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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">33550</article-id><article-id pub-id-type="doi">10.22363/1815-5235-2022-18-6-544-551</article-id><article-categories><subj-group subj-group-type="toc-heading" xml:lang="en"><subject>Analysis and design of building structures</subject></subj-group><subj-group subj-group-type="toc-heading" xml:lang="ru"><subject>Расчет и проектирование строительных конструкций</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">Fluctuations of pipelines of gas-containing liquids under changing bearing conditions</article-title><trans-title-group xml:lang="ru"><trans-title>Колебания трубопроводов газосодержащих жидкостей при изменяющихся условиях опирания</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-8805-8615</contrib-id><name-alternatives><name xml:lang="en"><surname>Leontiev</surname><given-names>Yevgeny V.</given-names></name><name xml:lang="ru"><surname>Леонтьев</surname><given-names>Евгений Владимирович</given-names></name></name-alternatives><bio xml:lang="en"><p>Candidate of Technical Sciences, Head of the Construction Solutions Department</p></bio><bio xml:lang="ru"><p>кандидат технических наук, начальник управления строительных решений</p></bio><email>e.leontyev@gge.ru</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-1991-7233</contrib-id><name-alternatives><name xml:lang="en"><surname>Travush</surname><given-names>Vladimir I.</given-names></name><name xml:lang="ru"><surname>Травуш</surname><given-names>Владимир Ильич</given-names></name></name-alternatives><bio xml:lang="en"><p>Vice President of the Russian Academy of Architecture and Construction Sciences, Doctor of Technical Sciences, Professor, Chief Designer - Deputy General Director for Science</p></bio><bio xml:lang="ru"><p>вице-президент РААСН, доктор технических наук, профессор, главный конструктор - заместитель генерального директора по науке</p></bio><email>travush@mail.ru</email><xref ref-type="aff" rid="aff2"/></contrib></contrib-group><aff-alternatives id="aff1"><aff><institution xml:lang="en">Main State Expertise of Russia</institution></aff><aff><institution xml:lang="ru">Главное управление государственной экспертизы</institution></aff></aff-alternatives><aff-alternatives id="aff2"><aff><institution xml:lang="en">Urban Planning Institute of Residential and Public Buildings</institution></aff><aff><institution xml:lang="ru">Городской проектный институт жилых и общественных зданий</institution></aff></aff-alternatives><pub-date date-type="pub" iso-8601-date="2022-12-15" publication-format="electronic"><day>15</day><month>12</month><year>2022</year></pub-date><volume>18</volume><issue>6</issue><issue-title xml:lang="en">Scientific Legacy of Academician Vitaly Mikhailovich Bondarenko</issue-title><issue-title xml:lang="ru">Научное наследие академика Виталия Михайловича Бондаренко</issue-title><fpage>544</fpage><lpage>551</lpage><history><date date-type="received" iso-8601-date="2023-02-10"><day>10</day><month>02</month><year>2023</year></date></history><permissions><copyright-statement xml:lang="en">Copyright ©; 2022, Leontiev Y.V., Travush V.I.</copyright-statement><copyright-statement xml:lang="ru">Copyright ©; 2022, Леонтьев Е.В., Травуш В.И.</copyright-statement><copyright-year>2022</copyright-year><copyright-holder xml:lang="en">Leontiev Y.V., Travush V.I.</copyright-holder><copyright-holder xml:lang="ru">Леонтьев Е.В., Травуш В.И.</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/">https://creativecommons.org/licenses/by-nc/4.0</ali:license_ref></license></permissions><self-uri xlink:href="https://journals.rudn.ru/structural-mechanics/article/view/33550">https://journals.rudn.ru/structural-mechanics/article/view/33550</self-uri><abstract xml:lang="en"><p style="text-align: justify;">The authors deal with the vibration of the pipeline that occurs during the transportation of a gas-containing liquid due to the uneven distribution of gas accumulation along the length of the pipeline, which produces pulsating movements of the center of gravity of the moving liquid, when the conditions for supporting the middle part change. The solution is constructed using the calculation scheme of a beam lying on an elastic foundation described by the Winkler model. To assess the impact on the stress-strain state of the beam of the sudden exclusion of the elastic foundation under the middle part of the beam, the circular frequencies and forms of natural transverse vibrations of the beam that occur in the absence of disturbing forces are determined. The given solution of the problem of vibrations of a pipe, through which a gas-containing liquid is transported, with a change in the conditions of support of the middle part of the beam, can be used to predict the durability of the pipe.</p></abstract><trans-abstract xml:lang="ru"><p style="text-align: justify;">Рассматривается колебание трубопровода, возникающее при транспортировании газосодержащей жидкости в связи с неравномерным распределением по длине трубопровода скопления газа, которое производит пульсирующие перемещения центра тяжести движущейся жидкости, при изменении условий опирания средней части. Решение построено с использованием расчетной схемы балки, лежащей на упругом основании, описываемым моделью Винклера. Для оценки влияния на напряженно-деформированное состояние балки внезапного исключения упругого основания под средней частью балки определены круговые частоты и формы собственных поперечных колебаний балки, происходящие при отсутствии возмущающих сил. Приведенное решение задачи о колебаниях трубы, по которой транспортируется газосодержащая жидкость, при изменении условий опирания средней части балки может быть использовано для прогноза долговечности трубы.</p></trans-abstract><kwd-group xml:lang="en"><kwd>pipeline</kwd><kwd>beam</kwd><kwd>elastic foundation</kwd><kwd>method of initial parameters</kwd><kwd>free vibrations</kwd><kwd>forced vibrations</kwd><kwd>dynamic analysis</kwd><kwd>change in support conditions</kwd></kwd-group><kwd-group xml:lang="ru"><kwd>трубопровод</kwd><kwd>балка</kwd><kwd>упругое основание</kwd><kwd>метод начальных параметров</kwd><kwd>свободные колебания</kwd><kwd>вынужденные колебания</kwd><kwd>динамический анализ</kwd><kwd>изменение условий опирания</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">Novatsky V. Dynamics of structures. Moscow: Gosstroizdat Publ.; 1963. 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