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

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


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.


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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).


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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

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