High resolution analysis of axisymmetric wave modes in cylindrical structure

The relation between frequency and complex wavenumber of guided, axisymmetric waves in circular cylindrical structures is investigated theoretically and experimentally. In particular, a theoretical model is derived to calculate the complex dispersion relation of axisymmetric wave modes in a thin-walled elastic shell containing a viscoelastic medium. The influence of the viscoelastic material properties on the dynamic response of the shell is discussed numerically and the results are confirmed by an extended series of experiments. New dynamic metrology is developed to measure complex dispersion relations, i.e. complex phase velocities as a function of frequency, in a range between 1 kHz and 2 MHz for up to 40 travelling wave modes. The phenomenon of 'backward wave propagation' is clearly measured. Excellent agreement between numerical and experimental results was found over a wide parameter range.