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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">19280</article-id><article-id pub-id-type="doi">10.22363/1815-5235-2018-14-4-323-336</article-id><article-categories><subj-group subj-group-type="toc-heading" xml:lang="en"><subject>Dynamics of structures and buildings</subject></subj-group><subj-group subj-group-type="toc-heading" xml:lang="ru"><subject>Динамика конструкций и сооружений</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">The modern state of the problem of analyzing the natural frequencies and modes of vibration of a composite structure</article-title><trans-title-group xml:lang="ru"><trans-title>Современное состояние вопроса анализа собственных частот и форм колебаний конструкции из композиционных материалов</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Nurimbetov</surname><given-names>Alibek U</given-names></name><name xml:lang="ru"><surname>Нуримбетов</surname><given-names>Алибек Усипбаевич</given-names></name></name-alternatives><bio xml:lang="en"><p>Dr Sci. (Eng.), Professor of Information Systems Department, Taraz State University named after M.H. Dulati. Research interests: constructions from composite materials, multi-layer composite blade, strength and design, statics, oscillations.</p></bio><bio xml:lang="ru"><p>доктор технических наук, профессор кафедры информационных систем, Таразский государственный университет им. М.Х. Дулати. Область научных интересов: конструкции из композиционных материалов, многослойная композиционная лопатка, прочность и проектирование, статика, колебания</p></bio><email>alibek_55@mail.ru</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Dudchenko</surname><given-names>Alexander A</given-names></name><name xml:lang="ru"><surname>Дудченко</surname><given-names>Александр Александрович</given-names></name></name-alternatives><bio xml:lang="en"><p>Dr Sci. (Eng.), Professor of the Department of Strength of Aviation and RocketSpace Constructions, Moscow Aviation Institute (National Research University). Research interests: aviation constructions, constructions from composite materials, mechanics of destruction, strength and design, statics, oscillations</p></bio><bio xml:lang="ru"><p>доктор технических наук, профессор кафедры прочности авиационных и ракетно-космических конструкций, Московский авиационный институт (МАИ). Область научных интересов: авиационные конструкции, конструкции из композиционных материалов, механика разрушения, прочность и проектирование, статика, колебания</p></bio><email>a_dudchenko@mail.ru</email><xref ref-type="aff" rid="aff2"/></contrib></contrib-group><aff-alternatives id="aff1"><aff><institution xml:lang="en">M.Kh. Dulaty Taraz State University</institution></aff><aff><institution xml:lang="ru">Таразский государственный университет им. М.Х. Дулати</institution></aff></aff-alternatives><aff-alternatives id="aff2"><aff><institution xml:lang="en">Moscow Aviation Institute (National Research University)</institution></aff><aff><institution xml:lang="ru">Московский авиационный институт</institution></aff></aff-alternatives><pub-date date-type="pub" iso-8601-date="2018-12-15" publication-format="electronic"><day>15</day><month>12</month><year>2018</year></pub-date><volume>14</volume><issue>4</issue><issue-title xml:lang="en">VOL 14, NO4 (2018)</issue-title><issue-title xml:lang="ru">ТОМ 14, №4 (2018)</issue-title><fpage>323</fpage><lpage>336</lpage><history><date date-type="received" iso-8601-date="2018-09-14"><day>14</day><month>09</month><year>2018</year></date></history><permissions><copyright-statement xml:lang="en">Copyright ©; 2018, Nurimbetov A.U., Dudchenko A.A.</copyright-statement><copyright-statement xml:lang="ru">Copyright ©; 2018, Нуримбетов А.У., Дудченко А.А.</copyright-statement><copyright-year>2018</copyright-year><copyright-holder xml:lang="en">Nurimbetov A.U., Dudchenko A.A.</copyright-holder><copyright-holder xml:lang="ru">Нуримбетов А.У., Дудченко А.А.</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/19280">https://journals.rudn.ru/structural-mechanics/article/view/19280</self-uri><abstract xml:lang="en"><p>Various methods for calculating the shapes and frequencies of natural vibrations of rod structures and blades are described in the literature. At present, there is still no one unified universal technique for ensuring the vibratory strength of blades, based on the exact solution of the problem of calculating the vibrational characteristics of modern impellers of complex design. Thus, the problem of the flexural-torsional flutter of working blades of turbo-machines is extremely relevant, in spite of the insufficient attention given to it in various literary sources. The above drawbacks can be avoided by applying various design analysis methods. Calculation methods for analyzing the strength of structures, as a rule, are divided into analytical and numerical. Analytical methods for studying the stress-strain and vibration state are based in most cases on simplified relations between the theories of rods, shells, and also the theory of oscillations. The advantage of analytical methods is the relative ease of use and convenience in performing valuation calculations at the initial stages of design. The paper reviews and analyzes works on the finding of frequencies and modes of vibrations of rod structures and compressor blades for their subsequent use for multi-layer anisotropic rod structures from composite materials (CM) during the design phase.</p></abstract><trans-abstract xml:lang="ru"><p>В литературе описаны различные способы расчета форм и частот собственных колебаний стержневых конструкции и лопаток. В настоящее время все еще не предложено единой универсальной методики обеспечения вибрационной прочности лопаток, основанной на точном решении задачи расчета вибрационных характеристик современных рабочих колес сложной конструкции. Таким образом, проблема изгибно-крутильного флаттера рабочих лопаток турбомашин чрезвычайно актуальна, несмотря на недостаточное внимание, уделяемое ей в различных литературных источниках. Указанных выше недостатков удается избежать, применяя различные расчетные методы анализа конструкций. Расчетные методы анализа прочности конструкций, как правило, разделяют на аналитические и численные. Аналитические методики исследования напряженно-деформированного и вибрационного состояний основаны в большинстве случаев на упрощенных соотношениях теории стержней, оболочек, а также теории колебаний. Преимуществом аналитических методик является относительная простота использования и удобство при проведении оценочных расчетов на начальных этапах проектирования. В статье проведен обзор и анализ работ по вопросам нахождения частот и форм колебаний стержневых конструкции и лопатки компрессора с целью их последующего использования для многослойных анизотропных стержневых конструкций из композиционных материалов (КМ) на этапе эскизного проектирования.</p></trans-abstract><kwd-group xml:lang="en"><kwd>deformation</kwd><kwd>anisotropic multilayer rod</kwd><kwd>kinematics</kwd><kwd>oscillation</kwd><kwd>torsion</kwd><kwd>stretching</kwd><kwd>bending</kwd></kwd-group><kwd-group xml:lang="ru"><kwd>деформация</kwd><kwd>анизотропный многослойный стержень</kwd><kwd>кинематика</kwd><kwd>колебание</kwd><kwd>кручение</kwd><kwd>растяжение</kwd><kwd>изгиб</kwd><kwd>лопатка</kwd><kwd>автоколебания</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">Svishcheva G.P., Birger I.A. (1969). 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