بررسی ارتعاشات آزاد نانوصفحات مرکب گرافن-برن نیترید در محیط حرارتی با استفاده از تئوری آیفانتیس توام با گرادیان سرعت و روش ریتز

نوع مقاله : مقاله پژوهشی

نویسنده

دانشکده مهندسی، دانشگاه یاسوج، یاسوج، ایران

چکیده

این مطالعه به بررسی ارتعاشات جانبی صفحات تک لایه و چند لایه با معماریهای متفاوت گرافن/برن نیترید در محیط حرارتی می‌پردازد. بدین منظور ابتدا نیروی واندوالز بین صفحات با استفاده از معادله لنارد-جونز 6- 12 شبیه سازی شده است. سپس از تئوری ورق اصلاح شده دو متغیره برای شبیه سازی رفتار ارتعاشی صفحات مرکب تک لایه گرافن/برن نیترید یا صفحات مرکب با چیدمان عمودی، استفاده شده است. برای آمیختن اثر سایز با فرضیات تئوری ورق اصلاح شده دو متغیره، از تئوری آیفانتیس برای استخراج انرژی پتانسیل غیر کلاسیک استفاده شده است، همچنین با یک مقیاس طول اضافی از گرادیان سرعت نیز در استخراج انرژی جنبشی بهره گرفته شده است. برای استخراج معادلات مقادیر ویژه حاکم بر مساله از اصل همیلتون توام با روش ریتز استفاده شده است. یافته‌ها نشان می‌دهند که در تعداد لایه‌های ثابت گرافن و برن نیترید با انتخاب چیدمانی مناسب می‌توان فرکانس پایه غیر هم فاز را کمینه یا بیشینه نمود. در نانوصفحات مرکب تک لایه با کنترل فضای اشغال شده توسط برن نیترید می‌توان فرکانس پایه نانو ورق را بهبود بخشید. صرف نظر از نوع ورق مرکب مورد مطالعه، با افزایش دما یا افزایش مقیاس طول، فرکانس پایه کاهش می‌یابد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Free Vibration of Heterostructures of Graphene and Boron Nitride in Thermal Environment via Aifantis Theory with Velocity Gradients and Ritz Method

نویسنده [English]

  • S. Ziaee
Faculty of Engineering, Yasouj University, Yasouj, Iran
چکیده [English]

This article aims to investigate the free vibration of mono-/ multi-layered hererostructures of graphene and boron nitride in thermal environment. To this end, at first, the nonlinear model of inter-layered interaction between different layers are estimated based on Lenard-Jones 6-12 potential, then two variable refined plate theory is used to model the vibrational behavior of in-plane heterostructures of graphnme/boron nitride or vertically stacked graphene/ boron nitride hybrid structures. To incorporate the size effect into two-variable refined plate hypothesis, Aifantis’s theory is used to derive potential energy. To formulate the kinetic energy, an additional length scale which adds gradient velocity to kinetic energy is also used. The eigen-frequency equations are obtained based on Hamilton principle and Ritz method. The results show that the layout of graphene and boron nitride layers only affect out-of-phase natural frequency of multilayered nano-plates. Also, the significant impact of number of boron nitride layers used in heterostructures on the reduction of natural frequency of hybrid structure is demostrated. By controlling the area occupied by boron nitride in mono-layered hybrid structures, one can enhance the natural frequency of nano-sheets. The effects of the value of length scale parameter and temperature change on natural frequencies are studied as well.

کلیدواژه‌ها [English]

  • Heterostructures
  • Refined plate theory
  • Aifantis’s Theory
  • Gradient velocity
  • Natural frequency
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