IJE TRANSACTIONS C: Aspects Vol. 28, No. 12 (December 2015) 1808-1817   

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A. Amiri, S. M. Fakhari, I. J. Pournaki, G. Rezazadeh and R. Shabani
( Received: October 16, 2015 – Accepted: December 24, 2015 )

Abstract    The present work mainly studies the free vibration of circular magneto-electro-elastic (MEE) nano-plates based on the Kirchhoff’s plate theory within the framework of nonlocal elasticity theory to account for the small scale effect. The MEE nano-plate studied here is considered to be fully clamped and subjected to the external magnetic and electric potentials. Using nonlocal constitutive relations of MEE materials, the governing equations are derived, by applying Maxwell’s equation and Hamilton’s principle. By employing Galerkin method, the eigen matrix form of the governing equation is obtained. A detailed numerical study is conducted to study the influences of the small scale effect, thickness and radius of the nano-plate and piezoelectric volume fraction of the MEE material on the natural frequencies of nano-plate. Furthermore, the effects of the applied magnetic and electric potentials on the size-dependent natural frequencies are investigated numerically.


Keywords    MEE, Nano-plates, Kirchhoff’s plate theory, Nonlocal elasticity, Natural frequency


چکیده    در این مقاله ارتعاشات نانو صفحهات مدور مگنتو- الکترو- الاستیک تحت بارگذاری های الکتریکی و مغناطیسی، با استفاده از تئوری غیرمحلی ارینگن و تئوری صفحه کیرشهف مورد بررسی قرار می گیرد. نانوصفحه مورد مطالعه به صورت کامل گیردار بوده و تحت پتانسیلهای مغناطیسی و الکتریکی خارجی میباشد. با در نظر گرفتن روابط بنیادی غیر موضعی حاکم بر مواد مگنتو-الکترو-الاستیک و با استفاده از معادلات ماکسول و اصل همیلتون، معادلات حاکم بر حرکت به دست آمده است. با اعمال روش گلرکین، فرم ماتریسی معادله حاکم بدست می آید. با حل عددی معادله حاکم، اثرهای پارامتر غیر محلی، ضخامت و شعاع صفحه و درصد حجمی فاز پیزوالکتریک برفرکانسهای طبیعی نانوصفحه بررسی می گردد. در نهایت اثرات پتانسیل های مغناطیسی و الکتریکی اعمالی با در نظر گرفتن اثرهای اندازه بر فرکانسهای طبیعی سیستم مورد بررسی قرار گرفته است



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