ارتعاش جانبی صفحة گرافنی تک‌لایه تحت تأثیر میدان مغناطیسی دو بعدی با روش مربعات دیفرانسیلی

نوع مقاله: مقاله پژوهشی

نویسندگان

1 دانشجوی کارشناسی ارشد / دانشکده مهندسی مکانیک، دانشگاه تبریز

2 عضو هیات علمی / دانشکده مهندسی مکانیک، دانشگاه تبریز

چکیده

در این مقاله، معادلة حاکم بر ارتعاش جانبی صفحة گرافنی تک­لایه تحت تأثیر میدان مغناطیسی دوبعدی درون‌صفحه‌ای، با احتساب نیرو و ممان خمشی ناشی از آن، برای شرایط تکیه‍گاهی مختلف برای نخستین‌بار توسط روش مربعات دیفرانسیلی بررسی شده است. برای تعیین معادلة حاکم بر ارتعاش صفحه از تئوری غیرمحلی با در نظر گرفتن نیروی مغناطیسی لورنتز بهره گرفته شده ‌است. پس از استخراج معادله دیفرانسیل حاکم، معادلة حاصل بی‌بعد شده و فرکانس ارتعاش به ازای شرایط تکیه‌گاهی مختلف به‌دست می‏آید. اثر سفتی بستر الاستیک، پارامتر غیرمحلی، نسبت منظر ورق و اثر میدان مغناطیسی دوبعدی بر فرکانس پایه مورد بحث و بررسی قرار گرفته است. نتایج این بررسی نشان می­دهد که افزایش سفتی بستر الاستیک، پارامتر غیرمحلی و نسبت منظر سبب افزایش فرکانس پایه می‌شود. اما اعمال میدان مغناطیسی دوبعدی داخل صفحه­ای باعث کاهش سفتی خمشی، افزایش نیروی فشاری داخل صفحه­ای و در نتیجه کاهش فرکانس پایه می­گردد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Transverse vibration of single-layer graphene sheet under 2D magnetic field action by differential quadrature method

نویسندگان [English]

  • Arezoo Esmaeili 1
  • Hasan Biglari 2
چکیده [English]

In this paper, governing equations of transverse vibration of single-layer graphene sheet with different boundary conditions under 2D in-plane magnetic field action, considering its consequent forces and moments, are investigated for the first time using differential quadrature method (DQM). Governing equations of motion are obtained using non-local theory and considering Lorentz's force. The partial differential equations of system are changed to the ordinary differential equations using separation of variables method. Using differential quadrature method, the obtained governing equations are solved for different boundary conditions. The effects of elastic foundation stiffness, non-local parameter, plate aspect ratio and 2D magnetic field effects on the natural frequency of graphene sheet are evaluated. The results show that increase of foundation stiffness, non-local parameter and aspect ratio result in increase of fundamental frequency, in all boundary conditions. But, action of in-plane magnetic field results in decrease of fundamental frequency, because of decreasing flexural stiffness and increasing in-plane pressure loading.

کلیدواژه‌ها [English]

  • graphene sheet
  • non-local theory
  • 2D magnetic field
  • Lorentz's force
  • DQM

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