Advertisement

Vibrations of Laminated Structures Composed of Smart Materials

  • Gennadi I. MikhasevEmail author
  • Holm Altenbach
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 106)

Abstract

In this chapter, we consider thin-walled laminated beams, plates and shells containing layers made of viscoelastic smart materials (VSMs). Generally, from all variety of these materials, the magnetorheological elastomer MRE-1 with properties specified in Chapt. 2 will be used for damping layers or core. To compare the damping capabilities of this material with others, we will study also vibrations of thin-walled laminates assembled from other smart materials (MREs, MRFs and ERCs) described in Chapt. 2.

The basic purpose of this chapter is to analyze free and forced vibrations of thin-walled laminated structures with adaptive physical properties and to show that the application of VSMs embedded between elastic layers allows changing not only the total rigidity, as detected in Chapt. 3, but more the total damping capability of the structure when subjected to the action of an external magnetic or electric field. In particular, it will be shown that the application of a magnetic field may result in significant enhance of the damping capacity of a MRE-based laminated structure and as a consequence, in effective damping of both free and forced vibrations.

The chapter begins with a brief review of the state of the art of research on vibration of MR/ER-based laminated structures (Sect. 5.1). In Sect. 5.2, free and forced vibrations of sandwich beams with MRF or MRE cores are examined. In Sect. 5.3, free and forced vibrations of MRE-based rectangular plates are shortly discussed. Section 5.4 is the main one, it is devoted to free and forced vibrations of laminated and sandwich MRE/ERC-based panels and shells affected by stationary magnetic fields. The detailed analysis of damping capability of different VSMs materials (MREs and ERCs with properties specified in Chapt. 2) incorporated with sandwich panels is given. Finally, in Sects. 5.5 and 5.6, the impact of magnetic field on localized modes and non-stationary vibrations in medium-length MRE-based cylindrical shells is studied. In particular, the effect of soft suppression of travelling localized waves under slowly varying magnetic field is demonstrated.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aguib S, Noura A, Zahloul H, Bossis G, Chevalier Y, Lançon P (2014) Dynamic behavior analysis of a magnetorheological elastomer sandwich plate. Int J Mech Sc 87:118–136CrossRefGoogle Scholar
  2. Aguib S, Nour A, Djedid T, Bossis G, Chikh N (2016) Forced transverse vibration of composite sandwich beam with magnetorheological elastomer core. J Mech Sc Techn 30(1):15–24CrossRefGoogle Scholar
  3. Allahverdizadeh A, Mahjoob M, Eshraghi I, Nasrollahzadeh N (2013) On the vibration behavior of functionally graded electrorheological sandwich beams. Int J Mech Sc 70:130–139CrossRefGoogle Scholar
  4. Avdoshka I, Mikhasev G (2001) Wave packets in a thin cylindrical shell under a non-uniform axial load. J Appl Maths Mechs 65(2):301–309zbMATHCrossRefGoogle Scholar
  5. Berg CD, Evans LF, Kermode PR (1996) Composite structure analysis of a hollow cantilever beam filled with electro-rheological fluid. J Intell Mater Syst Struct 7(5):494–502CrossRefGoogle Scholar
  6. Boczkowska A, Awietjan SF, Pietrzko S, Kurzydlowski KJ (2012) Mechanical properties of magnetorheological elastomers under shear deformation. Comp: Part B 43:636–640CrossRefGoogle Scholar
  7. Botogova M, Mikhasev G (1996) Free vibrations of non-uniformly heated viscoelastic cylindrical shell. Technische Mechanik 16(3):251–256Google Scholar
  8. Chikh N, Nour A, Aguib S, Tawfiq I (2016) Dynamic analysis of the non-linear behavior of a composite sandwich beam with a magnetorheological elastomer core. Acta Mechanica Solida Sinica 29(3):271–283CrossRefGoogle Scholar
  9. Choi W, Xiong Y, Shenoi R (2010) Vibration characteristics of sandwich beams with steel skins and magnetorheological elastomer cores. Advances in Structural Engineering 13(5):837–847CrossRefGoogle Scholar
  10. Choi Y, Sprecher AF, Conrad H (1990) Vibration characteristics of a composite beam containing an electrorheological fluid. J Intell Mater Syst Struct 1(1):91–104CrossRefGoogle Scholar
  11. DiTaranto RA (1965) Theory of vibratory bending for elastic and viscoelastic layered finite-length beams. Trans ASME J Appl Mech 32(4):881–886CrossRefGoogle Scholar
  12. Dwivedy SK, Mahendra N, Sahu KC (2009) Parametric instability regions of a soft and magnetorheological elastomer cored sandwich beam. J Sound Vibr 325(4–5):686–704CrossRefGoogle Scholar
  13. Eshaghi M, Sedaghati R, Rakheja S (2015) The effect of magneto-rheological fluid on vibration suppression capability of adaptive sandwich plates: experimental and finite element analysis. Journal of Intelligent Material Systems and Structures 26(14):1920–1935CrossRefGoogle Scholar
  14. Eshaghi M, Sedaghati R, Rakheja S (2016) Dynamic characteristics and control of magnetorheological/electrorheological sandwich structures: a state-of-the-art review. Journal of Intelligent Material Systems and Structures 27(15):2003–2037CrossRefGoogle Scholar
  15. Gandhi MV, Thompson BS (1992) Smart Materials and Structures. Chapman&Hall, LondonGoogle Scholar
  16. Gandhi MV, Thompson BS, Choi SB (1989) A new generation of innovative ultraadvanced intelligent composite materials featuring electro-rheological fluids: an experimental investigation. J Comp Mater 23(12):1232–1255CrossRefGoogle Scholar
  17. Hu B, Wang D, Xia P, Shi Q (2006) Investigation on the vibration characteristics of a sandwich beam with smart composites - MRF. World Journal of Modelling and Simulation 2(3):201–206Google Scholar
  18. Hu G, Guo M, Li W, Du H, Alici G (2011) Experimental investigation of the vibration characteristics of a magnetorheological elastomer sandwich beam under non-homogeneous small magnetic fields. Smart Materials and Structures 20(12):127,001–1–127,001–7CrossRefGoogle Scholar
  19. Hu G, Guo M, Li W (2012) Analysis of vibration characteristics of magnetorheological elastomer sandwich beam under non-homogeneous magnetic field. Appl Mech Mat 101–102:202–206Google Scholar
  20. Irazu L, Elejabarrieta M (2017) Magneto-dynamic analysis of sandwiches composed of a thin viscoelastic-magnetorheological layer. J Intel Mat Syst Struct 28(20):3106–3114CrossRefGoogle Scholar
  21. Kang Y, Kim J, Choi S (2001) Passive and active damping characteristics of smart electro-rheological composite beams. Smart Materials and Structures 10:724–729CrossRefGoogle Scholar
  22. Korobko EV, Mikhasev GI, Novikova ZA, Zurauski MA (2012) On damping vibrations of three-layered beam containing magnetorheological elastomer. J Intel Mat Syst Struct 23(9):1019–1023CrossRefGoogle Scholar
  23. Kozlowska J, Boczkowska A, Czulak A, Przybyszewski B, Holeczek K, Stanik R, Gude M (2016) Novel MRE/CFRP sandwich structures for adaptive vibration control. Smart Mater Struct 25(3):035,025CrossRefGoogle Scholar
  24. Lai J, Wang K (1996) Parametric contral of structural vibrations via adaptable stiffness dynamic absorbers. Journal of Vibration and Acoustics 118:41–47CrossRefGoogle Scholar
  25. Lara-Prieto V, Parkin R, Jackson M, Silberschmidt V, Kȩsy Z (2010) Vibration characteristics of MR cantilever sandwich beams: experimental study. Smart Mater Struct 19(1):015,005CrossRefGoogle Scholar
  26. Lee CY (1995) Finite element formulation of a sandwich beam with embedded electrorheological fluids. J Intell Mater Syst Struct 6(5):718–728CrossRefGoogle Scholar
  27. Li Y, Li J, Li W (2014) A state-of-the-art review on magnetorheological elastomer devices. Smart Materials and Structures 23(12):123,001–1–123,001–24CrossRefGoogle Scholar
  28. Long M, Hu G, Wang S (2013) Vibration response analysis of MRE cantilever sandwich beam under non-homogeneous magnetic fields. Applied Mechanics and Materials 303–306:49–52Google Scholar
  29. Lukasiewicz S (1979) Local loads in plates and shells. Springer NetherlandszbMATHCrossRefGoogle Scholar
  30. Mead DJ, Markus S (1970) Loss factors and resonant frequencies of encastrè damped sandwich beams. J Sound Vibr 12(1):99–112zbMATHCrossRefGoogle Scholar
  31. Megha S, Kumar N, D’Silva R (2016) Vibration analysis of magnetorheological elastomer sandwich beam under different magnetic fields. J Mech Engng Automat 6:75–80Google Scholar
  32. Mikhasev G (1996a) Localized families of bending waves in a non-circular cylindrical shell with sloping edges. Journal of Applied Mathematics and Mechanics 60(4):629–637MathSciNetzbMATHCrossRefGoogle Scholar
  33. Mikhasev G (1996b) Localized wave forms of motion of an infinite shell of revolution. Journal of Applied Mathematics and Mechanics 60(5):813–820MathSciNetzbMATHCrossRefGoogle Scholar
  34. Mikhasev G (1997) Free and parametric vibrations of cylindrical shells under static and periodic axial loads. Technische Mechanik 17(3):209–216Google Scholar
  35. Mikhasev G (1998) Travelling wave packets in an infinite thin cylindrical shell under internal pressure. Journal of Sound and Vibrations 209(4):543–559zbMATHCrossRefGoogle Scholar
  36. Mikhasev G (2002) Localized families of bending waves in a thin medium-lenght cylindrical shell under pressure. Journal of Sound and Vibrations 253(4):833–857zbMATHCrossRefGoogle Scholar
  37. Mikhasev G (2017) Some problems on localized vibrations and waves in thin shells. In: Altenbach H, Eremeev V (eds) Shell-like Structures. Advanced Theories and Applications, Courses and Lectures, vol 572, Springer, CISM International Center for Mechanical Sciences, pp 259–262Google Scholar
  38. Mikhasev G (2018) Thin laminated cylindrical shells containing magnetorheological elastomers: Buckling and vibrations. In: Pietraszkiewicz W, Witkowski W (eds) Shell Structures: Theory and Applications, vol 4, Taylor&Francis Group, London, pp 259–262Google Scholar
  39. Mikhasev G, Kuntsevich S (1997) Thermoparametric vibrations of noncircular cylindrical shell in nonstationary temperature field. Technische Mechanik 17(2):113–120Google Scholar
  40. Mikhasev G, Kuntsevich S (1999) Parametric vibrations of viscoelastic cylindrical shell under static and periodic axial loads. Technische Mechanik 19(3):187–195Google Scholar
  41. Mikhasev G, Botogova M, Korobko E (2011) Theory of thin adaptive laminated shells based on magnetorheological materials and its application in problems on vibration suppression. In: Altenbach H, Eremeyev V (eds) Shell-like Structures, Springer, Heidelberg, Advanced Structured Materials, vol 15, pp 727–750Google Scholar
  42. Mikhasev G, Mlechka I, Altenbach H (2016) Soft suppression of travalling localized vibrations in medium-length thin sandwich-like cylindrical shells containing magnetorheological layers via nonstationary magnetic field. In: Awrejcewicz J (ed) Dynamical Systems: Theoretical and Experimental Ananlysis, Springer Proceedings in Mathematics&Statistics, vol 182, Springer, Singapore, pp 241–260zbMATHCrossRefGoogle Scholar
  43. Mikhasev GI, Tovstik PE (1990) Stability of conical shells under external pressure. Mech Solids 25(4):106–119Google Scholar
  44. Mikhasev GI, Tovstik PE (2009) Localized Vibrations and Waves in Thin Shells. Asymptotic Methods (in Russ.). FIZMATLIT, MoscowGoogle Scholar
  45. Mikhasev GI, Korobko EV, Novikova ZA (2010) On suppression of vibrations of three-layered beam containing magnetorheological composite (in Russ.). Mechanics of Machines, Mechanisms and Materials 4:49–53Google Scholar
  46. Mikhasev GI, Altenbach H, Korchevskaya EA (2014) On the influence of the magnetic field on the eigenmodes of thin laminated cylindrical shells containing magnetorheological elastomer. Composite Structures 113:186 – 196CrossRefGoogle Scholar
  47. Mohammadi F, Sedaghati R (2012) Nonlinear free vibration analysis of sandwich shell structures with a constrained electrorheological fluid layer. Smart Materials and Structures 21(7):075,035CrossRefGoogle Scholar
  48. Nayak B, Dwivedy SK, Murthy KSRK (2011) Dynamic analysis of magnetorheological elastomer-based sandwich beam with conductive skins under various boundary conditions. J Sound Vibr 325(9):1837–1859CrossRefGoogle Scholar
  49. Nayak B, Dwivedy SK, Murthy KSRK (2012) Multi-frequency excitation of magnetorheological elastomer-based sandwich beam with conductive skins. Int J Non-Linear Mech 47(5):448–460CrossRefGoogle Scholar
  50. Nayak B, Dwivedy SK, Murthy KSRK (2014) Dynamic stability of a rotating sandwich beam with magnetorheological elastomer core. Eur J Mech A/Solids 47:143–155zbMATHCrossRefGoogle Scholar
  51. Oyadiji SO (1996) Applications of electro-rheological fluids for constrained layer damping treatment of structures. J Intell Mater Syst Struct 7(5):541–549CrossRefGoogle Scholar
  52. Phani AS, Venkatraman K (2003) Vibration control of sandwich beams using electrorheological fluids. Mech Syst and Signal Processing 17(5):1083–1095CrossRefGoogle Scholar
  53. Qatu MS, Sullivan RW, Wang W (2010) Recent research advances on the dynamic analysis of composite shells: 2000-2009. Composite Structures 93(1):14–31CrossRefGoogle Scholar
  54. Rajamohan V, Sedaghati R, Rakheja S (2010) Vibration analysis of a multi-layer beam containing magnetorheological fluid. Smart Materials and Structures 19(1):015,013–1–015,013–12CrossRefGoogle Scholar
  55. Shaw J (2000) Hybrid control of cantilevered er sandwich beam for vibration suppression. J Intell Material Systems and Struct, 11(1):26–31CrossRefGoogle Scholar
  56. Skudrzyk E (1968) Simple and Complex Vibratory Systems. Pennsylvania State Univ Pr (Trd), PennsylvaniaGoogle Scholar
  57. de Souza Eloy F, Gomes G, Ancelotti A, da Cunha S, Bombard A, Junqueira D (2018) Experimental dynamic analysis of composite sandwich beams with magnetorheological honeycomb core. Engineering Structures 176(1):231–242Google Scholar
  58. de Souza Eloy F, Gomes G, Ancelotti A, da Cunha S, Bombard A, Junqueira D (2019) A numerical-experimental dynamic analysis of composite sandwich beam with magnetorheological elastomer honeycomb core. Composite Structures 209(1):242–257Google Scholar
  59. Sun Q, Zhou JX, Zhang L (2003) An adaptive beam model and dynamic characteristics of magnetorheological materials. J Sound Vibr 261(3):465–481CrossRefGoogle Scholar
  60. Vemuluri R, Rajamohan V (2016) Dynamic analysis of tapered laminated composite magnetorheological elastomer (MRE) sandwich plates. Smart Materials and Structures 25(3):035,006Google Scholar
  61. Vemuluri R, Rajamohan V, Arumugam A (2018) Dynamic characterization of tapered laminated composite sandwich plates partially treated with magnetorheological elastomer. Journal of Sandwich Structures & Materials 20(3):308–350Google Scholar
  62. Wei K, Meng G, Zhang W (2008) Experimental investigation on vibration characteristics of sandwich beams with magnetorheological elastomers cores. Journal of Central South University of Technology 15(1):239–242CrossRefGoogle Scholar
  63. Yalcintas M, Coulter J (1995) Electrorheological material based adaptive beams subjected to various boundary conditionss. Journal of Intelligent Material Systems and Structures 6:700–717CrossRefGoogle Scholar
  64. Yalcintas M, Coulter JP (1998) Electrorheological material based non-homogeneous adaptive beams. Smart Mater Struct 7(1):128–143CrossRefGoogle Scholar
  65. Yalcintas M, Dai H (1999) Magnetorheological and electrorheological materials in adaptive structures and their performance comparison. Smart Mater Struct 8(5):560–573CrossRefGoogle Scholar
  66. Yalcintas M, Dai H (2004) Vibration suppression capabilities of magnetorheological materials based adaptive structures. Smart Mater Struct 13(1):1–11CrossRefGoogle Scholar
  67. Yeh JY (2011) Vibration and damping analysis of orthotropic cylindrical shells with electrorheological core layer. Aerospace Sc Technology 15(4):293–303CrossRefGoogle Scholar
  68. Yeh JY (2013) Vibration analysis of sandwich rectangular plates with magnetorheological elastomer damping treatment. Smart Mater Struct 22:035,010–035,018CrossRefGoogle Scholar
  69. Yeh JY (2014) Vibration characteristics analysis of orthotropic rectangular sandwich plate with magnetorheological elastomer. Procedia Engng 79:378–385CrossRefGoogle Scholar
  70. Yildirim T, Ghayesh M, Li W, Alici G (2016) Experimental nonlinear dynamics of a geometrically imperfect magneto-rheological elastomer sandwich beam. Composite Structures 138:381–390CrossRefGoogle Scholar
  71. Zeerouni N, Aguib S, Nour A, Djedid T, Nedjar A (2018) Active control of the nonlinear bending behavior of magnetorheological elastomer sandwich beam with magnetic field. Vibroengineering Procedia 18:73–78CrossRefGoogle Scholar
  72. Zhang J, Yildirim T, Alici G, Zhang S, Li W (2018) Experimental nonlinear vibrations of an mre sandwich plate. Smart Structures and Systems 22(1):71–79Google Scholar
  73. Zhou GY, Wang Q (2005) Magnetorheological elastomer-based smart sandwich beams with nonconductive skins. Smart Mater Struct 14(5):1001–1009CrossRefGoogle Scholar
  74. Zhou GY, Wang Q (2006a) Study on the adjustable rigidity of magnetorheological-elastomer-based sandwich beams. Smart Mater Struct 15(1):59–74CrossRefGoogle Scholar
  75. Zhou GY, Wang Q (2006b) Use of magnetorheological elastomer in an adaptive sandwich beam with conductive skins. Part I: magnetoelastic loads in conductive skins. Int J Solids Struct 43(17):5386–5402zbMATHCrossRefGoogle Scholar
  76. Zhou GY, Wang Q (2006c) Use of magnetorheological elastomer in an adaptive sandwich beam with conductive skins. Part II: dynamic properties. Int J Solids Struct 43(17):5403–5420zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Bio- and NanomechanicsBelarusian State UniversityMinskBelarus
  2. 2.Lehrstuhl für Technische MechanikOtto-von-Guericke-Universität MagdeburgMagdeburgGermany

Personalised recommendations