donstuAdvanced Engineering Research (Rostov-on-Don)Advanced Engineering Research (Rostov-on-Don)2687-1653Don State Technical University10.12737/6816donstu-348Research ArticleTECHNICAL SCIENCESТЕХНИЧЕСКИЕ НАУКИ1/3 SUBHARMONIC RESPONSE OF DUFFING OSCILLATOR UNDER PERIODIC AND RANDOM EXCITATIONSСубгармонический отклик третьего порядка для осциллятора Дуффинга, возмущенного гармоническим и случайным воздействиемАньН. Д.AnhN. D.ЗаковоротныйВ. Л.ZakovorotnyVilor Lavrentyevichvzakovorotny@dstu.edu.ruХаоД. Н.HaoD. N.

University of Le Quy Don, Hanoi, Vietnam

ТьемН. Х.ChiemN. Х.Институт механики академии наук и технологий Вьетнама, ВьетнамВьетнамInstitute of Mechanics, Hanoi, VietnamViet NamДонской государственный технический университет, РоссияРоссияDon State Technical University, RussiaRussian FederationУниверситет информационных технологий Хошимина, ВьетнамВьетнамUniversity of Information Technology, HochiMinh City, VietnamViet NamУниверситет Ле Куи Дон, ВьетнамВьетнамUniversity of Le Quy Don, Hanoi, VietnamViet Nam2014301220141443949Copyright © Anh N.D., Zakovorotny V.L., Hao D.N., Chiem N.Х., 20142014Ань Н.Д., Заковоротный В.Л., Хао Д.Н., Тьем Н.Х.Anh N.D., Zakovorotny V.L., Hao D.N., Chiem N.Х.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.vestnik-donstu.ru/jour/article/view/348

The subharmonic response of one third order of Duffing oscillator under harmonic and random excitations is investigated for the first time by a technique combining the stochastic averaging method, the equivalent linearization method, and the technique of auxiliary function for Fokker-Planck equation. The averaged equations are linear zed so that the stationary density function of the approximate response can be found exactly by the technique of auxiliary function. The one third order subharmonic response obtained by the present technique is validated by numerical simulation. The significant contribution of this work is that it may lead to a new trend in investigating subharmonic oscillators in random nonlinear systems.

В статье впервые исследуется субгармонический отклик третьего порядка осциллятора Дуффинга на основе метода стохастического усреднения и одновременно стохастической линеаризации. При этом используется разрабатываемый авторами метод вспомогательных функций для уравнения Фоккера – Планка. Усредненные уравнения линеаризованы так, что плотностная стационарная функция приближенного отклика может быть получена точно с помощью метода вспомогательной функции. Полученные на основе разработанного метода решения сравниваются с численными решениями. Значение этой работы заключается в том, что предложенный метод может привести к новой тенденции в исследовании субгармонических осцилляторов в случайных нелинейных систем.

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The authors declare that there are no conflicts of interest present.