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ارتعاشات آزاد خطی و غیرخطی صفحه مدرج تابعی مگنتو-الکترو-الاستیک مستطیلی شکل براساس نظریۀ تغییر شکل برشی مرتبه سوم | ||
| نشریه مهندسی مکانیک امیرکبیر | ||
| مقاله 9، دوره 49، شماره 4، اسفند 1396، صفحه 743-758 اصل مقاله (2.03 M) | ||
| نوع مقاله: مقاله پژوهشی | ||
| شناسه دیجیتال (DOI): 10.22060/mej.2016.763 | ||
| نویسندگان | ||
| علیرضا شوشتری* ؛ رامین منتشلو | ||
| گروه مهندسی مکانیک، دانشکده مهندسی دانشگاه بوعلی سینا، همدان، ایران | ||
| چکیده | ||
| در این مقاله ارتعاشات آزاد غیرخطی ورق مستطیل شکل مدرج تابعی با خواص مگنتو-الکترو-الاستیک مورد بررسی قرار گرفته است. شرایط مرزی ساده برای کلیه لبه های ورق در نظر گرفته شده است. همچنین معادلات حرکت بر اساس تئوری برشی مرتبه سوم به دست آمده اند. در این مساله فرض شده است که سطوح بالا و پایین ورق تحت اختلاف پتانسیل‌های الکتریکی و مغناطیسی قرار دارند که با استفاده از قوانین گاوس برای حالت‌های الکترواستاتیک و مگنتواستاتیک، رفتار الکتریکی و مغناطیسی ورق مدل شده است. همچنین خواص مدرجی بودن تابعی ورق بر اساس تابع توانی در نظر گرفته شده است.پس از تعیین معادلات حرکت با استفاده از روش گلرکین معادلات دیفرانسیل جزئی حرکت به معادلات دیفرانسیل معمولی تبدیل شده است. سپس با استفاده از تئوری پرتوربیشن مساله حل شده است و رابطه‌ای تحلیلی برای فرکانس طبیعی، نسبت فرکانس غیرخطی به فرکانس طبیعی خطی به دست آمده‌اند. نتایج بدست آمده از روابط تحلیلی بدست آمده با نتایج بدست آمده از سایر منابع مرتبط صحه‌گذاری شده است و نشان میدهد مدل پیشنهادی دارای دقت بسیار خوبی می باشد. سپس با استفاده از نتایج موجود، تعدادی مثل عددی برای بررسی اثر پارامترهای مختلف بر روی رفتار ارتعاشی غیرخطی ورق‌های مدرج تابعی مگنتو-الکترو-الاستیک ارائه شده است. | ||
| کلیدواژه‌ها | ||
| ورق هوشمند مدرج تابعی؛ نظریۀ تغییر شکل برشی مرتبه سوم؛ قوانین گاوس؛ روش لیندشتات پوانکاره؛ ارتعاشات آزاد | ||
| عنوان مقاله [English] | ||
| Linear and Nonlinear free vibration of a Functionally Graded Magneto-electro-elastic Rectangular Plate Based on the Third Order Shear Deformation Theory | ||
| نویسندگان [English] | ||
| A. Shooshtari؛ R. Mantashloo | ||
| Mechanical Engineering Department, Bu-Ali Sina University, Hamedan, Iran | ||
| چکیده [English] | ||
| In this paper, linear and nonlinear free vibration of one functionally graded magnetoelectro- elastic rectangular plate is studied. The boundary conditions in all side of plate have been considered as simply supported. Also the equations of motions have been derived calculation the kinetic energy and potential energy based on the third order shear deformation theory using Hamilton principle. Considering the top surface of the plate as an pizeomagnetic material and the bottom surface as a piezoelectric material, the bottom and upper surfaces of the plate are subjected to electric and magnetic potentials. The electric and magnetic behaviors of the plate are modeled by using Gauss’s laws. Then, the equations of motions have been transformed from partial differential equations to ordinary differential equations by using Galerkin Method. Then, Using Lindeshtot- Poincare method a closed form expression for linear and nonlinear natural frequency has been obtained. for validation of the proposed model, some numerical examples have been presented and comparisons between the obtained results with the results in literature have been down. It is shown that good agreement exist between obtained results and previous works. Then, to study the effects of several parameters on the nonlinear vibration response of functionally graded magneto-electro-elastic rectangular plates | ||
| کلیدواژه‌ها [English] | ||
| Functionally graded smart plate, Third order shear deformation theory, Gauss’s laws, Perturbation method, free vibration | ||
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| مراجع | ||
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