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<article xmlns:xlink="http://www.w3.org/1999/xlink" dtd-version="1.4" article-type="research-article" xml:lang="en"><front><journal-meta><journal-title-group><journal-title xml:lang="ru">Проблемы прочности и пластичности</journal-title></journal-title-group><journal-id journal-id-type="issn">1814-9146</journal-id></journal-meta><article-meta><article-id pub-id-type="doi">10.32326/1814-9146-2026-88-1-20-30</article-id><article-id pub-id-type="uri">http://ppp.mech.unn.ru/index.php/ppp/article/view/922</article-id><self-uri>http://ppp.mech.unn.ru/index.php/ppp/article/view/922</self-uri><title-group><article-title xml:lang="ru">ОПРЕДЕЛЕНИЕ УПРУГИХ МОДУЛЕЙ ПОЛИМЕРНЫХ МАТЕРИАЛОВ ПО МЕДЛЕННОСТЯМ БЕГУЩИХ ВОЛН В ОБРАЗЦАХ, ИЗГОТОВЛЕННЫХ МЕТОДОМ ПОСЛОЙНОГО НАПЛАВЛЕНИЯ</article-title><trans-title-group xml:lang="en"><trans-title>DETERMINATION OF ELASTIC MODULI OF POLYMER MATERIALS USING SLOWNESSES OF GUIDED WAVES IN SAMPLES MANUFACTURED BY FUSED DEPOSITION MODELING</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><name><surname>Голуб</surname><given-names>М.В.</given-names></name><name-alternatives><name xml:lang="ru"><surname>Голуб</surname><given-names>М.В.</given-names></name><name xml:lang="en"><surname>Golub</surname><given-names>M.V.</given-names></name></name-alternatives><xref ref-type="aff" rid="aff1"/><email>m_golub@inbox.ru</email></contrib><contrib contrib-type="author"><name><surname>Арсенов</surname><given-names>М.А.</given-names></name><name-alternatives><name xml:lang="ru"><surname>Арсенов</surname><given-names>М.А.</given-names></name><name xml:lang="en"><surname>Arsenov</surname><given-names>M.A.</given-names></name></name-alternatives><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><name><surname>Канищев</surname><given-names>К.К.</given-names></name><name-alternatives><name xml:lang="ru"><surname>Канищев</surname><given-names>К.К.</given-names></name><name xml:lang="en"><surname>Kanishchev</surname><given-names>K.K.</given-names></name></name-alternatives><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><name><surname>Еремин</surname><given-names>А.А.</given-names></name><name-alternatives><name xml:lang="ru"><surname>Еремин</surname><given-names>А.А.</given-names></name><name xml:lang="en"><surname>Eremin</surname><given-names>A.A.</given-names></name></name-alternatives><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><name><surname>Шилько</surname><given-names>С.В.</given-names></name><name-alternatives><name xml:lang="ru"><surname>Шилько</surname><given-names>С.В.</given-names></name><name xml:lang="en"><surname>Shil'ko</surname><given-names>S.V.</given-names></name></name-alternatives><xref ref-type="aff" rid="aff2"/></contrib><aff-alternatives id="aff1"><aff><institution xml:lang="en">Kuban State University (Krasnodar, Russian Federation)</institution></aff><aff><institution xml:lang="ru">Кубанский государственный университет (Краснодар, Российская Федерация)</institution></aff></aff-alternatives><aff-alternatives id="aff2"><aff><institution xml:lang="en">V.A. Belyi Metal-Polymer Research Institute of National Academy of Sciences of Belarus (Gomel, Belarus)</institution></aff><aff><institution xml:lang="ru">Институт механики металлополимерных систем имени В.А. Белого НАН Беларуси (Гомель, Республика Беларусь)</institution></aff></aff-alternatives></contrib-group><pub-date pub-type="epub" iso-8601-date="2026-03-30"><day>30</day><month>03</month><year>2026</year></pub-date><volume>88</volume><issue>1</issue><fpage>20</fpage><lpage>30</lpage><permissions><license><license-p xml:lang="ru">CC BY 4.0</license-p></license></permissions><abstract xml:lang="ru"><p>Представлена методика определения упругих модулей термопластов на образцах в виде пластин, изготовленных методом послойного наплавления. Предлагаемый подход основан на анализе распространения бегущих упругих волн в образце и статистической обработке результатов решения соответствующей обратной коэффициентной задачи. С помощью лазерной доплеровской виброметрии в прямоугольных пластинах регистрировались скорости вертикальных колебаний точек их поверхности, возбуждаемых пьезоэлектрическим преобразователем, который был прикреплен к поверхности пластин с помощью цианоакрилатного клея. Для определения дисперсионных характеристик волн Лэмба по регистрируемым волновым сигналам применялся метод матричного пучка. Решение обратной задачи по определению значений упругих модулей выполнялось численно методом дифференциальной эволюции. При построении целевой функции использовалось свойство обращения фурье-символа матрицы Грина для однородного упругого слоя в бесконечность в точках, соответствующих измеренным волновым числам. Для повышения эффективности метода процедура выполнялась для нескольких линий, проходящих через центр источника колебаний. Проведен статистический анализ значений упругих модулей, восстановленных с использованием различных линий сканирования, получены оценки упругих характеристик материала и выполнено сравнение с результатами стандартизованных механических испытаний на одноосное растяжение. Таким образом, показана эффективность разработанной методики, которая может быть использована для определения и контроля упругих характеристик тонкостенных полимерных конструкций, изготовленных с использованием аддитивных технологий.</p></abstract><trans-abstract xml:lang="en"><p>This paper presents a method for determining the elastic moduli of thermoplastics using plate-shaped specimens fabricated by fused deposition modeling (FDM 3D printing). The proposed approach is based on the analysis of guided elastic wave propagation in the sample and the statistical processing of the results of the corresponding inverse coefficient problem solution. Laser Doppler vibrometry was used to register the velocities of vertical vibrations on the surface of the rectangular plate, which were excited by a piezoelectric transducer glued at the surface via cyanoacrylate. The matrix pencil method was applied to the recorded wave signals to determine dispersion characteristics of Lamb waves. The inverse coefficient problem for elastic moduli was solved numerically using the differential evolution method. The objective function was constructed utilizing the property that the Fourier symbol of the Green's matrix for a homogeneous elastic layer tends to infinity at the points corresponding to the measured wavenumbers. To increase the efficiency of the method, the procedure is performed for several lines starting from the center of the source of vibration. Statistical analysis of the elastic moduli recovered using different scan lines was conducted, providing estimates of the elastic properties of the material. A comparison with the results of standardized uniaxial tensile mechanical tests was performed. Therefore, the effectiveness of the developed method for determining and monitoring the elastic characteristics of thin-walled polymer structures manufactured using additive technologies is demonstrated.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>полимерные материалы</kwd><kwd>аддитивные технологии</kwd><kwd>упругие модули</kwd><kwd>бегущие упругие волны</kwd><kwd>обратная коэффициентная задача</kwd><kwd>численный анализ</kwd></kwd-group><kwd-group xml:lang="en"><kwd>polymer materials</kwd><kwd>additive manufacturing</kwd><kwd>elastic moduli</kwd><kwd>guided elastic waves</kwd><kwd>inverse coefficient problem</kwd><kwd>numerical analysis</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Выполнено при финансовой поддержке Кубанским научным фондом и ООО «Орто-Маркет» в рамках проекта № НТИП-25.1/8.</funding-statement><funding-statement xml:lang="en">The research is carried out with the financial support of the Kuban Science Foundation, Ortho-Market LLC in the framework of the project Num. 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