Elastic wave radiation from a high frequency finite-length transducer

A simple model of a high frequency piezoelectric transducer affixed to an elastic half-space is analysed. The problem is reformulated as a modified matrix Wiener–Hopf equation, containing a kernel for which there is no known exact factorisation. An approximate factorisation is obtained, and the resulting integral equation is solved by iteration, in limit that the length of the transducer is very much larger than a typical wavelength.