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Radial Oscillations of Cylindrical and Spherical Shells

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Mathematical Models with Singularities

Part of the book series: Atlantis Briefs in Differential Equations ((ABDE,volume 1))

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Abstract

In this chapter, we study the radial vibrations of a cylindrical or spherical shell made of a hyperelastic, homogeneous, isotropic and incompressible material subjected to time-periodic pressures exerted at the inner and outer surface of the shell, respectively.

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Notes

  1. 1.

    Rubber is the canonical example of material close to this ideal setting. From a physical point of view, rubber is simply a network of polymeric chains. Such chains are composed by linked monomers, and the nature of such links conforms the particular elastic properties of the material.

  2. 2.

    Precisely, the regularity condition on \(h\) is only used to prove the continuability of the solutions. In ny opinion, it may be a technical assumption.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Granada, Granada, Spain

    Pedro J. Torres

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  1. Pedro J. Torres
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Correspondence to Pedro J. Torres .

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Torres, P.J. (2015). Radial Oscillations of Cylindrical and Spherical Shells. In: Mathematical Models with Singularities. Atlantis Briefs in Differential Equations, vol 1. Atlantis Press, Paris. https://doi.org/10.2991/978-94-6239-106-2_10

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