نوع مقاله: مقاله پژوهشی

نویسندگان

1 استادیار، مهندسی مکانیک، دانشگاه اصفهان، اصفهان، ایران

2 دانشجوی کارشناسی ارشد، مهندسی مکانیک، دانشگاه کاشان، کاشان

3 دانشیار، مهندسی مکانیک، دانشگاه کاشان، کاشان، ایران

چکیده

در این پژوهش، ارتعاشات آزاد یک نانو ورق ناهمسانگرد دو لایه‌ی تقویت شده با نانولوله‌های کربنی به‌صورت تحلیلی حل شده است. نانو‌لوله‌های کربنی در راستای ضخامت ورق به‌صورت مدرج تابعی با دو فرم یکنواخت و کاهشی-افزایشی توزیع شده‌اند. محیط الاستیک اطراف ورق به‌صورت بستر الاستیک پاسترناک مدل‌سازی شده و اثرات نیروی واندروالس بین دو لایه نیز لحاظ شده است. معادلات حاکم با استفاده از روش انرژی و تئوری غیر محلی ارینگن به‌دست آمده و برای یک ورق مستطیلی با شرایط مرزی چهار طرف تکیه‌گاه ساده با استفاده از روش ناویر حل شده‌اند. در نهایت، اثر پارامترهای مختلف مانند ثابت فنری نوع وینکلر، ثابت برشی نوع پاسترناک، چیدمان‌های مختلف ذرات نانو و پارامترهای غیر محلی روی رفتار ارتعاشی نانو ورق دو لایه بررسی شده است. نتایج به‌دست آمده نشان می‌دهند با افزایش ثابت فنری نوع وینکلر فرکانس طبیعی نانو ورق افزایش می‌یابد در حالی‌که تاثیر ثابت برشی نوع پاسترناک بر فرکانس طبیعی نانو‌ ورق دولایه بسیار کم است. همچنین با افزایش ضریب غیرمحلی در یک طول ثابت نسبت فرکانس طبیعی کاهش می‌یابد. با افزایش نسبت طول به ضخامت ورق (L/h) فرکانس طبیعی غیر محلی کاهش پیدا کرده و در (L/h) ثابت، فرکانس طبیعی چیدمان کاهشی-افزایشی بیشتر از توزیع یکنواخت می‌باشد. نتایج حاصل از این تحقیق می‌تواند در ساخت وسایل نانو استفاده شده و همچنین الگویی برای ادامه کارهای دیگر باشد.

کلیدواژه‌ها

عنوان مقاله [English]

Analytical solution for free vibration of functionally graded carbon nanotubes (FG-CNT) reinforced double-layered nano-plates resting on elastic medium

نویسندگان [English]

  • Mohammad Heidari-Rarani1 1
  • Sajad Alimirzaei 2
  • Keivan Torabi 3

1 Department of Mechanical Engineering, Faculty of Engineering, University of Isfahan, Isfahan, Iran

2 Department of Mechanical Engineering, University of Kashan, Kashan, Iran

3 Department of Mechanical Engineering, University of Kashan, Kashan, Iran

چکیده [English]

In this paper, free vibration of an embedded double-layered nano-plate reinforced by functionally graded carbon nanotubes (FG-CNT) is analytically investigated. Carbon nanotubes are distributed through the thickness in two ways: uniform distribution and symmetrically linear distribution (or decreasing-increasing layup). To accurately model this nanocomposite behavior, the elastic medium around the nano-plate is modeled by Pasternak elastic foundation and the Van der waals forces between two nano-plates are taken into account. Governing equations of motions are obtained using energy method in association with Eringen nonlocal theory and solved by Navier method for a simply-supported rectangular plate. Finally, the effect of elastic foundation parameters, different distributions of CNT and nonlocal parameters are investigated on the vibration behavior of orthotropic double-layer nano-plate. Results show that natural frequencies of a double-layer nano-plate increase by increasing the Winkler elastic constants while Pasternak elastic constant has less effect on the results. Also, increasing the nonlocal parameter at a constant length decreases the natural frequencies. By increasing the length to thickness ratio (L/h) of nano-plate, the nonlocal frequencies reduce and natural frequency of symmetrically linear distribution is more than those of uniform distribution for constant value of L/h.

کلیدواژه‌ها [English]

  • Free vibration
  • Nano-plate
  • CNT
  • Functionally graded

 

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