David Taylor Res. Ctr., Annapolis, MD 21402
The temporal response of a long (~100-ft) pipe is calculated and measured. The calculation is based on a formalism that describes a complex of coupled one-dimensional dynamic systems [J. Acoust. Soc. Am. 89, 1--9 (1991)]. The flexural, longitudinal, and torsional waves in the pipe are considered as separate systems in the model and interact only at discontinuities; the ends of the pipe in this case. In the experiment, the pipe is subjected to an impact that excites all three types of propagation and the response is measured by an accelerometer mounted on the outside of the pipe, or, in the case when the pipe contains water, by a hydrophone inside the pipe. In the model, the excitation is simulated by forming initial wave packets in each of the three systems, and the relative amplitudes of the initial excitations in the systems are adjustable parameters. Other adjustable parameters include the reflection coefficients of a particular wave type, the coupling between wave types at the ends of the pipe, and the wave speeds and losses in the systems. The calculated response versus time is assessed in the flexural wave system (assuming that this is the only wave type which the accelerometer responds to), or in the fluid system when present, and compared with the experimental data and the model parameters are adjusted for an optimal fit. Once the model parameters are optimized, the adjustable parameters can be deduced and the model can be extended to more complicated situations. The noninteraction of the mode types propagating in the systems is a basic premise in the model and is violated in the fluid filled case since the fluid wave is strongly coupled to the structural waves; nevertheless, the model shows qualitative agreement in this case and good agreement for the air-filled case. The model also includes the dispersive nature of the flexural wave propagation and demonstrates the complexity in the response which develops over time but which ultimately simplifies into a model pattern.