<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">ast</journal-id><journal-title-group><journal-title xml:lang="ru">Архитектура, строительство, транспорт</journal-title><trans-title-group xml:lang="en"><trans-title>Architecture, Construction, Transport</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2782-232X</issn><issn pub-type="epub">2713-0770</issn><publisher><publisher-name>Industrial University of Tyumen</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.31660/2782-232X-2024-2-67-83</article-id><article-id custom-type="elpub" pub-id-type="custom">ast-160</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>СТРОИТЕЛЬСТВО</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>CONSTRUCTION</subject></subj-group></article-categories><title-group><article-title>Сейсмическая защита зданий и сооружений с применением метаматериалов: текущее состояние и перспективы развития</article-title><trans-title-group xml:lang="en"><trans-title>Seismic protection of buildings and structures using metamaterials: current status and development prospects</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-4776-5118</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Митрошин</surname><given-names>В. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Mitroshin</surname><given-names>V. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Митрошин Василий Александрович, старший преподаватель кафедры строительной и теоретической механики</p><p>Москва</p></bio><bio xml:lang="en"><p>Vasilii A. Mitroshin, Senior Lecturer at the Department of Theoretical and Structural Mechanics</p><p>Moscow</p></bio><email xlink:type="simple">mitroshinva@mgsu.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Национальный исследовательский Московский государственный строительный университет (НИУ МГСУ)</institution><country>Россия</country></aff><aff xml:lang="en"><institution>National Research Moscow State University of Civil Engineering (NRU MGSU)</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2024</year></pub-date><pub-date pub-type="epub"><day>28</day><month>06</month><year>2024</year></pub-date><volume>0</volume><issue>2</issue><fpage>67</fpage><lpage>83</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Митрошин В.А., 2024</copyright-statement><copyright-year>2024</copyright-year><copyright-holder xml:lang="ru">Митрошин В.А.</copyright-holder><copyright-holder xml:lang="en">Mitroshin V.A.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://ast.tyuiu.ru/jour/article/view/160">https://ast.tyuiu.ru/jour/article/view/160</self-uri><abstract><p>Ввиду уплотнения и увеличения этажности городской застройки в мире растет число исследований в области защиты зданий и сооружений от сейсмических волн, поскольку распространяющийся в массиве грунта волновой сейсмический фронт способен привести к колоссальным разрушениям и массовым жертвам. Наиболее распространенными методами сейсмозащиты зданий и сооружений в гражданском строительстве в настоящее время являются конструктивные и территориальные способы. Первый метод включает комплекс конструктивных мероприятий, среди которых важное место занимает применение сейсмоизоляторов – специальных устройств, вводимых в фундамент и снижающих инерционные сейсмические воздействия на строительные конструкции. Второй способ предполагает использование различных барьеров на пути распространения сейсмических волн. В последние годы явно обозначилась тенденция поиска новых подходов к территориальной сейсмозащите. Анализ академических баз данных позволил выявить большое число исследований (преимущественно зарубежных), посвященных разработке способов защиты зданий и сооружений от волнового воздействия с помощью различного рода композиционных структур – метаматериалов. Эти способы некоторые исследователи условно делят на две группы: одни выполняют задачи маскировки, когда волновой фронт отклоняется и огибает защищаемый объект, другие создают искусственную теневую зону, в которой сейсмические волны затухают, не оказывая существенного влияния на здания и сооружения. Так как для российской науки разработка сейсмических метаматериалов пока является новым, но, безусловно, перспективным направлением исследований, целью данного обзора была систематизация имеющихся сведений о способах эффективной защиты зданий и сооружений от волновых воздействий.</p></abstract><trans-abstract xml:lang="en"><p>Due to the compaction of urban development and increase in its number of floors, the number of studies in the field of protection of buildings and structures from seismic waves is growing in the world, as the wave seismic front in the soil mass can lead to enormous destruction and mass casualties. The most common methods of seismic protection of buildings and structures in civil engineering today are constructive and territorial methods. The first method includes a set of structural measures, among of them an important place is occupied by the use of seismic isolators – special devices inserted into the foundation and reducing inertial seismic effects on building structures. The second way is the use of various barriers in the path of seismic wave propagation. In recent years, there has been a clear trend towards finding new approaches to territorial seismic protection. The analysis of academic databases revealed a large number of studies (mostly foreign) devoted to the development of ways to protect buildings and structures from wave action using various kinds of composite structures – metamaterials. Some researchers conditionally divide these methods into two groups: the first performs the tasks of masking, when the wave front deviates and wraps around the protected object, and the second creates an artificial shadow zone where seismic waves are damped without significantly affecting buildings and structures. Since the development of seismic metamaterials is still a new but certainly promising area of research for Russian science, the purpose of this review was to systematise the available data on the methods of effective protection of buildings and structures from wave impacts.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>метаматериалы</kwd><kwd>сейсмические волны</kwd><kwd>искусственный барьер</kwd><kwd>затухание волн</kwd><kwd>аналитический обзор</kwd></kwd-group><kwd-group xml:lang="en"><kwd>metamaterials</kwd><kwd>seismic waves</kwd><kwd>artificial barrier</kwd><kwd>seismic-waves attenuation</kwd><kwd>analytical review</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Работа профинансирована Министерством науки и высшего образования РФ, проект № FSWG-2023-0004 «Система территориальной сейсмической защиты критически важных объектов инфраструктуры на основе гранулированных метаматериалов, обладающих свойствами широкодиапазонных фононных кристаллов».</funding-statement><funding-statement xml:lang="en">The study was funded by the Ministry of Science and Higher Education of the Russian Federation, project No. FSWG-2023-0004 "System of territorial seismic protection of critical infrastructure based on granular metamaterials with the properties of broadband phononic crystals".</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Pendry, J. B. Controlling electromagnetic fields / J. B. Pendry, D. Schurig, D. R. Smith. – DOI 10.1126/science.1125907. – Текст : непосредственный // Science. – 2006. – No. 312 (5781). – P. 1780–1782.</mixed-citation><mixed-citation xml:lang="en">Pendry, J. B., Schurig, D., Smith, D. R. (2006). Controlling electromagnetic fields. Science, 312(5781), pp. 1780-1782. (In English). DOI 10.1126/science.1125907.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Дубинов, А. Е. Маскировка материальных тел методом волнового обтекания / А. Е. Дубинов, Л. А. Мытарева. – DOI 10.3367/ufnr.0180.201005b.0475. – Текст : непосредственный // Успехи физических наук. – 2010. – Т. 180, № 5. – С. 475–501.</mixed-citation><mixed-citation xml:lang="en">Dubinov, A. E., &amp; Mytareva, L. A. (2010). Invisible cloaking of material bodies using the wave flow method. Uspekhi Fizicheskih Nauk, 180(5), Pp. 475-501. DOI 10.3367/ufnr.0180.201005b.0475. (In Russian).</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Розанов, Н. Н. Невидимость: за и против / Н. Н. Розанов. – Текст : непосредственный // Природа. – 2008. – № 6. – C. 3–10.</mixed-citation><mixed-citation xml:lang="en">Rozanov, N. N. (2008). Nevidimost': za i protiv. Priroda, (6), pp. 3-10. (In Russian).</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Schurig, D. Calculation of material properties and ray tracing in transformation media / D. Schurig, J. B. Pendry, D. R. Smith. – DOI 10.1364/oe.14.009794. – Текст : непосредственный // Optics Express. – 2006. – Vol. 14, Issue 21. – P. 9794–9804.</mixed-citation><mixed-citation xml:lang="en">Schurig, D., Pendry, J.B., &amp; Smith, D. R. (2006). Calculation of material properties and ray tracing in transformation media. Optics Express, 14(21), pp. 9794-9804. (In English). DOI 10.1364/oe.14.009794.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Metamaterial electromagnetic cloak at microwave frequencies / D. Schurig, J. J. Mock, B. J. Justice [et al.]. – DOI 10.1126/science.1133628. – Текст : непосредственный // Science. – 2006. – Vol. 314, Issue 5801. – P. 977–980.</mixed-citation><mixed-citation xml:lang="en">Schurig, D., Mock, J. J., Justice, B. J., Cummer, S. A., Pendry, J. B., Starr, A. F., &amp; Smith, D. R. Metamaterial electromagnetic cloak at microwave frequencies. Science, 314(5801), pp. 977-980. (In English). DOI 10.1126/science.1133628.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Material parameter equation for elliptical cylindrical cloaks / H. Ma, S. Qu, Z. Xu [et al.] – DOI 10.1103/ PhysRevA.77.013825. – Текст : непосредственный // Physical Review A – Atomic, Molecular and Optical Physics. – 2008. – No. 77 (1). – P. 1–4.</mixed-citation><mixed-citation xml:lang="en">Ma, H., Qu, S., Xu, Z., Zhang, J., Chen, B., &amp; Wang, J. (2008). Material parameter equation for elliptical cylindrical cloaks. Physical Review A – Atomic, Molecular, and Optical Physics, 77(1), pp. 1-4. (In English). DOI 10.1103/PhysRevA.77.013825.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Electromagnetic Concentrators with Reduced Material Parameters Based on Coordinate Transformation. / W. Wang, L. Lin, J. Ma [et al.]. – DOI 10.1364/oe.16.011431. – Текст : непосредственный // Optics Express. – 2008. – Vol. 16, Issue 15. – P. 11431–11437.</mixed-citation><mixed-citation xml:lang="en">Wang, W., Lin, L., Ma, J., Wang, C., Cui, J., Du, C., &amp; Luo, X. (2008). Electromagnetic Concentrators with Reduced Material Parameters Based on Coordinate Transformation. Optics Express, 16(15), pp. 11431-11437. (In English). DOI 10.1364/oe.16.011431.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Full-wave analysis of prolate spheroidal and hyperboloidal cloaks / Y. Luo, J. Zhang, H. Chen, B.-I. Wu. – DOI 10.1088/0022-3727/41/23/235101. – Текст : непосредственный // Journal of Physics D: Applied Physics. – 2008. – Vol. 41, Issue 23. – P. 5101.</mixed-citation><mixed-citation xml:lang="en">Luo, Y., Zhang, J., Chen, H., &amp; Wu, B.-I. (2008). Full-wave analysis of prolate spheroidal and hyperboloidal cloaks. Journal of Physics D: Applied Physics, 41(23), 5101. (In English). DOI 10.1088/0022-3727/41/23/235101.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Interaction of an electromagnetic wave with a cone-shaped invisibility cloak and polarization rotator. / Y. Luo, J. Zhang, B.-I. Wu, H. Chen. – DOI 10.1103/PhysRevB.78.125108. – Текст : непосредственный // Physical Review B - Condensed Matter and Materials Physics. – 2008. – No. 78:125108.</mixed-citation><mixed-citation xml:lang="en">Luo Y., Zhang, J., Wu, B.-I., &amp; Chen, H. (2008). Interaction of an electromagnetic wave with a cone-shaped invisibility cloak and polarization rotator. Physical Review B - Condensed Matter and Materials Physics, (78), 125108. (In English). DOI 10.1103/PhysRevB.78.125108.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Kim, S. H. Artificial seismic shadow zone by acoustic metamaterials / S. H. Kim, M. P. Das. – DOI 10.1142/ S0217984913501406. – Текст : электронный // Modern Physics Letters B. – 2013. – Vol. 27, No. 20:1350140.</mixed-citation><mixed-citation xml:lang="en">Kim, S. H., &amp; Das, M. P. (2013). Artificial seismic shadow zone by acoustic metamaterials. Modern Physics Letters B, 27(20), 1350140. (In English). DOI 10.1142/S0217984913501406.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Forests as a natural seismic metamaterial: Rayleigh wave bandgaps induced by local resonances. / A. Colombi, P. Roux, S. Guenneau [et al.]. – DOI 10.1038/srep19238. – Текст : непосредственный // Scientific Reports. – 2016. – No. 6(1):19238.</mixed-citation><mixed-citation xml:lang="en">Colombi, A., Roux, P., Guenneau, S., Gueguen, P., &amp; Craster, R. V. (2016). Forests as a natural seismic metamaterial: Rayleigh wave bandgaps induced by local resonances. Scientific Reports, (6(1)), 19238. (In English). DOI 10.1038/srep19238.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Experiments on seismic metamaterials: Molding surface waves. / S. Brûlé, E. H. Javelaud, S. Enoch, S. Guenneau. – DOI 10.1103/PhysRevLett.112.133901. – Текст : непосредственный // Physical Review Letters. – 2013. – No. 112:133901.</mixed-citation><mixed-citation xml:lang="en">Brûlé, S., Javelaud, E. H., Enoch, S., &amp; Guenneau, S. (2013). Experiments on seismic metamaterials: Molding surface waves. Physical Review Letters, (112), 133901. (In English). DOI 10.1103/PhysRevLett.112.133901.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Brûlé, S. Emergence of seismic metamaterials: Current state and future perspectives / S. Brûlé, S. Enoch, S. Guenneau. – DOI 10.1016/j.physleta.2019.126034. – Текст : электронный // Physics Letters, Section A: General, Atomic and Solid State Physics. – 2020. – No. 384(1):126034.</mixed-citation><mixed-citation xml:lang="en">Brûlé, S., Enoch, S., &amp; Guenneau, S. (2020). Emergence of seismic metamaterials: Current state and future perspectives. Physics Letters, Section A: General, Atomic and Solid State Physics, (384(1)), 126034. (In English). DOI 10.1016/j.physleta.2019.126034.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Walser, R. M. Metamaterials: What are they? What are they good for? – Текст : непосредственный // APS March Meeting Abstracts. – 2000. – No. 1. – P. 5001.</mixed-citation><mixed-citation xml:lang="en">Walser, R. M. (2000). Metamaterials: What are they? What are they good for? APS March Meeting Abstracts, (1), pp. 5001. (In English).</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Direct calculation of permeability and permittivity for a left-handed metamaterial / D. R. Smith, D. C. Vier, N. Kroll, S. Schultz. – DOI 10.1063/1.1314884. – Текст : непосредственный // Applied Physics Letters. – 2000. – No. 77(14). – P. 2246–2248.</mixed-citation><mixed-citation xml:lang="en">Smith, D. R., Vier, D. C., Kroll, N., &amp; Schultz, S. (2000). Direct calculation of permeability and permittivity for a lefthanded metamaterial. Applied Physics Letters, (77(14)), pp. 2246-2248. (In English). DOI 10.1063/1.1314884.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Walser, R. M. Electromagnetic metamaterials. Complex Mediums II: beyond linear isotropic dielectrics / R. M. Walser. – DOI 10.1117/12.432921. – Текст : непосредственный // International Society for Optics and Photonics. – 2001. – No. 4467. – P. 1–15.</mixed-citation><mixed-citation xml:lang="en">Walser, R. M. (2001). Electromagnetic metamaterials. Complex Mediums II: Beyond linear isotropic dielectrics. International Society for Optics and Photonics, (4467), pp. 1-15. (In English).</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Strutt, J. W. On the Remarkable Phenomenon of Crystalline Reflexion described by Prof. Stokes. / J. W. Strutt. – DOI 10.1017/cbo9780511703980.010. – Текст : непосредственный // Scientific Papers : Cambridge Library Collection – Mathematics. – Cambridge : Cambridge University Press. – 2011. – P. 204–212.</mixed-citation><mixed-citation xml:lang="en">Strutt, J. W. (2011). On the Remarkable Phenomenon of Crystalline Reflexion described by Prof. Stokes. Scientific Papers. Cambridge Library Collection - Mathematics. Cambridge, Publ. Cambridge University Press, pp. 204- 212. (In English). DOI 10.1017/cbo9780511703980.010.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Могилевский, И. Е. Математическое моделирование метода волнового обтекания в задачах маскировки / И. Е. Могилевский, В. В. Ровенко. – Текст : непосредственный // Физические основы приборостроения. – 2014. – Т. 3, № 4 (13). – С. 28–39.</mixed-citation><mixed-citation xml:lang="en">Mogilevsky, I. E., &amp; Rovenko, V. V. (2014). Mathematical modeling of the cloaking method for problems of radiolocating masking. Physical Bases of Instrumentation, (3(4)), pp. 28-39. (In Russian).</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Ohtaka, K. Energy band of photons and low-energy photon diffraction / K. Ohtaka. – DOI 10.1103/PhysRevB.19.5057. – Текст : непосредственный // Physical Review B. – 1979. – Vol. 19, Issue 10:5057.</mixed-citation><mixed-citation xml:lang="en">Ohtaka, K. (1979). Energy band of photons and low-energy photon diffraction. Physical Review B, 19(10), pp. 5057-5067. (In English). DOI 10.1103/PhysRevB.19.5057.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Sajeev, J. Strong localization of photons in certain disordered dielectric superlattices / J. Sajeev. – DOI 10.1103/ PhysRevLett.58.2486. – Текст : непосредственный // Physical Review Letters. – 1987. – Vol. 58, No. 23. – P. 2486–2489.</mixed-citation><mixed-citation xml:lang="en">Sajeev, J. (1987). Strong localization of photons in certain disordered dielectric superlattices. Physical Review Letters, (58(23)), pp. 2486-2489. (In English). DOI 10.1103/PhysRevLett.58.2486.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Classical vibrational modes in phononic lattices: Theory and experiment. / M. Sigalas, M. S. Kushwaha, E. N. Economou [et al.]. – DOI 10.1524/zkri.2005.220.9-10.765. – Текст : непосредственный // Zeitschrift fur Kristallographie [Crystalline Materials]. – 2005. – Vol. 220, No. 9–10. – P. 765–809.</mixed-citation><mixed-citation xml:lang="en">Sigalas, M., Kushwaha, M. S., Economou, E. N., Kafesaki, M., Psarobas, I. E., &amp; Steurer, W. (2005). Classical vibrational modes in phononic lattices: theory and experiment. Zeitschrift für Kristallographie - Crystalline Materials, (220(9-10)), pp. 765-809. (In English). DOI 10.1524/zkri.2005.220.9-10.765.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Bao, J. Dynamic Responses of a Structure with Periodic Foundations. / J. Bao, Z. Shi, H. Xiang. – DOI 10.1061/ (asce)em.1943-7889.0000383. – Текст : непосредственный // Journal of Engineering Mechanics. – 2012. – Vol. 138, Issue 7. – P. 761–769.</mixed-citation><mixed-citation xml:lang="en">Bao, J., Shi, Z., &amp; Xiang, H. (2012). Dynamic responses of a structure with periodic foundations. Journal of Engineering Mechanics, (138(7)), pp. 761–769. (In English). DOI 10.1061/(asce)em.1943-7889.0000383.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Periodic materials-based vibration attenuation in layered foundations: experimental validation / H. J. Xiang, Z. F. Shi, S. J. Wang, Y. L. Mo. – DOI 10.1088/0964-1726/21/11/112003. – Текст : непосредственный // Smart Materials and Structures. – 2012. – No. 21(11):112003.</mixed-citation><mixed-citation xml:lang="en">Xiang, H. J., Shi, Z. F., Wang, S. J., &amp; Mo, Y. L. (2012). Periodic materials-based vibration attenuation in layered foundations: experimental validation. Smart Materials and Structures, (21(11)), 112003. (In English). DOI 10.1088/0964-1726/21/11/112003.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Cheng, Z. Novel composite periodic structures with attenuation zones. / Z. Cheng, Z. Shi. – DOI 10.1016/j. engstruct.2013.07.003. – Текст : непосредственный // Engineering Structures. – 2013. – Vol. 56. – P. 1271–1282.</mixed-citation><mixed-citation xml:lang="en">Cheng, Z., &amp; Shi, Z. (2013). Novel composite periodic structures with attenuation zones. Engineering Structures, (56), pp. 1271-1282. (In English). DOI 10.1016/j.engstruct.2013.07.003.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Cheng, Z. Locally resonant periodic structures with low-frequency band gaps. / Z. Cheng, Z. Shi, Y. L. Mo, H. Xiang. – DOI 10.1063/1.4816052. – Текст : непосредственный // Journal of Applied Physics. – 2013. – No. 114: 033532.</mixed-citation><mixed-citation xml:lang="en">Cheng, Z., Shi, Z., Mo, Y. L., &amp; Xiang, H. (2013). Locally resonant periodic structures with low-frequency band gaps. Journal of Applied Physics, (114), 033532. (In English). DOI 10.1063/1.4816052.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Huang, J. Application of periodic theory to rows of piles for horizontal vibration attenuation / J. Huang, Z. Shi. – DOI 10.1061/(asce)gm.1943-5622.0000193. – Текст : непосредственный // International Journal of Geomechanics. – 2013. – Vol. 13, No. 2 – P. 132–142.</mixed-citation><mixed-citation xml:lang="en">Huang, J., &amp; Shi, Z. (2013). Application of periodic theory to rows of piles for horizontal vibration attenuation. International Journal of Geomechanics, (13(2)), pp. 132-142. (In English). DOI 10.1061/(asce)gm.1943-5622.0000193.</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Seismic isolation of two dimensional periodic foundations / Y. Yan, A. Laskar, Z. Cheng [et al.]. – DOI 10.1063/1.4891837. – Текст : непосредственный // Journal of Applied Physics. – 2014. – No. 116(4):044908.</mixed-citation><mixed-citation xml:lang="en">Yan, Y., Laskar, A., Cheng, Z., Menq, F., Tang, Y., Mo, Y. L., &amp; Shi, Z. (2014). Seismic isolation of two dimensional periodic foundations. Journal of Applied Physics, (116(4)). (In English). DOI 10.1063/1.4891837.</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Yan, Y. Three dimensional periodic foundations for base seismic isolation / Y. Yan, Z. Cheng, F. Menq [et al.]. – DOI 10.1088/0964-1726/24/7/075006. – Текст : непосредственный // Smart Materials and Structures. – 2015. – Vol. 24, No. 7:075006.</mixed-citation><mixed-citation xml:lang="en">Yan, Y., Cheng, Z., Menq, F., Mo, Y. L., Tang, Y., &amp; Shi, Z. (2015). Three dimensional periodic foundations for base seismic isolation. Smart Materials and Structures, (24(7)). (In English). DOI 10.1088/0964-1726/24/7/075006.</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Large scale mechanical metamaterials as seismic shields / M. Miniaci, A. Krushynska, F. Bosia, N. M. Pugno. – DOI 10.1088/1367-2630/18/8/083041. – Текст : непосредственный // New Journal of Physics. – 2016. – No. 18(8):083041.</mixed-citation><mixed-citation xml:lang="en">Miniaci, M., Krushynska, A., Bosia, F., &amp; Pugno, N. M. (2016). Large scale mechanical metamaterials as seismic shields. New Journal of Physics, (18(8)), 083041. (In English). DOI 10.1088/1367-2630/18/8/083041.</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">Krödel, S. Wide band-gap seismic metastructures / S. Krödel, N. Thomé, C. Daraio. – DOI 10.1016/j.eml.2015.05.004. – Текст : непосредственный // Extreme Mechanics Letters. – 2015. – No. 4. – P. 111–117.</mixed-citation><mixed-citation xml:lang="en">Krödel, S., Thomé, N., &amp; Daraio, C. (2015). Wide band-gap seismic metastructures. Extreme Mechanics Letters, (4), pp. 111-117. (In English). DOI 10.1016/j.eml.2015.05.004.</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">Dertimanis, V. K. Feasibility analysis on the attenuation of strong ground motions using finite periodic lattices of mass-in-mass barriers / V. K. Dertimanis, I. A. Antoniadis, E. N. Chatzi. – DOI 10.1061/(asce)em.1943-7889.0001120. – Текст : непосредственный // Journal of Engineering Mechanics. – 2016. – Vol. 142, Issue 9. – P. 1–10.</mixed-citation><mixed-citation xml:lang="en">Dertimanis, V. K., Antoniadis, I. A., &amp; Chatzi, E. N. (2016). Feasibility analysis on the attenuation of strong ground motions using finite periodic lattices of mass-in-mass barriers. Journal of Engineering Mechanics, (142(9)), pp. 1–10. (In English). DOI 10.1061/(asce)em.1943-7889.0001120.</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">Robust-to-uncertainties optimal design of seismic metamaterials / P.-R. Wagner, V. K. Dertimanis, E. N. Chatzi, J. L. Beck. – DOI 10.1061/(asce)em.1943-7889.0001404. – Текст : непосредственный // Journal of Engineering Mechanics. – 2018. – Vol. 144, Issue 3. – P. 1–17.</mixed-citation><mixed-citation xml:lang="en">Wagner, P.-R., Dertimanis, V. K., Chatzi, E. N., &amp; Beck, J. L. (2018). Robust-to-uncertainties optimal design of seismic metamaterials. Journal of Engineering Mechanics, (144(3)), pp. 1-17. (In English). DOI 10.1061/(asce)em.1943-7889.0001404.</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">Cacciola, P. Vibrating barrier: A novel device for the passive control of structures under ground motion / P. Cacciola, A. Tombari. – DOI 10.1098/rspa.2015.0075. – Текст : непосредственный // Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. – 2015. – No. 471:2179.</mixed-citation><mixed-citation xml:lang="en">Cacciola, P., &amp; Tombari, A. (2015). Vibrating barrier: A novel device for the passive control of structures under ground motion. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, (471), 2179. (In English). DOI 10.1098/rspa.2015.0075.</mixed-citation></citation-alternatives></ref><ref id="cit34"><label>34</label><citation-alternatives><mixed-citation xml:lang="ru">Engineered metabarrier as shield from seismic surface waves / A. Palermo, S. Krödel, A. Marzani, C. Daraio. – DOI 10.1038/srep39356. – Текст : непосредственный // Scientific Reports. – 2016. – No. 6(1):39356.</mixed-citation><mixed-citation xml:lang="en">Palermo, A., Krödel, S., Marzani, A., &amp; Daraio, C. (2016). Engineered metabarrier as shield from seismic surface waves. Scientific Reports, (6(1)), 39356. (In English). DOI 10.1038/srep39356.</mixed-citation></citation-alternatives></ref><ref id="cit35"><label>35</label><citation-alternatives><mixed-citation xml:lang="ru">Seismic cloaking protection from earthquakes / R. W. Haupt, V. Liberman, M. Rothschild, C. G. Doll. – DOI 10.1109/THS.2018.8574152. – Текст : непосредственный // 2018 IEEE International Symposium on Technologies for Homeland Security (HST). – 2018. – P. 1–7.</mixed-citation><mixed-citation xml:lang="en">Haupt, R. W., Liberman, V., Rothschild, M., &amp; Doll, C. G. (2018). Seismic cloaking protection from earthquakes. 2018 IEEE International Symposium on Technologies for Homeland Security (HST), pp. 1-7. (In English). DOI 10.1109/THS.2018.8574152.</mixed-citation></citation-alternatives></ref><ref id="cit36"><label>36</label><citation-alternatives><mixed-citation xml:lang="ru">Geng, Q. Issues in design of one-dimensional metamaterials for seismic protection / Q. Geng, S. Zhu, K. P. Chong. – DOI 10.1016/j.soildyn.2018.01.028. – Текст : непосредственный // Soil Dynamics and Earthquake Engineering. – 2018. – No. 107 (14). – P. 264–278.</mixed-citation><mixed-citation xml:lang="en">Geng, Q., Zhu, S., &amp; Chong, K. P. (2018). Issues in design of one-dimensional metamaterials for seismic protection. Soil Dynamics and Earthquake Engineering, (107(14)), pp. 264–278. (In English). DOI 10.1016/j.soildyn.2018.01.028.</mixed-citation></citation-alternatives></ref><ref id="cit37"><label>37</label><citation-alternatives><mixed-citation xml:lang="ru">Flat lens effect on seismic waves propagation in the subsoil / S. Brûlé, E. H. Javelaud, S. Enoch, S. Guenneau. – DOI 10.1038/s41598-017-17661-y. – Текст : непосредственный // Scientific Reports. – 2017. – No. 7(1): 18066.</mixed-citation><mixed-citation xml:lang="en">Brûlé, S., Javelaud, E. H., Enoch, S., &amp; Guenneau, S. (2017). Flat lens effect on seismic waves propagation in the subsoil. Scientific Reports, (7(1)), 18066. (In English). DOI 10.1038/s41598-017-17661-y.</mixed-citation></citation-alternatives></ref><ref id="cit38"><label>38</label><citation-alternatives><mixed-citation xml:lang="ru">Seismic metamaterial: how to shake friends and influence waves? / S. Brûlé, E. Javelaud, S. Enoch, S. Guenneau. – DOI 10.58550/arXiv.1301.7642. – Текст : непосредственный // arXiv. – 2013. – No. 1301.7642.</mixed-citation><mixed-citation xml:lang="en">Brûlé, S., Javelaud, E. H., Enoch, S., &amp; Guenneau, S. (2013). Seismic metamaterial: how to shake friends and influence waves? arXiv, 1301.7642. (In English). DOI 10.58550/arXiv.1301.7642.</mixed-citation></citation-alternatives></ref><ref id="cit39"><label>39</label><citation-alternatives><mixed-citation xml:lang="ru">A seismic metamaterial: The resonant metawedge / A. Colombi, D. Colquitt, P. Roux [et al.]. – DOI 10.1038/srep27717. – Текст : непосредственный // Scientific Reports. – 2016. – No. 10(6):27717.</mixed-citation><mixed-citation xml:lang="en">Colombi, A., Colquitt, D., Roux, P., Guenneau, S., &amp; Craster, R. V. (2016). A seismic metamaterial: The resonant metawedge. Scientific Reports, (10(6)), 27717. (In English). DOI 10.1038/srep27717.</mixed-citation></citation-alternatives></ref><ref id="cit40"><label>40</label><citation-alternatives><mixed-citation xml:lang="ru"></mixed-citation><mixed-citation xml:lang="en"></mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
