بررسی اثر سطح بر روی ارتعاشات آزاد ورق نانو گرافن با سوراخ ناهم مرکز

نوع مقاله : مقاله پژوهشی

نویسندگان

گروه مکانیک، دانشکده فنی مهندسی، دانشگاه صنعتی قم، قم، ایران

چکیده

در این مقاله، با استفاده از یک روش تحلیلی، اثرات سطحی و عیب هندسی بر روی ارتعاشات نانو ورق‌های دایروی مورد بررسی قرار گرفته است. در طی پروسه تولید و قیود ساختی، امکان مواجهه نانو ورق با عیوب هندسی وجود دارد. برخی از این عیوب را می‌توان با استفاده از یک سوراخ دایروی مدل کرد. تئوری الاستیک گورتین-موردوخ و تئوری ورق نازک برای مدلسازی ورق نانو استفاده شده است. در حل تحلیلی معادله حرکت نانو ورق، روش جداسازی متغیرها همزمان با تئوری افزودگی برای توابع بسل مرتبه اول و دوم ساده و بهبود یافته بکار رفته است. برای صحه سنجی، نتایج روش حاضر با منابع موجود مقایسه گردیده است. هر دو حالتِ ارتعاشات متقارن و غیر متقارن مورد تحلیل قرار گرفته است. برای ایجاد حس فیزیکی بهتر، چندین شکل مود ارتعاشی نانو ورق ارائه شده است. در پایان، تاثیر پارامترهای هندسی و مادی مختلف بر روی فرکانس‌های طبیعی نانو ورق بررسی شده است. همپنین اثر شرایط مرزی گوناگون بر روی فرکانس های طبیعی، بخوبی دیده شده است. نتایج نشان می‌دهد که اثرات سطح و عیب دایروی خارج از مرکز، نقش مهمی در رفتار ارتعاشی نانو ورق ایفا می‌کند. این در حالیست که تاثیر سوراخ ناهم مرکز در حالت شرط مرزی آزاد کمتر می شود.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Surface effect on free vibration behavior of circular graphene sheet with an eccentric hole

نویسندگان [English]

  • E. Allahyari
  • M. Fadaee
Department of Mechanical Engineering, College of Engineering, Qom University of Technology, Qom, Iran
چکیده [English]

In this article, an analytical method is used to study surface and geometrical defect effects on free vibrations behavior of circular nanoplates. Due to production process and constrains conditions, nanoplates may be opposed to structural defect. Some of the defects can be modelled as an eccentric hole. Gurtin-Murdoch and thin plate theories are employed to model the eccentric circular nanoplate. In order to solve equation of motion, separation of variables method as well as additional theorem for the regular and modified of first and second kinds of Bessel functions are used. To validate the approach, present results are compared to those obtained by literature. Both of symmetric and antisymmetric vibration modes are analyzed. Some mode shapes are illustrated to make the better physical sense. Finally, effects of various geometrical and material properties on natural frequencies of the nanoplates are investigated. Also, effects of various boundary conditions as free, clamped and simply supported on the natural frequencies are investigated using a wide range of results. Results show that surface effects and eccentric circular defect play an important role in vibrational behavior of an eccentric circular nanoplate. It is observed that the free boundary condition has no more effect on the fundamental natural frequency.

کلیدواژه‌ها [English]

  • Nanoplate
  • Surface effects
  • Eccentric hole
  • Natural frequency
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