Date of Award


Level of Access Assigned by Author

Open-Access Dissertation

Degree Name

Doctor of Philosophy (PhD)


Mechanical Engineering


Michael L. Peterson

Second Committee Member

Donald A. Grant

Third Committee Member

Richard C. Hill


Solid circular cylinders as wavaguides for the propagation of longitudinal elastic waves are used pximarily as buffer rods in high temperature nondestructive evaluation (NDE), and are also found in the split Hopkinson pressure bar (SHPB). Experiments are typically designed so that only the nondispersive range of the first mode propagates. Design constraints sometimes require larger wavcguides and higher ficquencies that propagate multiple dispersive modes, which can add considerable con1plexity to the signal. This thesis presents an analytical modcl for multiple mode wave propagation in a finite solid cylindrical waveguide as a means of interpreting the complex signals and possibly removing the complexity. The model uses the phase velocities and normal stresses of the axially symmetric modes calculated by the Pochhammer-Chree equations to calculate atransfer hnction for each of the propagating modes. The sum of the tranxfcr functions of the propag:,ting modes is the transfer function of the waveguide, which can be used to predict the change of a signal in the waveguide. The ability of the model to accurately capture the general physics of multiple mode wave propagation is demonstrated in the time, frequency and joint time-frequency domain. In the time-reverral domain the calculated dispersed signal for a dispersive multi-mode waveguide is shown to producc a s i p a l with compact support in the time domain. A range of diameter to wavelength ratios is considered for these comparisons, which show the limitations of the model for wavelengths less than th.e raditls. The transfer functions generated by the model indicate which modes are dominant over a particular range of frequencies and which modes have a much smaller magnitude. The transfer functions further indicate that broadband signals are composed of multiple modes. It is found that observed trailing pulses contain energy from multiple propagating modes, and it is the superposition of the modes that creates the trailing pulses. The information from the transfer functions is also used to show the conditions for a sufficiently narrow band signal to excite a single higher order mode with little dispersion.