بررسی ارتعاشات غیرخطی بعد از کمانش ناشی از بار حرارتی و تحلیل پایداری نانوورق گرافن دو لایه

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشگاه یاسوج، دانشکده مهندسی، گروه مهندسی مکانیک

2 دانشگاه شیراز، دانشکده مهندسی، گروه مهندسی مکانیک

چکیده

در این تحقیق رفتار ارتعاش بعد از کمانش یک نانو ورق گرافن دولایه تحت بار حرارتی بررسی شده است. بدین منظور، نانو ورق گرافن به صورت یک ورق اورتوتروپیک غیرکلاسیک مدل شده است که در آن اثر مقیاس کوچک لحاظ شده است. فرمول بندی مسئله بر اساس تئوری ورق کیرشهف انجام شده که فرضیات غیرخطی فون کارمن در روابط کرنش – جابجایی در نظر گرفته شده است و از تئوری الاستیسیته غیر محلی ایرینگن برای اعمال اثر اندازه بهره گرفته شده است. اثرات حرارتی، نیروهای واندروالس بین لایه‌ای و کایرالیتی نیز در نظر گرفته شده و خواص مواد وابسته به دما فرض شده است. به کمک روش مقیا سهای زمانی چندگانه یک پاسخ نیمه تحلیلی به دست آمده است. اثر تغییر مقیاس کوچک بر فرکانس‌های طبیعی، جابجایی و منحنی پاسخ بررسی و نتایج عددی با استفاده از مدل نانو ورق غیرمحلی استخراج شده است. نتایج عددی با نتایج تحقیقات مشابه مقایسه شده است. تأثیر پارامترهای مختلف بر ارتعاشات بعد از کمانش نانو ورق گرافن دولایه در محیط حرارتی از جمله پارامتر مقیاس، ابعاد، و بار حرارتی ارائه شده است. پایداری مودهای ارتعاشی حول یک وضعیت کمانشی بررسی شده است. نتایج نشان می‌دهد که پارامتر مقیاس و تغییر دما نقش مهمی در رفتار ارتعاش غیرخطی نانوساختارهای کمانش کرده دارند.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Nonlinear Vibration and Stability Analysis of Thermally Postbuckled Double-Layered Graphene Sheet

نویسندگان [English]

  • GholamAli Varzandian 1
  • Sima Ziaee 1
  • Mehrdad Farid 2
  • Abbas Niknejad 1
1 Department of Mechanical Engineering, Yasouj University
2 Department of Mechanical Engineering, Shiraz University
چکیده [English]

In the present research, the vibration behavior is presented for a thermally postbuckled double layered graphene sheet. For this purpose, the graphene sheet is modeled as a non-classical orthotropic plate. The formulations are based on the Kirchhoff’s plate theory, and the von Karman-type nonlinearity is considered in the strain-displacement relations. Eringen’s nonlocal elasticity theory is employed to incorporate the size effects. The thermal effects, van der Waals forces between layers and chirality are also included and the material properties are assumed to be temperature-dependent. A semi analytical solution is obtained using multiple time scales method. The effects of variation of the small scale parameter to the natural frequencies, deflections and response curve of double layered graphene sheet are analyzed and the numerical results are obtained from the nonlocal plate model. Numerical results are compared with those of similar researches. Effects of various parameters on the postbuckled vibration of graphene sheet in thermal environments such as the scale parameter, length, and thermal load are presented. The stability of vibration modes around a buckled configuration is investigated. The results show that the scale parameter and thermal changes have very important roles on the nonlinear vibrational behavior of the nano scale buckled structures.

کلیدواژه‌ها [English]

  • Double layered Graphene sheet
  • Thermal postbuckling
  • Nonlocal plate model
  • Multiple time scales methods
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