اثر میدان و سیال مغناطیسی بر پاسخ فرکانسی اولیه و ثانویه نانولوله‌های کربنی حامل سیال با استفاده از مدل انتگرال غیرمحلی مبتنی بر تنش

نوع مقاله : مقاله پژوهشی

نویسنده

دانشکده فنی مهندسی، دانشگاه آزاد اسلامی، واحد بروجرد، بروجرد، ایران

چکیده

در این مقاله ارتعاشات اجباری غیرخطی نانولوله‌های کربنی حامل نانو سیال مغناطیسی و تحت یک میدان مغناطیسی طولی بررسی شده است. با استفاده از میدان کرنش غیرخطی ون کارمن و تئوری تیر اولر برنولی، معادلات حاکم بر ارتعاشات غیرخطی نانولوله کربنی دوسر مفصل استخراج می‌شوند. با استفاده از روش مقیاس‌های چندگانه پاسخ فرکانسی در رزنانس اولیه، رزنانس فوق هارمونیک و رزنانس زیرهارمونیک بدست می‌آید. برای در نظر گرفتن اثرات نانو از مدل انتگرال غیرمحلی مبتنی بر تنش استفاده شده است. در پایان اثر سیال مغناطیسی و شدت میدان مغناطیسی بر پاسخ فرکانسی و پاسخ نیرویی بررسی شده است. از نتایج می‌توان دریافت که وجود میدان مغناطیسی باعث می‌شود که دامنه ارتعاشی سیستم  ناپایدار و دچار چرخه حدی شود. در این شرایط پاسخ ارتعاشی شبه متناوب است. ولی، وجود سیال مغناطیسی باعث می‌شود که دامنه ارتعاشی پایدار بوده و پاسخ زمانی متناوب شود؛ به گونه‌ای که نمودار پوانکاره یک نقطه را در صفحه فاز نشان می‌دهد. در رزنانس اولیه با وجود میدان مغناطیسی طولی، با افزایش دامنه تحریک، منحنی‌های پاسخ فرکانسی شامل دو زیر دامنه می‌باشد. که یکی منحنی مجانبی با محور افقی است و دیگری شامل یک منحنی بسته است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

The Effect of Magnetic Field and Fluid on the Primary and Secondary Frequency Response of Fluid-Conveying Carbon Nanotubes Using a Stress-Driven Nonlocal Integral Model

نویسنده [English]

  • Ebrahim Mahmoudpour
Department of mechanical engineering, Borujerd branch,Borujerd,Iran
چکیده [English]

In this article, the nonlinear forced vibrations of carbon nanotubes conveying magnetic nanofluid under a longitudinal magnetic field have been investigated. Using Von Karman's nonlinear strain field and the Euler-Bernoulli beam theory, the equations governing the nonlinear vibrations of carbon nanotubes are extracted. Using the method of multiple scales, the frequency response in primary resonance, superharmonic resonance, and subharmonic resonance is obtained. In order to consider the effects of small size, a stress-driven non-local integral model has been used. In the end, the effect of magnetic fluid and magnetic field intensity on frequency response and force response has been investigated. From the results, it can be seen that the presence of a magnetic field causes the system's vibration amplitude to be unstable and have a limited cycle. In this condition, the vibration response is quasi-periodic. However, the presence of magnetic fluid causes the vibration amplitude to be stable and the time response to alternate; In such a way that the Poincaré diagram shows a point in the phase plane. In the primary resonance, with the presence of the longitudinal magnetic field, as the excitation amplitude increases, the frequency response curves include two sub-amplitudes. One is an asymptotic curve with a horizontal axis and the other is a closed curve.

کلیدواژه‌ها [English]

  • Nonlinear vibrations
  • Carbon nanotube conveying fluid
  • Longitudinal magnetic field
  • Magnetic fluid
  • Secondary resonance
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