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Piezoelectric transducers are commonly used to excite waves in elastic waveguides such as pipes, rock bolts and rails.
While it is possible to simulate the operation of these transducers attached to the waveguide, in the time domain, using
conventional finite element methods available in commercial software, these models tend to be very large. An
alternative method is to use specially formulated waveguide finite elements (sometimes called Semi-Analytical Finite
Elements). Models using these elements require only a two-dimensional finite element mesh of the cross-section of the
waveguide. The waveguide finite element model was combined with a conventional 3-D finite element model of the
piezoelectric transducer to compute the frequency response of the waveguide. However, it is difficult to experimentally
verify such a frequency domain model. Experiments are usually conducted by exciting a transducer, attached to the
waveguide, with a short time signal such as a tone-burst and measuring the response at a position along the waveguide
before reflections from the ends of the waveguide are encountered. The measured signals are a combination of all the
modes that are excited in the waveguide and separating the individual modes of wave propagation is difficult if there are
numerous modes present. Instead of converting the measured signals to the frequency domain we transform the modeled
frequency responses to time domain signals in order to verify the models against experiment. The frequency response
was computed at many frequency points and multiplied by the frequency spectrum of the excitation signal, before an
inverse Fourier transform was used to transform from the frequency domain to the time domain. The time response of a
rail, excited by a rectangular piezoelectric ceramic patch, was computed and found to compare favorably with
measurements performed using a laser vibrometer. By using this approach it is possible to determine which modes of
propagation dominate the response and to predict the signals that would be obtained at large distances, which cannot be
measured in the lab, and would be computationally infeasible using conventional finite element modeling.
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