بررسی ارتعاشات آزاد غیرخطی تیر نانوکامپوزیتی با روش شبیه‌سازی چند مقیاسه

نوع مقاله: مقاله پژوهشی

نویسندگان

1 عضو هیات علمی / مجتمع دانشگاهی هوافضا، دانشگاه صنعتی مالک ‌اشتر

2 دانشجوی دکتری / مجتمع دانشگاهی هوافضا، دانشگاه صنعتی مالک‌ اشتر

چکیده

هدف از این مقاله بررسی رفتار ارتعاشات آزاد عرضی غیرخطی المان حجمی معرف نانوکامپوزیت متشکل از رزین و نانولوله کربنی براساس تئوری ون‌کارمن به‌منظور پیش­بینی رفتار ارتعاشات آزاد تیر نانوکامپوزیتی است. برای این منظور؛ تخست رفتار مکانیکی المان حجمی با روش چند مقیاسه به‌منظور استخراج رفتار ارتعاشی آن تعیین شده است. در این راستا المان‌های حجمی مختلفی با نسبت‌های طولی گوناگون نانولوله در نظر گرفته شده است که هر یک بیانگر گونه‌ای از توزیع نانولوله در فاز ماکرو می‌باشند. در ادامه با مدلسازی المان محدود و حل تحلیلی، فرکانس طبیعی المان حجمی بررسی شده است. برای صحت‌سنجی بیشتر نتایج، تحلیل مودال روی نانولولة مجزا انجام و با کارهای گذشته مقایسه شده است. سپس معادلة ارتعاشاتی المان حجمی استخراج و رفتار ارتعاشات آزاد غیرخطی المان معرف ناشی از عاملیت غیرخطی هندسی بر اساس تئوری ون‌کارمن در شرایط مرزی مختلف مورد بررسی قرار گرفته است. نمودارهای فرکانس طبیعی براساس شرایط توزیع نانوذرات در محیط رزین نشان داد که توزیع مناسب سبب افزایش فرکانس نوسان خطی و غیرخطی المان می‌شود. همچنین براساس نمودارهای فرکانس غیرخطی تحت شرایط مرزی مختلف ملاحظه شد شرایط مرزی سیستم بر میزان غیرخطی بودن رفتار تأثیر زیادی دارد. نتایج نشان داد با افزایش دامنة نوسان در شرایطی که سیستم قید کمتری دارد (مفصل - گیردار)، انحراف فرکانس غیرخطی حدود 20 درصد از حالت مقیدتر (حالت دوسر درگیر) بیشتر است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Investigating the nonlinear free vibrations of Nanocomposite beam based on multiscale modeling

نویسندگان [English]

  • Majid Jamal-Omidi 1
  • Mahdi ShayanMehr 2
  • Saeed Shokrollahi 1
چکیده [English]

The main aim of this paper is to investigate the nonlinear free transverse vibration of representative volume element (RVE) of nanocomposites based on multiscale method, in order to predict the vibration behavior of nanocomposite beam at macro scale. To reach this object, first, mechanical properties of volume element containing carbon nanotube (CNT) is determined. In this regard, various RVEs with different length ratios are considered, where each of them represents a kind of distribution in the nanocomposite environment. Then with finite element modeling and analytical solutions, in linear domain, modal analysis of CNTs and RVEs are investigated. The results indicate that the higher ratio of nanotubes, which represents the uniform distribution of the nanotubes in the resin, has a higher natural frequency. Also, the results of analytical solution have shown good agreement with the FE modeling. In order to further validate the results of modal analysis is performed on CNT and compared with previous studies. Then, the vibration equations of volume element based on the Von-Kármán theory are obtained and nonlinear free vibration behavior of RVEs are investigated in different boundary conditions. The nonlinear frequency of volume element as a function of vibration amplitude showed that the boundary conditions and dispersion state of CNTs have a great effect on the rate of the system nonlinear behavior. Results indicate that in clamp-pinned condition the nonlinear frequency rate is approximately 20% more than clamp-clamp condition and also the values of frequency increase by improving the dispersion state of system.

کلیدواژه‌ها [English]

  • free transverse vibration
  • Nanocomposite
  • Carbon Nanotube
  • multiscale modeling
  • nonlinear frequency

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