Energy trapping of circumferential shear horizontal wave in a hollow cylinder

Abstract

This paper describes energy trapping of circumferential shear horizontal wave (C-SH wave) at a circumferential inner groove of a hollow cylinder. We first derive exact solutions of resonant frequencies of the C-SH wave from the classical theory of guided waves propagating in a hollow cylinder and approximated solutions from the relationship between wavelength of the C-SH wave and length of circumferential path of the hollow cylinder. Next, we examined the energy trapping conditions using the dispersion curves of a guided wave propagating in the longitudinal direction of a hollow cylinder, and showed that C-SH waves trap energy when the hollow cylinder has a circumferential groove on the inner surface, rather than on the outer surface. The energy trapping at an inner groove was confirmed for the C-SH wave with the circumferential order of n = 6 using eigen frequency analysis of finite element method and experiments with electromagnetic transducers. Moreover, when the energy trap mode was used to determine the change in resonance frequency for glycerin solution of different concentrations, it was confirmed that the resonance frequency decreased monotonically as the concentration increased, indicating the possibility of using the energy trap mode as a QCM-like sensor.