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Shell-like Structures pp 149–209Cite as

Some Problems on Localized Vibrations and Waves in Thin Shells

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Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 572))

Abstract

Some problems on localized vibrations and waves in thin isotropic and laminated cylindrical shells are considered in this Chapter. To study vibrations of thin laminated shells, the equivalent single layer model for the whole packet of a sandwich is proposed. The basic goal of this paper is to demonstrate two asymptotic approaches for studying localized vibrations of thin shells. At first, the asymptotic method of Tovstik is applied to study free stationary vibrations localized in a neighbourhood of a fixed generatrix or parallel called the weakest one. As an interesting example, free localized vibrations of a laminated cylindrical shell containing polarized magnetorheological elastomer and affected by an external magnetic field are analyzed. Then the asymptotic method for investigation of running localized waves (wave packets) in thin shells is stated. The solution of governing equations is constructed in the form of a superposition of wave packets running in a thin non-circular prestressed cylinder in the circumferential direction. The influence of non-uniform stationary and dynamic pressures on running wave packets is briefly studied.

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Authors and Affiliations

  1. Belarusian State University, Minsk, Belarus

    Gennadi Mikhasev

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  1. Gennadi Mikhasev
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Correspondence to Gennadi Mikhasev .

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Editors and Affiliations

  1. Faculty of Mechanical Engineering, Otto-von-Guericke-University Magdeburg, Magdeburg, Germany

    Holm Altenbach

  2. Technical Mechanics, Otto-von-Guericke-University Magdeburg, Magdeburg, Germany

    Victor Eremeyev

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Mikhasev, G. (2017). Some Problems on Localized Vibrations and Waves in Thin Shells. In: Altenbach, H., Eremeyev, V. (eds) Shell-like Structures. CISM International Centre for Mechanical Sciences, vol 572. Springer, Cham. https://doi.org/10.1007/978-3-319-42277-0_4

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  • DOI: https://doi.org/10.1007/978-3-319-42277-0_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42275-6

  • Online ISBN: 978-3-319-42277-0

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