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Dispersion curves of fluid-filled elastic-tubes are used for non-destructive measurement of material acoustic properties. The underlying physics leads to a singular numerical procedure when several modes or long-wavelength scenarios take part in the tube dynamics. The literature describes several methods to identify dispersion curves that require a large ratio of samples per length. Described is a method to enrich the amount of available information of an otherwise ill-posed problem, by multiple boundary phase perturbations at each excitation frequency. The method uses two actuators, one at either end of the waveguide to produce different relative phases, followed by a nonlinear model fitting procedure. Presented are a model-based derivation and experimental verification of the proposed approach on an air-filled elastic-tube. The latter shows the capability of the method to recover the dispersion curves even for very weak structural-acoustic coupling and at low frequencies. The portrayed scheme can be applied on various waveguides by using two actuators and only a single sensor, and hence makes dispersion curve estimation realistic in formerly inaccessible cases.

The problem in the creation of traveling waves is approached here from an unconventional angle. The formulation makes use of normal vibration modes, which are standing waves, to express both traveling waves and the required force distribution. It is shown that a localized force is required at any discontinuity along the structure to absorb reflected waves. This convention is demonstrated for one- and two-dimensional structures modeled as continua, and as discretized numerical approximation of the mass and stiffness matrices. Harmonic vibrations can be characterized as standing or traveling waves or as a combination of both. By applying forces that have been specially designed for the purpose, the vibratory response can become a pure traveling wave. The force distribution is important for the design of ultrasonic motors and in control applications, attempting to absorb and create outgoing and incoming waves.

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