مهندسی مکانیک مدرس

مهندسی مکانیک مدرس

ارتعاشات صفحات گرافن با اثر نیروی محوری در محیط الاستیک بر اساس الاستیسیته غیر‌موضعی و تئوری مرتبه سوم برشی

نویسندگان
دانشگاه سمنان
چکیده
این مطالعه با هدف بررسی ارتعاشات عرضی صفحات گرافن تک‌لایه و دو‌لایه واقع در محیط الاستیک بر اساس تئوری تغییر شکل مرتبه سوم برشی با در نظر گرفتن اثر نیروی محوری و در غالب نظریه الاستیسیه غیرموضعی ارینگن انجام شده است که در آن معادلات حاکم بر حرکت با استفاده از اصل همیلتون بدست آمده است. برتری مدل پیوسته غیرموضعی مورد مطالعه نسبت به همتای موضعی آن، در نظر گرفتن اثر اندازه روی رفتار مکانیکی سازه می‌باشد. نتایج حاصل از یک تحلیل فرکانس طبیعی برای شرایط مختلف مانند تأثیر اندازه و نسبت ابعادی، نیروی محوری، ضریب غیرموضعی و اثرات ناشی از تغییر در خواص سفتی محیط الاستیک اطراف با استفاده از روش ناویر و برای شرایط مرزی تکیه‌گاه ساده بدست آمده است. با توجه به اینکه در صفحه گرافن دولایه، سیستم دارای یک مود ارتعاشی هم‌فاز ویک مود ارتعاشی غیر‌هم‌فاز با اختلاف فاز 180 درجه است، تأثیر نیروی ون‌دروالس در هر دو مود ارتعاشی مورد بررسی قرار گرفته و نشان داده شد که نیروی ون‌دروالس اثری روی مود ارتعاشی هم‌فاز نداشته و با افزایش آن فرکانس غیرهم‌فاز افزایش می‌یا‌بد. همچنین مشخص شد که پارامتر غیرموضعی یک پارامتر ثابت نبوده بلکه مقدار آن به اندازه و ساختار اتمی مانند آرایش کایرال یا زیگزاگ و حتی به نوع شرایط مرزی وابسته است.
کلیدواژه‌ها

موضوعات


عنوان مقاله English

Vibration of graphene sheets with axial force effect in elastic medium based on nonlocal elasticity and third-order shear deformation theory

نویسندگان English

Ahmad Ghasemi Ghalebahman
Ali Khakbaz
چکیده English

This study aims to investigate the transverse vibration of single- and double-layered graphene sheets embedded in an elastic medium based on the third-order shear deformation theory considering the axial force effect within the framework of Eringen’s nonlocal elasticity theory, where the governing equations of motion are obtained using Hamilton’s principle. The superiority of the studied non-local continuum model to its local counterpart is to consider the effect of size on the mechanical behavior of the structure. The results from a natural frequency analysis are obtained for different conditions such as the effect of size and aspect ratio, axial force, nonlocal coefficient, and change in the stiffness properties of the surrounding elastic medium by using the Navier-type solution for simply supported boundary conditions. Given that in a double-layered graphene sheet, the system has an in-phase vibrational mode and anti-phase vibrational mode with 180-degrees phase difference, the effect of van der Waals force on both vibrational modes is attempted to be investigated and it is shown that the van der Waals force has no effect on in-phase vibrational mode and by increasing it, the anti-phase frequency increases. It is also demonstrated that the nonlocal parameter is not a constant parameter but its value depends on the size and atomic structure, like chiral and zigzag configurations, and even on the type of boundary conditions.

کلیدواژه‌ها English

Nonlocal theory
Free vibration
Graphene sheet
Third-order shear deformation theory
Axial Force
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