Ghorbanpour Arani, A., Khoddami Maraghi, Z., Khani Arani, H. (2016). Smart Vibration Control of Magnetostrictive Nano-Plate Using Nonlocal Continuum Theory. Journal of Solid Mechanics, 8(2), 300-314.

A Ghorbanpour Arani; Z Khoddami Maraghi; H Khani Arani. "Smart Vibration Control of Magnetostrictive Nano-Plate Using Nonlocal Continuum Theory". Journal of Solid Mechanics, 8, 2, 2016, 300-314.

Ghorbanpour Arani, A., Khoddami Maraghi, Z., Khani Arani, H. (2016). 'Smart Vibration Control of Magnetostrictive Nano-Plate Using Nonlocal Continuum Theory', Journal of Solid Mechanics, 8(2), pp. 300-314.

Ghorbanpour Arani, A., Khoddami Maraghi, Z., Khani Arani, H. Smart Vibration Control of Magnetostrictive Nano-Plate Using Nonlocal Continuum Theory. Journal of Solid Mechanics, 2016; 8(2): 300-314.

Smart Vibration Control of Magnetostrictive Nano-Plate Using Nonlocal Continuum Theory

^{1}Faculty of Mechanical Engineering, University of Kashan--Institute of Nanoscience& Nanotechnology, University of Kashan

^{2}Faculty of Mechanical Engineering, University of Kashan

Abstract

In this research, a control feedback system is used to study the free vibration response of rectangular plate made of magnetostrictive material (MsM) for the first time. A new trigonometric higher order shear deformation plate theory are utilized and the results of them are compared with two theories in order to clarify their accuracy and errors. Pasternak foundation is selected to modelling of elastic medium due to considering both normal and shears modulus. Also in-plane forces are uniformly applied on magnetostrictive nano-plate (MsNP) in x and y directions. Nonlocal motion equations are derived using Hamilton’s principle and solved by differential quadrature method (DQM) considering different boundary conditions. Results indicate the effect of various parameters such as aspect ratio, thickness ratio, elastic medium, compression and tension loads and small scale effect on vibration behaviour of MsNP especially the controller effect of velocity feedback gain to minimizing the frequency. These finding can be used to active noise and vibration cancellation systems in micro and nano smart structures.

[1] Liu J.P., Fullerton E., Gutfleisch O., Sellmyer D.J., 2009, Nanoscale Magnetic Materials and Applications, Springer Publisher, New York. [2] Hong C.C., 2013, Application of a magnetostrictive actuator, Materials and Design 46: 617-621. [3] Aboudi J., Zheng X., Jin K., 2014, Micromechanics of magnetostrictive composites, International Journal of Engineering Science 81: 82-99. [4] Radic N., Jeremic D., Trifkovic S., Milutinovic M., 2014, Buckling analysis of double-orthotropic nanoplates embedded in Pasternak elastic medium using nonlocal elasticity theory, Composites Part B 61: 162-171. [5] Li Y.S., Cai Z.Y., Shi S.Y., 2014, Buckling and free vibration of magnetoelectroelastic nanoplate based on nonlocal theory, Composite Structures 111: 522-529. [6] Kiani K., 2014, Free vibration of conducting nanoplates exposed to unidirectional in-plane magnetic fields using nonlocal shear deformable plate theories, Physica E 57: 179-192. [7] Jia Z.Y., Liu H.F., Wang F.J., Liu W., Ge C.Y., 2011, A novel magnetostrictive static force sensor based on the giant magnetostrictive material, Measurement 44: 88-95. [8] Aboudi J., Zheng X., Jin K., 2014, Micromechanics of magnetostrictive composites, International Journal of Engineering Science 81: 82-99. [9] Pradhan S.C., Kumar A., 2010, Vibration analysis of orthotropic graphene sheets embedded in Pasternak elastic medium using nonlocal elasticity theory and differential quadrature method, Computational Materials Science 50: 239-245. [10] Pradhan S.C., Phadikar J.K., 2009, Nonlocal elasticity theory for vibration of nanoplates, Journal of Sound and Vibration 325: 206-223. [11] Malekzadeh P., Shojaee M., 2013, Free vibration of nanoplates based on a nonlocal two-variable refined plate theory, Composite Structures 95: 443-452. [12] Pradhan S.C., 2009, Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory, Physics Letters A 373: 4182-4188. [13] Zenkour A.M., Sobhy M., 2013, Nonlocal elasticity theory for thermal buckling of nanoplates lying on Winkler–Pasternak elastic substrate medium, Physica E 53: 251-259. [14] Mantari J.L., Oktem A.S., Soares C.G., 2012, A new trigonometric layerwise shear deformation theory for the finite element analysis of laminated composite and sandwich plates, Computers and Structures 94-95: 45-53. [15] Mantari J.L., Bonilla E.M., Soares C.G., 2014, A new tangential-exponential higher order shear deformation theory for advanced composite plates, Composites Part B 60: 319-328. [16] Mantari J.L., Oktem A.S. Soares C.G., 2012, A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates, International Journal of Solids and Structures 49: 43-53. [17] Mantari J.L., Soares C.G., 2013, A novel higher-order shear deformation theory with stretching effect for functionally graded plates, Composites Part B 45: 268-281. [18] Hong C.C., 2009, Transient responses of magnetostrictive plates without shear effects, Journal of Sound and Vibration 47: 355-362. [19] Hong C.C., 2010, Transient responses of magnetostrictive plates by using the GDQ method, European Journal of Mechanics A/Solids 29: 1015-1021. [20] Timoshenko S.P., 1922, On the transverse vibrations of bars of uniform cross-section, Philosophical Magazine A 43: 125-131. [21] Krishna M., Anjanappa M., Wu Y.F., 1997, The use of magnetostrictive particle actuators for vibration attenuation of flexible beams, Journal of Sound and Vibration 206: 133-149. [22] Eringen A.C., 2002, Nonlocal Continuum Field Theories, New York, Springer. [23] Alibeygi Beni A., Malekzadeh P., 2012, Nonlocal free vibration of orthotropic non-prismatic skew nanoplates, Composite Structures 94: 3215-3222. [24] Rahim Nami M., Janghorban M., 2013, Static analysis of rectangular nanoplates using trigonometric shear deformation theory based on nonlocal elasticity theory, Beilstein Journal of Nanotechnolgy 4: 968-973. [25] Reddy J.N., 2004, Energy Principles and Variational Methods in Applied Mechanics, John Wiley & Sons Publishers, Texas. [26] Malekzadeh K., Khalili S.M.R., Abbaspour P., 2010, Vibration of non-ideal simply supported laminated plate on an elastic foundation subjected to in-plane stresses, Composite Structures 92: 1478-1484. [27] Ghorbanpour Arani A., Vossough H., Kolahchi R., Mosallaie Barzoki A.A., 2012, Electro-thermo nonlocal nonlinear vibration in an embedded polymeric piezoelectric micro plate reinforced by DWBNNTs using DQM, Journal of Mechanical Science and Technology 26: 3047-3057. [28] Shu C., 2000, Differential Quadrature and its Application in Engineering, Springer publishers, Singapore.