The response of rectangular piezoelectric sensors to Rayleigh and Lamb ultrasonic waves

A fundamental understanding of the response of piezoelectric transducer patches to ultrasonic waves is of increasing interest to the field of structural health monitoring. While analytical solutions exist on the interaction of a piezoelectric actuator with the generated Lamb waves, the behavior of a piezoelectric sensor has only been examined for the limited case of a piezo-actuated Lamb wave in a pitch-catch configuration. This paper focuses on the fundamental response of surface-bonded piezoelectric sensors to ultrasonic waves. The response to both Rayleigh waves and Lamb waves is examined, starting with harmonic excitation fields and moving to broadband and narrowband excitation fields. General oblique incidence of the wave on rectangular sensors is treated first; parallel incidence is then derived as a particular case. The solutions are developed analytically for the harmonic and the narrowband excitations, and semianalytically for the broadband excitation. The results obtained can be used to design ultrasonic sensors that are either particularly sensitive to a given mode or possess unique directivity behavior which, in turn, can greatly simplify current algorithms for damage detection and localization.