The effect of the free edge of a semi-infinite elastic cylinder with circular cross section is considered. It is shown that there exists a complex resonance frequency associated with an axially symmetric localized vibration near the free edge for every value of the Poisson ratio v. For two particular values of v, v = 0 and v = 0.1267, the imaginary part of the complex resonance frequency is zero which corresponds to a trapped mode of the semi-infinite rod. This resonance is also shown to be associated with two eigenfrequencies of the finite length cylinder.
ShawEAG. On the resonant vibrations of thick barium titanate disks. J Acoust Soc Am1956; 28: 38–50.
2.
TorvikPJ. Reflection of wave trains in semi-infinite plates. J Acoust Soc Am1967; 41: 346–353.
3.
AuldBATsaoEM. A variational analysis of edge resonance in a semi-infinite plate. IEEE Trans Son Ultrason1977; 24: 317–326.
4.
KoshibaMKarakidaSSuzukiM. Finite-element analysis of edge resonance in a semi-infinite plate. Electron Lett1983; 19, 256–257.
5.
GregoryRDGladwellI. The reflection of a symmetric Rayleigh–Lamb wave at the fixed or free edge of a plate. J Elasticity1983; 13: 185–206.
6.
Le ClezioEPredoiMVCastaingsMHostenBRousseauM. Numerical predictions and experiments on the free-plate edge mode. Ultrasonics2003; 41: 25–40.
7.
Wilkie-ChancelierNDufloHTinelADuclosJ. Numerical description of the edge mode at the beveled extremity of a plate. J Acoust Soc Am2005; 117: 194–199.
8.
RoitbergIVassilievDWeidlT. Edge resonance in an elastic semi-strip. Q J Mech Appl Math1998; 51: 1–13.
9.
FlaxLDragonetteLRÜberallH. Theory of elastic resonance excitation by sound scattering. J Acoust Soc Am1978; 63: 723–731.
10.
FlaxLGaunaurdGÜberallH. Theory of resonance scattering. In: MasonWPThurstonRN (eds) Physical acoustics, Vol. XV. New York: Academic, 1981, pp. 191–294.
