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Flutter of a viscoelastic strip

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Abstract

An approximate solution of the problem of flutter of a cantilever clamped viscoelastic strip is obtained under conditions where the flow velocity vector is parallel to the plane of the strip and forms an angle with its edges, which can take arbitrary values. The approximate solution in all the cases is based on the linear combinations of polynomials, which satisfy the boundary conditions. Approximate estimates of the values of the critical flutter speed are obtained by using the Laplace transform in time and a Galerkin expansion for the spatial structures. The nature of the changes in the critical speed with respect to the value of the angle of flow is examined. It is shown that for any non-negative angle of flow with increasing velocity of flow there is an instability in the form of flutter. For negative angles of the flow, either flutter or a cylindrical bending of the strip is observed. Principally, a new mechanical effect is found: there is a whole sector of directions for which increase in flow rate leads to a cylindrical bending.

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Authors and Affiliations

  1. Mechanical and Mathematical Faculty of Moscow State University, Vorob’evy Gory, Moscow, Russia, 119991

    I. A. Kiiko

  2. Moscow State Technical University “MAMI”, 38 Bol’shaya Semenovskaya Street, Moscow, Russia, 105839

    V. V. Pokazeyev

Authors
  1. I. A. Kiiko
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  2. V. V. Pokazeyev
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Correspondence to V. V. Pokazeyev.

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Kiiko, I.A., Pokazeyev, V.V. Flutter of a viscoelastic strip. J Eng Math 78, 213–222 (2013). https://doi.org/10.1007/s10665-012-9534-4

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  • DOI: https://doi.org/10.1007/s10665-012-9534-4

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