Vibration suppression analysis for laminated composite beams embedded actuating magnetostrictive layers

Document Type: Research Paper

Authors

1 Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, SAUDI ARABIA

2 Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, EGYPT

3 Department of Mathematics, Faculty of Science, Bisha University, Bisha, SAUDI ARABIA

Abstract

This paper presents the analysis of vibration control of a laminated composite beam that including magnetostrictive layers. The formulation of problem is presented based on the shear deformation beam theory. For vibration suppression, the velocity feedback control with constant gain distributed is considered. Navier's method is applied to analyze the solution of vibration suppression of laminated beam with the simply-supported boundary conditions. The influence of lamination schemes, modes, number of smart layers at the structure, the control gain of the agnetic field intensity and smart layer position on suppress of the vibration are discussed. In addition, the  ntrolled motion of some special laminated composite beam is tested.

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  1. Goodfriend M.J, Shoop K.M., 1992, Adaptive characteristics of the magnetostrictive alloy, Terfenol-D, for active vibration control, Journal of Intelligent Material Systems and Structures 3: 245-254.
  2. Reddy J.N., Barbosa J.I., 2000, On vibration suppression of magnetostrictive beams, Smart Materials and Structures 9: 49-58.
  3. Reddy J.N., 1997, Mechanics of Laminated Composite Plates: Theory and Analysis, CRC Press, Boca Raton, FL.
  4. Murty A.V.K., Anjanappa M., Wu Y-F., Bhattacharya B., Bhat M.S., 1998, Vibration suppression of laminated composite beams using embedded magnetostrictive layers, Institution of Engineers (India) Journal of Aerospace 78: 38-44.
  5. Pradhan S.C., Ng T.Y., Lam K.Y., Reddy J.N., 2001, Control of laminated composite plates using magnetostrictive layers, Smart Materials and Structures 10: 1-11.
  6. Kumar J.S., Ganesan N., Swarnamani S., Padmanabhan C., 2004, Active control of simply supported plates with a magnetostrictive layer, Smart Materials and Structures 13(3): 487-492.
  7. Zhang Y., Zhou H., Zhou Y., 2015, Vibration suppression of cantilever laminated composite plate with nonlinear giant magnetostrictive material layers, Acta Mechanica Solida Sinca 28: 50-60.
  8. Subramanian P., 2002, Vibration suppression of symmetric laminated composite beams, Smart Materials and Structures 11(6): 880–885.
  9. Kumar J.S., Ganesan N., Swarnamani S., Padmanabhan C., 2003, Active control of beam with magnetostrictive layer, Computers and Structures 81(13): 1375-1382.
  10. Ghosh D.P., Gopalakrishnan S., 2005, Coupled analysis of composite laminate with embedded magnetostrictive patches, Smart Materials and Structures 14(6): 1462-1473.
  11. Zhou H.M., Zhou Y.H., 2007, Vibration suppression of laminated composite beams using actuators of giant magnetostrictive materials, Smart Materials and Structures 16(1): 198-206.
  12. Murty A.V.K., Anjanappa M., Wu Y-F, 1997, The use magnetostrictive particle actuators for vibration attenuation of flexible beams, Journal of Sound and Vibrations 206(2): 133-149.
  13. Lee S.J., Reddy J.N., Rostam-Abadi F., 2004, Transient analysis of laminated composite plates with embedded smart-material layers, Finite Elements in Analysis and Design 40(5-6): 463-483.
  14. Snowdon J.N., 1968, Vibration and Shock in Damped Mechanical Systems, Wiley, New York.
  15.  Rostam-Abadi F., Reddy J.N., Lee S.J., 2002, Vibration suppression of cross-ply laminated plates with magnetostrictive layers, Proceedings of SECTAM XXI.
  16. Reddy J.N., 2002, Energy Principles and Variational Methods in Applied Mechanics, Wiley, New York.
  17. Hiller M.W., Bryant M.D., Umegaki J., 1989, Attenuation and transformation of vibration through active control of magnetostrictive Terfenol, Journal of Sound and Vibrations 134: 507-519.
  18. Pratt J.R., Flatau A.B., 1995, Development and analysis of self-sensing magnetostrictive actuator design Journal of Intelligent Material Systems and Structures 6: 639-648.
  19. Anjanappa M., Bi J., 1993, Modelling, design and control of embedded Terfenol-D actuator, Smart Structures and Intelligent Systems 1917: 908-918.
  20. Anjanappa M., Bi J., 1994, A theoretical and experimental study of magnetostrictive mini actuators, Smart Materials and Structures 1: 83-91.
  21. Arani A.G., Maraghi Z.K., 2016, A feedback control system for vibration of magnetostrictive plate subjected to follower force using sinusoidal shear deformation theory, Ain Shams Engineering Journal 7(1): 361-369.
  22. Reddy J.N., 1999, On laminated composite plates with integrated sensors and actuators, Engineering Structures 21(7): 568-593.
  23. Koconis D.B., Kollar L.P., Springer G.S., 1994, Shape control of composite plates and shells with embedded actuators I: voltage specified, Journal of Composite Materials 28: 415-458.
  24. Shankar G., Kumar S.K., Mahato P.K., 2017, Vibration analysis and control of smart composite plates with delamination and under hygrothermal environment, Thin-Walled Structures 116: 53-68.
  25. Arani A.G., Maraghi Z.K., Arani H.K., 2017, Vibration control of magnetostrictive plate under multi-physical loads via trigonometric higher order shear deformation theory, Journal of Vibration and Control 23(19): 3057-3070.
  26. Li J., Ma Z., Wang Z., Narita Y., 2016, Random vibration control of laminated composite plates with piezoelectric fiber reinforced composites, Acta Mechanica Solida Sinca 29(3): 316-327.
  27. Zenkour A.M., 2015, Thermal bending of layered composite plates resting on foundations using four-unknown shear and normal deformations theory, Composite Structures 122: 260-270.
  28. Li J., Narita Y., 2013, Vibration suppression for laminated composite plates with arbitrary boundary conditions, Mechanics of Composite Materials 49(5): 519-530.
  29. Song G., Qiao P.Z., Binienda W.K., Zou G.P., 2002, Active vibration damping of composite beam using smart sensors and actuators, Journal of Aerospace Engineering 15(3): 97-103.
  30. Kim H.S., Sohn J.W., Choi S.B., 2011, Vibration control of a cylindrical shell structure using macro fiber composite actuators, Mechanics Based Design of Structures and Machines 39(4): 491-506.
  31. Touratier M., 1991, An efficient standard plate theory, International Journal of Engineering Science 29(8): 901-916.
  32. Zenkour A.M., 2013, Bending analysis of functionally graded sandwich plates using a simple four-unknown shear and normal deformations theory, Journal of Sandwich Structures and Materials 15(6): 629-656.
  33. Zenkour A.M., 2013, A simple four-unknown refined theory for bending analysis of functionally graded plates, Applied Mathematical Modelling 37(20-21): 9041-9051.
  34. Zenkour A.M., 2013, Bending of FGM plates by a simplified four-unknown shear and normal deformations theory, International Journal of Applied Mechanics 5(2): 1350020, 1-15.
  35. Al Khateeb S.A., Zenkour A.M., 2014, A refined four-unknown plate theory for advanced plates resting on elastic foundations in hygrothermal environment, Composite Structures 111(1): 240-248.
  36. Zenkour A.M., 2015, A simplified four-unknown shear and normal deformations theory for bidirectional laminated plates, Sādhanā 40(1): 215-234.
  37. Bouazza M., Zenkour A.M., N. Benseddiq, 2018, Closed-from solutions for thermal buckling analyses of advanced nanoplates according to a hyperbolic four-variable refined theory with small-scale effects, Acta Mechanica 229(5): 2251-2265.
  38. Farajpour A., Yazdi M.R.H., Rastgoo A., Loghmani M., Mohammadi M., 2016, Nonlocal nonlinear plate model for large amplitude vibration of magneto-electro-elastic nanoplates, Composite Structures 140: 323-336.