Effect of Follower Force on Vibration Frequency of Magneto-Strictive-Faced Sandwich Plate with CNTR Composite Core

Subject Areas : Engineering

M.R Ghorbanpour Arani ¹ , Z Khoddami Maraghi ²

1 - Electrical Engineering Department, Amirkabir University of Technology, Tehran, Iran
2 - Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran

Received: 2018-06-30 Accepted : 2018-08-31 Published : 2018-12-30

Keywords: Sandwich plate, Follower force, Feedback control system, Nano-Composite, Magneto-strictive sheets,

Abstract :

This study deals with the vibration response of sandwich plate with nano-composite core and smart magneto-strictive face sheets. Composite core is reinforced by carbon nanotubes (CNTs) and its effective elastic properties are obtained by the rule of Mixture. Terfenol-D films are used as the face sheets of sandwich due to magneto-mechanical coupling in magneto-strictive material (MsM). In order to investigate the magnetization effect on the vibration characteristics of sandwich plate, a feedback control system is utilized. Also the sandwich plate undergoes the follower forces in opposite direction of x. Based on energy method, equations of motions are derived using Reddy’s third order shear deformation theory, and Hamilton’s principle and solved by differential quadrature method (DQM). A detailed numerical study is carried out based on third-order shear deformation theory to indicate the significant effect of follower forces, volume fraction of CNTs, temperature change, core-to-face sheet thickness ratio and controller effect of velocity feedback gain on dimensionless frequency of sandwich plate. These finding can be used to automotive industry, aerospace and building industries.

References:

[1] Reddy J.N., 2004, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, Boca Raton.
[2] Panda S., Ray M.C., 2009, Active control of geometrically nonlinear vibrations of functionally graded laminated composite plates using piezoelectric fiber reinforced composites, Journal of Sound and Vibration 325(1-2): 186-205.
[3] Wang Z.X., Shen H.S., 2012, Nonlinear vibration and bending of sandwich plates with nanotube-reinforced composite face sheets, Composites Part B-Engineering 43(2): 411-421.
[4] Lei Z.X., Liew K.M., Yu J.L., 2013, Free vibration analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method in thermal environment, Composite Structures 106: 128-138.
[5] Natarajan S., Haboussi M., Manickam G., 2014, Application of higher-order structural theory to bending and free vibration analysis of sandwich plates with CNT reinforced composite face sheets, Composite Structures 113: 197-207.
[6] 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.
[7] Lee S.J., Reddy J.N., Rostam-Abadi F., 2004, Transient analysis of laminate embedded smart-material layers, Finite Elements in Analysis and Design 40(5-6): 463-483.
[8] Hong C.C., 2010, Transient responses of magneto-strictive plates by using the GDQ method, European Journal of Mechanics A-Solids 29(6): 1015-1021.
[9] Kim J.H., Kim H.S., 2000, A study on the dynamic stability of plates under a follower force, Computers and Structures 74: 351-363.
[10] Jayaraman G., Struthers A., 2005, Divergence and flutter instability of elastic specially orthotropic plates subject to follower forces, Journal of Sound and Vibration 281: 357-373.
[11] Guo X., Wang Z., Wang Y., 2011, Dynamic stability of thermoelastic coupling moving plate subjected to follower force, Applied Acoustics 72: 100-107.
[12] Pourasghar A., Kamarian S., 2013, Dynamic stability analysis of functionally graded nanocomposite non-uniform column reinforced by carbon nanotube, Journal of Vibration and Control 21: 2499-2508.
[13] Shen H.S., 2009, Nonlinear bending of functionally graded carbon nanotube reinforced composite plates in thermal environments, Composite Structures 91: 9-19.
[14] Han Y., Elliott J., 2007, Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites, Computational Materials Science 39(2): 315-323.
[15] Hong C.C., 2009, Transient responses of magneto-strictive plates without shear effects, International Journal of Engineering Science 47(3): 355-362.
[16] Krishna M., Anjanappa M., Wu Y.F., 1997, The use of magneto-strictive particle actuators for vibration attenuation of flexible beams, Journal of Sound and Vibration 206(2): 133-149.
[17] Daneshmehr A., Rajabpoor A., Pourdavood M., 2014, Stability of size dependent functionally graded nano-plate based on nonlocal elasticity and higher order plate theories and different boundary conditions, International Journal of Engineering Science 82: 84-100.
[18] Wang C.M., Reddy J.N., Lee K.H. 2000, Shear Deformable Beams and Plates, Elsevier Science Ltd, UK.
[19] Reddy J.N., 2000, Energy Principles and Variational Methods in Applied Mechanics,John Wiley and Sons Publishers, Texas.
[20] 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(10): 3047-3057.
[21] Shu C., 2000, Differential Quadrature and its Application in Engineering, Singapore, Springer publishers.
[22] Leissa A.W., 1973, The free vibration of rectangular plates, Journal of Sound and Vibration 31(3): 257-293.