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<article 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" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" article-type="research-article" dtd-version="1.2" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">Structural Mechanics of Engineering Constructions and Buildings</journal-id><journal-title-group><journal-title xml:lang="en">Structural Mechanics of Engineering Constructions and Buildings</journal-title><trans-title-group xml:lang="ru"><trans-title>Строительная механика инженерных конструкций и сооружений</trans-title></trans-title-group></journal-title-group><issn publication-format="print">1815-5235</issn><issn publication-format="electronic">2587-8700</issn><publisher><publisher-name xml:lang="en">Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University)</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">16915</article-id><article-id pub-id-type="doi">10.22363/1815-5235-2017-5-27-33</article-id><article-categories><subj-group subj-group-type="toc-heading" xml:lang="en"><subject>Articles</subject></subj-group><subj-group subj-group-type="toc-heading" xml:lang="ru"><subject>Статьи</subject></subj-group><subj-group subj-group-type="article-type"><subject>Research Article</subject></subj-group></article-categories><title-group><article-title xml:lang="en">ON FREE VIBRATION OF A NONHOMOGENEOUS ORTHOTROPIC RECTANGULAR PLATE ON A NONHOMOGENEOUS VISCO-ELASTIC FOUNDATION</article-title><trans-title-group xml:lang="ru"><trans-title>О СВОБОДНОМ КОЛЕБАНИИ НЕПРЕРЫВНО НЕОДНОРОДНО ОРТОТРОПНОЙ ПРЯМОУГОЛЬНОЙ ПЛАСТИНКИ, ЛЕЖАЩЕЙ НА НЕОДНОРОДНО ВЯЗКОУПРУГОМ ОСНОВАНИИ</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>HACIYEV</surname><given-names>VAGIF OGLY</given-names></name><name xml:lang="ru"><surname>ГАДЖИЕВ</surname><given-names>ВАГИФ ОГЛЫ</given-names></name></name-alternatives><bio xml:lang="en"><p>Doctor of Physical and Mathematical Sciences, Professor, Head of the Department, Department of Theory of Elasticity and Plasticity</p></bio><bio xml:lang="ru"><p>ГАДЖИЕВ ВАГИФ ДЖАМАЛ ОГЛЫ - доктор физико-математических наук, профессор, заведующий отделом, Отдел теории упругости и пластичности, Институт математики и механики, Национальная академия наук Азербайджана. Научные интересы: теория упругости и пластичности.</p></bio><email>vagif.haciyev.imm@gmail.com</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>MIRZAYEVA</surname><given-names>GULNAR ROVSHAN</given-names></name><name xml:lang="ru"><surname>МИРЗОЕВА</surname><given-names>ГЛЮНАР КЫЗЫ</given-names></name></name-alternatives><bio xml:lang="en"><p>PhD of mechanic, Senior Researcher</p></bio><bio xml:lang="ru"><p>доктор философии по механике, старший научный сотрудник, Отдел теории упругости и пластичности, Институт математики и механики, Национальная академия наук Азербайджана. Научные интересы: теория упругости и пластичности.</p></bio><email>vagif.haciyev.imm@gmail.com</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>SHIRIEV</surname><given-names>AZIZ INTIZAR</given-names></name><name xml:lang="ru"><surname>ШИРИЕВ</surname><given-names>АЗИЗ ОГЛЫ</given-names></name></name-alternatives><email>vagif.haciyev.imm@gmail.com</email><xref ref-type="aff" rid="aff1"/></contrib></contrib-group><aff-alternatives id="aff1"><aff><institution xml:lang="en">Institute Mathematics and Mechanics of NASA, Baku, Azerbaijan</institution></aff><aff><institution xml:lang="ru">Институт математики и механики, Национальная академия наук Азербайджана</institution></aff></aff-alternatives><pub-date date-type="pub" iso-8601-date="2017-10-15" publication-format="electronic"><day>15</day><month>10</month><year>2017</year></pub-date><issue>5</issue><issue-title xml:lang="en">NO5 (2017)</issue-title><issue-title xml:lang="ru">№5 (2017)</issue-title><fpage>27</fpage><lpage>33</lpage><history><date date-type="received" iso-8601-date="2017-10-09"><day>09</day><month>10</month><year>2017</year></date></history><permissions><copyright-statement xml:lang="en">Copyright ©; 2017, HACIYEV V.O., MIRZAYEVA G.R., SHIRIEV A.I.</copyright-statement><copyright-statement xml:lang="ru">Copyright ©; 2017, ГАДЖИЕВ В.О., МИРЗОЕВА Г.К., ШИРИЕВ А.О.</copyright-statement><copyright-year>2017</copyright-year><copyright-holder xml:lang="en">HACIYEV V.O., MIRZAYEVA G.R., SHIRIEV A.I.</copyright-holder><copyright-holder xml:lang="ru">ГАДЖИЕВ В.О., МИРЗОЕВА Г.К., ШИРИЕВ А.О.</copyright-holder><ali:free_to_read xmlns:ali="http://www.niso.org/schemas/ali/1.0/"/><license><ali:license_ref xmlns:ali="http://www.niso.org/schemas/ali/1.0/">http://creativecommons.org/licenses/by/4.0</ali:license_ref></license></permissions><self-uri xlink:href="https://journals.rudn.ru/structural-mechanics/article/view/16915">https://journals.rudn.ru/structural-mechanics/article/view/16915</self-uri><abstract xml:lang="en"><p>In the paper, by using approximate analytic methods, the study a problem of vibrations of a nonhomogeneous rectilinear plate and a visco - elastic foundation, the boundary conditions are homogeneous. It is assumed that the modules of elasticity and density of the plate are characteristic functions of three space coordinates, the Poisson ratios are accepted to be constant [1]. The numerical calculation is carried out under specific values of characteristic functions, characterizing the properties of the plate and foundation, and the results are represented in the form of tables and dependence graphs</p></abstract><trans-abstract xml:lang="ru"><p>В работе с применением приближенно аналитических методов исследуется зада- ча свободного колебания неоднородно ортотропной прямоугольной пластинки, лежа- щей на вязко упругом основании, причем краевые условия являются однородными. Предполагается, что модули упругости и плотность пластинки являются непрерыв- ными функциями трех пространственных координат и коэффициенты Пуассона при- нимаются постоянными. При конкретных значениях характерных функций, характе- ризующих свойства пластинки и основания, проведен численный расчет, и результаты представлены в виде таблиц и графиками зависимостей.</p></trans-abstract><kwd-group xml:lang="en"><kwd>plate</kwd><kwd>continuity</kwd><kwd>orthotropic</kwd><kwd>density</kwd><kwd>foundation</kwd><kwd>frequency</kwd><kwd>elastic mod- ule</kwd><kwd>motion equation</kwd></kwd-group><kwd-group xml:lang="ru"><kwd>пластинка</kwd><kwd>непрерывность</kwd><kwd>ортотропность</kwd><kwd>плотность</kwd><kwd>ос- нования</kwd><kwd>частота</kwd><kwd>модули упругости</kwd><kwd>уравнение движения</kwd></kwd-group><funding-group/></article-meta></front><body></body><back><ref-list><ref id="B1"><label>1.</label><citation-alternatives><mixed-citation xml:lang="en">Lomakin, V.A. (1977). Theory of Elasticity of Inhomogeneous Bodies. Moscow: MSU. 376 (in Russian).</mixed-citation><mixed-citation xml:lang="ru">Ломакин В.А. Теория упругости неоднородных тел. - Изд-во. 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