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

PDF URL: http://www.ije.ir/Vol28/No12/C/15-2150.pdf  
downloaded Downloaded: 303   viewed Viewed: 2506

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



1.        Farajpour, A., Mohammadi, M., Shahidi, A.R. and Mahzoon, M., “Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model”, Physica E, Vol. 43,(2011),1820-1825.

2.        Shah-Mohammadi-Azar, A., Khanchehgardan, A., Rezazadeh, G. and Shabani, R., “Mechanical response of a piezoelectrically sandwiched nano-beam based on the nonlocal theory”, International Journal of Engineering-Transactions C: Aspects, Vol. 26, No. 12, (2013), 1515-1524.

3.        Shabani, R., Sharafkhani, N. and Gharebagh, V.M., “Static and dynamic response of carbon nanotube-based nano-tweezers”, International Journal of Engineering-Transactions A: Basics, Vol. 24, No. 4, (2011), 377.

4.        Malekzadeh, P. and Shojaee, M., “Free vibration of nanoplates based on a nonlocal two-variable refined plate theory”, Composite Structures, Vol.95,(2013), 443-453.

5.        Khanchehgardan, A., Shah-Mohammadi Azar, A., Rezazadeh, G. and Shabani, R., “Thermo-elastic damping in nano-beam resonators based on nonlocal theory”, International Journal of Engineering-Transactions C: Aspects, Vol. 26, No. 12, (2013), 1505-1514.

6.        JafarSadeghi-Pournaki, I., Zamanzadeh, M.R., Madinei, H. and Rezazadeh, G., “Static pull-in analysis of capacitive FGM nanocantilevers subjected to thermal moment using Eringen’s nonlocal elasticity”, International Journal of Engineering-Transactions A: Basics, Vol. 27, No. 4, (2014), 633-642.

7.        Liu, C., Ke, L.L., Wang, Y.S., Yang, J.and Kitipornchai, S.,“Thermo-electro-mechanical vibration of piezoelectric nanoplates based on the nonlocal theory”,Composite Structures, Vol. 106, (2013),167-174.

8.        Farajpour, A., Dehnaghy, M.and Shahidi, A.R., “Surface and nonlocal effects on the axisymmetric buckling of circulargraphene sheets in thermal environment”, Composites Part B: Engineering, Vol. 50, (2013), 333-343.

9.        Cheng, C.H.and Chen, T.,“Size-dependent resonance and buckling behavior of nanoplates with High-order surface stress effects”,Physica E, Vol. 67, (2015), 12-17.

10.     Zhou, Z.G., Wang, B.and Sun, Y.G., “Two collinear interface cracks in magneto-electro-elastic composites”, Inernational Journal of Engineering Science, Vol. 42, (2004), 1155-1167.

11.     Li, J.Y.,“Magnetoelectroelastic multi-inclusion and inhomogeneity problems and their applications in composite materials”,Inernational Journal of Engineering Science, Vol. 38, (2000), 1993-2011.

12.     Pan, E.and Heyliger, P.R.,“Exact solutions for magneto-electro-elastic laminates in cylindrical bending”,International Journalof Solids and Structures, Vol. 40, (2003), 6859-6876.

13.     Pakam, N.and Arockiarajan, A.,“Study on effective properties of 1-3-2 type magneto-electro-elastic composites”,Sensors and Actuators A: Physical, Vol. 209, (2014),87-99.

14.     Giordano, S.,“Explicit nonlinear homogenization for magneto-electro-elastic laminated materials”, Mechanics Research Communications, Vol. 55, (2014), 18-29.

15.     Chang, T.P,“On the natural frequency of transversely isotropic magneto-electro-elastic plates in contact with fluid”,Applied Mathematical Modelling, Vol. 37, (2013),2503-2515.

16.     Li, Y.S.,“Buckling analysis of magnetoelectroelastic plate resting on Pasternak elastic foundation”, Mechanics Research Communications, Vol. 56, (2014), 104-114.

17.     Alaimo, A., Milazzo, A.and Orlando, C., “A four-node MITC finite element for magneto-electro-elastic multilayered plates”, Composite Structures, Vol. 129, (2013), 120-133.

18.     Chang, T.P., “Deterministic and random vibration analysis of fluid-contacting transversely isotropic magneto-electro-elastic plates”, Computers & Fluids, Vol. 84,(2013), 247-254.

19.     Liu, M.F.,“An exact deformation analysis for the magneto-electro-elastic fiber-reinforced thin plate”, Applied Mathematical Modelling, Vol. 35, (2011), 2443-2461.

20.     Xue, C.X., Pan, E., Zhang, S.Y.and Chu, H.J.,“Large deflection of a rectangular magnetoelectroelastic thin plate”, Mechanics Research Communications, Vol. 38, (2011), 518-523.

21.     Li, Y.S., Cai, Z.Y.and Shi, S.Y.,“Buckling and free vibration of magnetoelectroelastic nanoplate based on nonlocal theory”, Composite Structures, Vol. 111, (2014), 522-529.

22.     Xue, C.X.and Pan, E.,“On the longitudinal wave along a functionally graded magneto-electro-elastic rod”, Inernational Journal of Engineering Science, Vol. 62, (2013), 48-55.

23.     Ke, L.L.and Wang, Y.S.,“Free vibration of size-dependent magneto-electro-elastic nanobeams based on the nonlocal theory”, Physica E, Vol. 63, (2014), 52-61.

24.     Chan, K. and Zhao, Y., “The dispersion characteristics of the waves propagating in a spinning single-walled carbon nanotube”, Science China Physics, Mechanics and Astronomy, Vol. 54, No. (10), (2011), 1854-1865.

Download PDF 

International Journal of Engineering
E-mail: office@ije.ir
Web Site: http://www.ije.ir