تحلیل ارتعاش آزاد نانو صفحه مستطیلی با استفاده از تئوری الاستیسیته غیرمحلی به روش توابع پتانسیل
پذیرفته شده برای ارائه شفاهی ، صفحه 1-9 (9)
کد مقاله : 1026-ISAV2022 (R1)
نویسندگان
1گروه سازه و زلزله،دانشکده مهندسی عمران، دانشگاه صنعتی نوشیروانی بابل
2دانشکده مهندسی عمران، دانشگاه صنعتی نوشیروانی بابل
3دانشکده مهندسی عمران، دانشگاه تهران، تهران،ایران
چکیده
هدف از تحقیق حاضر، تحلیل سه بعدی ارتعاش آزاد نانو صفحات همسانگرد با استفاده از تئوری الاستیسیته غیرمحلی می‌باشد. بدین منظور ابتدا معادلات حرکت سه بعدی برای محیط همسانگرد همگن با استفاده از تئوری وابسته به ابعاد الاستیسیته غیرمحلی محاسبه می‌شود. سپس با استفاده از توابع پتانسیل تغییرمکان مناسب معادلات حرکت مستقل می‌گردد. معادلات حاکم مستقل بدست آمده شامل معادله دیفرانسیل جزیی از مرتبه 4 است. در ادامه، معادلات حاکم مذکور به روش جداسازی متغیرها و اعمال دقیق شرایط مرزی حل و نتایج عددی برای مساله ارتعاش آزاد ارائه می‌گردد. مقایسه نتایج بدست آمده از این تحقیق و نتایج موجود شبیه-سازی دینامیک مولکولی صحت روش ارائه شده را به خوبی اثبات می‌کند. روش ارائه شده در این تحقیق را می‌توان برای تعیین دقیق فرکانس‌های طبیعی نانو صفحات همسانگرد بدون محدودیت در ابعاد و ضخامت صفحه، به‌کار برد. همچنین نتایج تحلیل نشان می-دهد که، افزایش پارامتر غیرمحلی با درنظر گرفتن اثر کرنش‌های دوردست باعث کاهش میزان فرکانس طبیعی نانو صفحه خواهد شد.
کلیدواژه ها
Title
Free vibration analysis of rectangular Nano plate using non-local elasticity theory by potential functions method
Authors
Parvaneh Nateghi-Babagi, Bahram Navayi Neya, Morteza Eskandari-Ghadi
Abstract
The aim of the present research is the three-dimensional free vibration analysis of isotropic Nano plates using the non-local elasticity theory. For this purpose, the three-dimensional motion equations for the homogeneous isotropic medium are calculated using the dimension-dependent theory of non-local elasticity. Then, by using potential functions, the appropriate displacement equations are independent. The obtained independent governing equations include the 4th order partial differential equation. In the following, the mentioned governing equations are presented by the method of separating the variables and applying the boundary conditions of the solution and numerical results for the free vibration problem. The comparison of the results obtained from this research and the existing results of molecular dynamics simulation proves the correctness of the presented method. Also, the method presented in this research can be used to accurately determine the natural frequencies of isotropic Nano plates without limitations on plate dimensions and thickness. Also, the results of the analysis show that increasing the non-local parameter, taking into account the effect of distant strains, will reduce the natural frequency of the Nano plate.
Keywords
Displacement Potential Function, Non local elasticity theory, Nano plate, Free vibration
مراجع
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