| Long-range monitoring of rails by guided wave ultrasound requires the development of transducers that can effectively and selectively excite modes of wave propagation. A method for modeling the excitation of guided waves in a rail by piezoelectric transducers was developed. The method combines a 2-D semi-analytical finite element model of the rail with a 3-D finite element model of the piezoelectric transducer. The model computes the response of the modes of wave propagation and also the time domain responses at points on the rail. Time domain measurements verified the accuracy of the model. An algorithm for extracting the responses of the modes of propagation from measured signals was demonstrated. The method uses wavenumber and mode shape information from the model of the rail and measured point responses to estimate the modal responses. |