{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:23:46Z","timestamp":1760235826323,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,9,28]],"date-time":"2021-09-28T00:00:00Z","timestamp":1632787200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In our study we analyse the vibration of a right cylinder which consists of an elastic material with dipolar structure and has pores. One end of this cylinder is subjected to an excitation, harmonically in time. The other end of the cylinder and its lateral surface are free of loads. We prove that the presence of the voids does not affect the spatial decay of effects away from the excited end, if the harmonic excitation level is below a predetermined threshold.<\/jats:p>","DOI":"10.3390\/sym13101804","type":"journal-article","created":{"date-parts":[[2021,9,28]],"date-time":"2021-09-28T21:39:29Z","timestamp":1632865169000},"page":"1804","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["The Influence of Voids in the Vibrations of Bodies with Dipolar Structure"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1552-3763","authenticated-orcid":false,"given":"Marin","family":"Marin","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, Transilvania University of Brasov, 500036 Brasov, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8679-2579","authenticated-orcid":false,"given":"Sorin","family":"Vlase","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Transilvania University of Brasov, 500036 Brasov, Romania"}]},{"given":"Adina","family":"Chirila","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Transilvania University of Brasov, 500036 Brasov, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/BF00049455","article-title":"Some decay estimates in continuum dynamics","volume":"17","author":"Flavin","year":"1987","journal-title":"J. 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Anal."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1007\/BF01302942","article-title":"A theory of thermoelastic materials with voids","volume":"60","author":"Iesan","year":"1986","journal-title":"Acta Mech."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/BF00248490","article-title":"Micro-structure in linear elasticity","volume":"16","author":"Mindlin","year":"1964","journal-title":"Arch. Ration. Mech. Anal."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1007\/BF00253051","article-title":"Multipolar continuum mechanics","volume":"17","author":"Green","year":"1964","journal-title":"Arch. Ration. Mech. Anal."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"104177","DOI":"10.1016\/j.euromechsol.2020.104177","article-title":"Thermoelastic waves in double porosity materials","volume":"86","author":"Chirita","year":"2021","journal-title":"Eur. J. Mech. 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(2020). Entropy Analysis on the Blood Flow through Anisotropically Tapered Arteries Filled with Magnetic Zinc-Oxide (ZnO) Nanoparticles. Entropy, 22.","DOI":"10.3390\/e22101070"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1002\/zamm.201200293","article-title":"Stress concentration in an anisotropic body with three equal collinear cracks in Mode II of fracture. I. Analytical study","volume":"94","author":"Craciun","year":"2014","journal-title":"ZAMM"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1023\/A:1007549317153","article-title":"Interaction of two unequal cracks in a prestressed fiber reinforced composite","volume":"94","author":"Craciun","year":"1998","journal-title":"Int. J. Fract."},{"key":"ref_16","first-page":"278","article-title":"The influence of dimensional and structural shifts of the elastic constant values in cylinder fiber composites","volume":"15","author":"Modrea","year":"2013","journal-title":"J. Optoelectron. Adv. Mater."},{"key":"ref_17","first-page":"424","article-title":"Simulation of the elastic properties of some fibre-reinforced composite laminates under off-axis loading system","volume":"5","author":"Vlase","year":"2011","journal-title":"Optoelectron. Adv. Mater. Rapid Commun."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Iesan, D. (2004). Thermoelastic Models of Continua, Kluwer Academic.","DOI":"10.1007\/978-1-4020-2310-1"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1291","DOI":"10.1016\/0020-7225(90)90076-U","article-title":"Theory of thermo-microstretch elastic solids","volume":"28","author":"Eringen","year":"1990","journal-title":"Int. J. Eng. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1453","DOI":"10.1007\/s00161-019-00766-2","article-title":"On adaptive thermo-electro-elasticity within a Green-Naghdi type II or III theory","volume":"31","author":"Chirila","year":"2019","journal-title":"Contin. Mech. Thermodyn."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1080\/10236190801953864","article-title":"Approximate solution of multipoint boundary value problems for linear differential equations by polynomial functions","volume":"14","author":"Groza","year":"2008","journal-title":"J. Differ. Equ. Appl."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Fichera, G. (1972). Existence theorems in Elasticity. 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