":"Analyses on the In-Plane Impact Resistance of Auxetic Double Arrowhead Honeycombs","volume":"82","author":"Qiao","year":"2015","journal-title":"J. Appl. Mech."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/j.matdes.2016.12.067","article-title":"Design and modeling of auxetic and hybrid honeycomb structures for in-plane property enhancement","volume":"117","author":"Ingrole","year":"2016","journal-title":"Mater. Des."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Schultz, J., Griese, D., Shankar, P., Summers, J.D., and Thompson, L. (2011, January 28\u201331). Optimization of honeycomb cellular meso-structures for high speed impact energy absorption. Proceedings of the ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Washington, DC, USA.","DOI":"10.1115\/DETC2011-48000"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2043007","DOI":"10.1142\/S0219455420430075","article-title":"A Comparison of Nonlinear Bending and Vibration of Hybrid Metal\/CNTRC Laminated Beams with Positive and Negative Poisson\u2019s Ratios","volume":"20","author":"Yu","year":"2020","journal-title":"Int. J. Struct. Stab. Dyn."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"106105","DOI":"10.1016\/j.ijmecsci.2020.106105","article-title":"Study on blast resistance of a composite sandwich panel with isotropic foam core with negative Poisson\u2019s ratio","volume":"191","author":"Lv","year":"2021","journal-title":"Int. J. Mech. Sci."},{"key":"ref_28","first-page":"77","article-title":"Discrete variational method of multi-body system dynamics cased on center of gravity interpolation","volume":"30","author":"Pan","year":"2017","journal-title":"J. Qingdao Univ. (Nat. Sci. Ed.)"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/7\/1356\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:41:25Z","timestamp":1760139685000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/7\/1356"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,30]]},"references-count":28,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2022,7]]}},"alternative-id":["sym14071356"],"URL":"https:\/\/doi.org\/10.3390\/sym14071356","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6,30]]}}}