On the Extension of Horn Theory to Non Uniform Visco-Elastic Rods

  • L. M. B. C. Campos
Chapter

Summary

We extend the classical theory of horns, which applies (Eisner 1966, Campos 1986) to the longitudinal vibrations of elastic bars of non-uniform cross-section, to include viscosity effects. The present viscoelastic horn theory is (§1) relevant to the damping of oscillations in tapered rods, and addresses the following topics: (§2) the distinct wave equations for the displacement and strain; (§3) a transformation to account for the change from elastic to viscoelastic material properties; (§4) extension of the duality principle, in the original (Pyle 1965) and two other (Campos 1987) alternative forms; (§5) the only self-dual shape, viz. the exponential tapered bar; (§6) the bars with constant cut-off frequency for the displacement or strain, viz. respectively the catenoidal and inverse catenoidal shapes; (§7) displacement and strain, viz. respectively the sinusoidal and inverse sinusoidal shapes; (§8) the cases of elementary exact solution of the visco-elastic horn equation, viz. those stated in §5–7; (§9) a non-elementary solution, viz. vibrations of visco-elastic rods with power-law cross-section, including simple degenerate cases, e.g. spherical waves in a conical rod; (§10) another non-elementary solution, viz. damping of vibrations of a Gaussian rod, which would have uniform stress in the elastic case (Bies 1962); (§11) plots of the filtering-damping function applying in cases (§5–6) of constant cut-off frequency; (§12) plots of the transparency-damping function applying in cases (§7) when there is no cut-off frequency.

Keywords

Spherical Wave Longitudinal Vibration Level Contour Elastic Case Duality Principle 
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Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • L. M. B. C. Campos
    • 1
  1. 1.Instituto Superior TécnicoLisboa CodexPortugal

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