Advertisement

Effect of Magnetic Field on Free and Forced Vibrations of Laminated Cylindrical Shells Containing Magnetorheological Elastomers

  • Gennadi MikhasevEmail author
  • Ihnat Mlechka
  • Svetlana Maevskaya
Chapter
  • 764 Downloads
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 81)

Abstract

Free and forced vibrations of thin medium-length laminated cylindrical shells and panels assembled from elastic materials and magnetorheological elastomer (MRE) embedded between elastic layers are studied. The equivalent single layer model based on the generalized kinematic hypotheses of Timoshenko is used for the dynamic simulation of laminated shells. The full system of differential equations taking into account transverse shears, written in terms of the generalized displacements, is used to study free vibrations of long sandwich cylindrical shells with the MRE cores. To predict free and forced vibrations of medium-length sandwich cylindrical shells and panels, the simplified equations in terms of the force and displacement functions are utilized. The influence of an external magnetic field on the natural frequencies and logarithmic decrement for the MRE-based sandwich cylindrical shells is analyzed. If an applied magnetic field is nonuniform in the direction perpendicular to the shell axis, the natural modes of the medium-length cylindrical sandwich with the homogeneous MRE core are found in the form of functions decreasing far away from the generatrix at which the real part of the complex shear modulus has a local minimum. The high emphasis is placed on forced vibrations and their suppressions with the help of a magnetic field. Damping of medium-length cylindrical panels with the MRE core subjected to an external vibrational load is studied. The influence of the MRE core thickness, the level of an external magnetic field and the instant time of its application on the damping rate of forced vibrations is examined in details.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

The research leading to these results has received support from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme FP7/2007-2013/under REA grant agreement PIRSES-GA-2013-610547-TAMER. The first and second authors also acknowledge the support from both the ERASMUS+ Programme (Higher Education Mobility Agreement- 2016-2017 between Keele University, UK, and Belarusian State University, Belarus) and State Program of Scientific Investigations in Belarus “Physical Materials Science, New Materials and Technologies” (Assignment N 3.4.01).

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 87:118–136Google Scholar
  2. Banerjee JR, Cheung CW, Morishima R, Perera M, Njuguna J (2007) Free vibration of a threelayered sandwich beam using the dynamic stiffness method and experiment. Int J Solids Struct 44(22):7543 – 7563Google Scholar
  3. Boczkowska A, Awietjan SF, Pietrzko S, Kurzydlowski KJ (2012) Mechanical properties of magnetorheological elastomers under shear deformation. Composites: Part B 43:636–640Google Scholar
  4. Bolotin VV, Novichkov YN (1980) Mechanics of Multilayer Structures (in Russ.). Mashinostroenie, MoscowGoogle Scholar
  5. Carrera E (1999) Multilayered shell theories accounting for layerwise mixed description. Part 1: Governing equations. AIAA J 37(9):1107–1116Google Scholar
  6. Carrera E (2002) Theories and finite elements for multilayered, anisotropic, composite plates and shells. Arch Comput Methods Engng 9(2):87–140Google Scholar
  7. Carrera E (2003) Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking. Arch Comput Methods Engng 10:215–296Google Scholar
  8. Davis LC (1999) Model of magnetorheological elastomers. J Appl Phys 85:3348–3351Google Scholar
  9. Donnell LH (1976) Beams, Plates and Shells. McGraw-Hill Inc, New YorkGoogle Scholar
  10. Ferreira AJM, Carrera E, Cinefra M, Roque CMC (2011) Analysis of laminated doubly-curved shells by a layerwise theory and radial basis functions collocation, accounting for through-the-thickness deformations. Comput Mech 48(1):13–25Google Scholar
  11. Gibson RF (2010) A review of recent research on mechanics of multifunctional composite materials and structures. Comp Struct 92(12):2793–2810Google Scholar
  12. Ginder GM (1996) Rheology controlled by magnetic fields. Encycl Appl Phys 16:487–503Google Scholar
  13. Ginder GM, Schlotter WF, Nichhols ME (2001) Magnetorheological elastomers in tunable vibration absorbers. In: Proc. SPIE. 3985, pp 418–424Google Scholar
  14. Gol’denveiser AL (1961) Theory of Thin Elastic Shells. International Series of Monograph in Aeronautics and Astronautics, Pergamon Press, New YorkGoogle Scholar
  15. Grigolyuk EI, Kulikov GM (1988a) General direction of development of the theory of multilayered shells. Mechanics of Composite Materials 24(2):231–241Google Scholar
  16. Grigolyuk EI, Kulikov GM (1988b) Multilayer Reinforced Shells. Calculation of Pneumatic Tires (in Russ.). Mashinostroenie, MoscowGoogle Scholar
  17. Howson WP, Zare A (2005) Exact dynamic stiffness matrix for flexural vibration of three-layered sandwich beams. J Sound Vibr 282(3):753–767Google Scholar
  18. Hsu TM,Wang JTS (2005) A theory of laminated cylindrical shells consisting of layers of orthotropic laminae. AIAA J 8(12):2141–2146Google Scholar
  19. Jolly MR, Bender JW, Carlson DJ (1999) Properties and applications of comercial magnetorheological fluids. J Intell Mater Syst Struct 10:5–13Google Scholar
  20. Koiter WT (1966) On the nonlinear theory of thin elastic shells. Proc Koninkl Acad Westenschap B 69:1–54Google Scholar
  21. Korobko EV, Mikhasev GI, Novikova ZA, Zurauski MA (2012) On damping vibrations of threelayered beam containing magnetorheological elastomer. J Intell Mater Syst Struct 23(9):1019–1023Google Scholar
  22. Lara-Prieto V, Parkin R, Jackson M, Silberschmidt V, Kesy Z (2010) Vibration characteristics of mr cantilever sandwich beams: experimental study. Smart Mater Struct 19(9):015,005Google Scholar
  23. Mikhasev GI, G BM (2017) Effect of edge shears and diaphragms on buckling of thin laminated medium-length cylindrical shells with low effective shear modulus under external pressure. Acta Mech 228(6):2119–2140Google Scholar
  24. Mikhasev GI, Tovstik PE (2009) Localized Vibrations and Waves in Thin Shells. Asymptotic Methods (in Russ.). FIZMATLIT, MoscowGoogle Scholar
  25. Mikhasev GI, Seeger F, Gabbert U (2001) Comparison of analytical and numerical methods for the analysis of buckling and vibrations of composite shell structures. In: Proc. of “5th Magdeburg Days of Mechanical Engineering”, Otto-von-Guericke-University Magdeburg, Logos, Berlin, pp 175–183Google Scholar
  26. Mikhasev GI, Botogova MG, Korobko EV (2011a) 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
  27. Mikhasev GI, Mlechka I, Altenbach H (2011b) Soft suppression of traveling 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 Analysis, Springer, Switzerland, Springer Proceedings in Mathematics & Statistics, vol 182, pp 241–260Google Scholar
  28. Mikhasev GI, Altenbach H, Korchevskaya EA (2014) On the influence of the magnetic field on the eigenmodes of thin lami-nated cylindrical shells containing magnetorheological elastomer. Compos Struct 113:186–196Google Scholar
  29. Mushtari K, Galimov K (1961) Nonlinear Theory of Thin Elastic Shells. NSF-NASA, Washington Qatu MS (2004) Vibration of laminated shells and plates. Elsevier, San DiegoGoogle Scholar
  30. Qatu MS, Sullivan RW, Wang W (2010) Recent research advances on the dynamic analysis of composite shells: 2000-2009. Comp Struct 93(1):14–31Google Scholar
  31. Reddy JN (2003) Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. CRC Press, Boca RatonGoogle Scholar
  32. Sun Q, Zhou JX, Zhang L (2003) An adaptive beam model and dynamic characteristics of magnetorheological materials. J Sound Vibr 261:465–481Google Scholar
  33. Toorani MH, Lakis AA (2000) General equations of anisotropic plates and shells including transverse shear deformations, rotary inertia and initial curvature effects. J Sound Vibr 237(4):561–615Google Scholar
  34. Tovstik PE, Smirnov AL (2001) Asymptotic Metods in the Buckling Theory of Elastic Shells. World Scientific, SingaporeGoogle Scholar
  35. White JL, Choi DD (2005) Polyolefins: Processing, Structure, Development, and Properties. Carl Hanser Verlag, MunichGoogle Scholar
  36. Wlassow WS (1958) Allgemeine Schalentheorie und ihre Anwendung in der Technik. Akademie-Verlag, BerlinGoogle Scholar
  37. Yeh JY (2011) Vibration and damping analysis of orthotropic cylindrical shells with electrorheological core layer. Aerospace Sc Techn 15(4):293–303Google Scholar
  38. Yeh JY (2013) Vibration analysis of sandwich rectangular plates with magnetorheological elastomer damping treatment. Smart Mater Struct 22(3):035,010Google Scholar
  39. Yeh JY (2014) Vibration characteristics analysis of orthotropic rectangular sandwich plate with magnetorheological elastomer. Proc Engng 79:378–385Google Scholar
  40. Ying ZG, Ni YQ, Ye SQ (2014) Stochastic micro-vibration suppression of a sandwich plate using a magneto-rheological visco-elastomer core. Smart Mater Struct 23(2):025,019Google Scholar
  41. Zhou GY, Wang Q (2005) Magnetorheological elastomer-based smart sandwich beams with nonconductive skins. Smart Mater Struct 14(5):1001–1009Google Scholar
  42. Zhou GY, Wang Q (2006) Use of magnetorheological elastomer in an adaptive sandwich beam with conductive skins. Part II: Dynamic properties. International Journal of Solids and Structures 43(17):5403–5420Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Gennadi Mikhasev
    • 1
    Email author
  • Ihnat Mlechka
    • 1
  • Svetlana Maevskaya
    • 2
  1. 1.Belarusian State UniversityMinskBelarus
  2. 2.Vitebsk State UniversityVitebskBelarus

Personalised recommendations