Generation and propagation of elastic waves on a pipe by open-shell transducers

This paper deals with the generation and propagation of elastic waves on an empty pipe and on a water-filled pipe by open-shell transducers theoretically, numerically, and experimentally. The dispersion equations relating wave speed to frequency were derived by using the cylindrical shell theory. The theoretical analysis was verified by comparing the calculated dispersion curves with the frequency wavenumber spectrums obtained from the finite-element analysis and by comparing the calculated wave speeds with the results measured by using open-shell transducers as transmitters and receivers. The finite-element analysis revealed that the waves of only even numbered wave modes were generated by the open-shell transducers symmetrically located along the circumference of the pipe and that the axisymmetric wave propagates faster than non-axisymmetric waves