Vibration Analysis of Magnetostrictive Nano-Plate by Using Modified Couple Stress and Nonlocal Elasticity Theories

Authors: Hamed Khani Arani, Mohammad Shariyat, Armaghan Mohammadian

Abstract:

In the present study, the free vibration of magnetostrictive nano-plate (MsNP) resting on the Pasternak foundation is investigated. Firstly, the modified couple stress (MCS) and nonlocal elasticity theories are compared together and taken into account to consider the small scale effects; in this paper not only two theories are analyzed but also it improves the MCS theory is more accurate than nonlocal elasticity theory in such problems. A feedback control system is utilized to investigate the effects of a magnetic field. First-order shear deformation theory (FSDT), Hamilton’s principle and energy method are utilized in order to drive the equations of motion and these equations are solved by differential quadrature method (DQM) for simply supported boundary conditions. The MsNP undergoes in-plane forces in x and y directions. In this regard, the dimensionless frequency is plotted to study the effects of small scale parameter, magnetic field, aspect ratio, thickness ratio and compression and tension loads. Results indicate that these parameters play a key role on the natural frequency. According to the above results, MsNP can be used in the communications equipment, smart control vibration of nanostructure especially in sensor and actuators such as wireless linear micro motor and smart nano valves in injectors.

Keywords: Feedback control system, magnetostrictive nano-plate, modified couple stress theory, nonlocal elasticity theory, vibration analysis.

References:

[1] Y.S. Li, Z.Y. Cai, and S.Y. Shi, Buckling and free vibration of magnetoelectro elastic nanoplate based on nonlocal theory. Compos. Struct., 2014, vol. 111, pp.522-529.
[2] N. Radic, D. Jeremic, and S. Trifkovic, buckling analysis of double-orthotropic nano-plates embedded in Pasternak elastic medium using nonlocal elasticity theory. Compos Part B., 2014; vol. 61, pp. 162–171.
[3] J.P. Liu, E. Fullerton, O. Gutfleisch, D.J. Sellmyer, Nanoscale Magnetic Materials and Applications, Springer Publisher, New York, 2009.
[4] M. Di Sciuva, and M. Sorrenti, Bending, free vibration and buckling of functionally graded carbon nanotube-reinforced sandwich plates, using the extended Refined Zigzag Theory. Compos. Struct., 2019, vol. 227.
[5] C. Albrechts, Magnetostrictive materials M205. Technische Fakultat der Christian- Albrechts, University Zu Kiel, 2015.
[6] L. Jing Hua, J. Cheng Bao, and X. Hui Bin, Giant magnetostrictive materials, Science China Technological Sciences, 2012, vol. 5, pp. 1319–1326.
[7] C.C. Hong, Application of a magnetostrictive actuator, Mater. Des. 2013, vol. 46, pp. 617-621.
[8] C.C. Hong, Thermal vibration and transient response of magnetostrictive functionally graded material plates. Eur J Mech A Solids, 2014, vol. 43, pp. 78–88
[9] S.C. Pradhan, and A. Kumar, Vibration analysis of orthotropic graphene sheets embedded in Pasternak elastic medium using nonlocal elasticity theory and differential quadrature method, Comput. Mater. Sci, 2010, vol. 50, pp. 239- 245.
[10] A. Ghorbanpour Arani, Z. Khoddami Maraghiand, and H. Khani Arani, Orthotropic patterns of Pasternak foundation in smart vibration analysis of magnetostrictive nanoplate. Proc IMechE Part C, 2015, vol. 230, pp. 1–14.
[11] H.T. Thai, and S.E Kim, A size-dependent functionally graded reddy plate model based on a modified couple stress theory, Compos. Part B, 2013, vol. 45, pp. 1636–1645.
[12] B. Akgöz, and Ö. Civalek, Modeling and analysis of micro-sized plates resting on elastic medium using the modified couple stress theory, Meccanica, 2013, vol. 48, pp. 863–873.
[13] A. Ghorbanpour Arani, H. Khani Arani, and Z. Khoddami Maraghi, Size-dependent in vibration analysis of magnetostrictive sandwich composite micro-plate in magnetic field using modified couple stress theory, J. Sandwich Struct. Mater, 2017, vol. 21, pp.580–603.
[14] R. D. Mindlin, Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates, ASME Journal of Applied Mechanics., 1951, vol. 18, pp. 31–38.
[15] C.C. Hong, Transient responses of magnetostrictive plates by using the GDQ method. Eur J Mech A Solids, 2010, vol. 29, pp. 1015–1021.
[16] S.P. Timoshenko, On the transverse vibrations of bars of uniform cross-section, Philos, Mag. A., 1922, vol. 43, pp. 125–131.
[17] M. Krishna, M. Anjanappa, and Y.F. Wu, The use of magnetostrictive particle actuators for vibration attenuation of flexible beams, J. Sound Vib., 1997, vol. 206, pp. 133-149.
[18] A.C. Eringen, Nonlocal continuum field theories, Springer Publisher, New York, 2002.
[19] J.N. Reddy, Energy principles and variational methods in applied mechanics, Texas John Wiley & Sons Publishers, 2004.
[20] Y.S. Li, buckling analysis of magneto electro elastic plate resting on Pasternak elastic foundation. Mechanics Research Communications. 2015, vol. 56, pp. 104–114.
[21] E. Jomehzadeh, H.R. Noori, and A.R. Saidi, the size-dependent vibration analysis of micro-plates based on a modified couple stress theory. Physica E., 2011, vol. 43, pp. 877–883.
[22] K. Malekzadeh, S.M.R. Khalili, and p. Abbaspour, Vibration of non-ideal simply supported laminated plate on an elastic foundation subjected to in-plane stresses, Compos. Struct., 2010, vol. 92, pp. 1478-1484.
[23] A. Ghorbanpour Arani, H. Khani Arani, and Z. Khoddami Maraghi, Vibration analysis of sandwich composite micro-plate under electro-magneto-mechanical loadings. Appl. Math. Modell, 2016, vol. 40, pp. 10596–10615.
[24] C. Shu, “Differential quadrature and its application in engineering. Singapore,” Springer, 2000.