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Forced Radial Motions of Nonlinearly Viscoelastic Shells

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Abstract

This paper contains an extensive global treatment of radial motions of compressible nonlinearly viscoelastic cylindrical and spherical shells under time-dependent pressures. It furnishes a variety of conditions on a general class of material properties and on the pressure terms ensuring that there are solutions existing for all times, there are unbounded globally defined solutions, there are solutions that blow up in finite time, and there are solutions having the same period as that of the pressure terms. The shells are described by a geometrically exact 2-dimensional theory in which the shells suffer thickness strains as well as the standard stretching of their base surfaces. Consequently their motions are governed by fourth-order systems of semilinear ordinary differential equations. This work shows that there are major qualitative differences between the nonlinear dynamical behaviors of cylindrical and spherical shells.

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Authors and Affiliations

  1. Department of Mathematics, Institute for Physical Science and Technology, and Institute for Systems Research, University of Maryland, College Park, MD, 20742-4015, USA

    Stuart S. Antman

  2. Dipartimento di Ingegneria Strutturale e Geotecnica, Università di Roma La Sapienza, via Eudossiana 18, 00184, Rome, Italy

    Walter Lacarbonara

Authors
  1. Stuart S. Antman
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  2. Walter Lacarbonara
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Correspondence to Stuart S. Antman.

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Antman, S.S., Lacarbonara, W. Forced Radial Motions of Nonlinearly Viscoelastic Shells. J Elasticity 96, 155–190 (2009). https://doi.org/10.1007/s10659-009-9203-7

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  • DOI: https://doi.org/10.1007/s10659-009-9203-7

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