Contribution of Fundamental Lamb Wave Modes to the Voltage Signal Output of a Piezoelectric Transducer

Abstract

Structural Health Monitoring (SHM) systems are a very useful tool to know in real time the actual condition of a structure. Most of these systems are based on the generation, propagation, reception and interpretation of elastic waves in complex structures such as those used in aeronautics. An exemplary SHM system, like for example PAMELA SHMâ„¢ system has a wide range of potential applications, from structural integrity, impact detection, to stress, vibration or deformation distribution mappings. These specific applications have common difficulties associated, mainly related with the output signal analysis and interpretation. The signal analysis is a complex task due to dispersive and multimode characteristics of ultrasonic Lamb waves in elastic thin plate-like structures which makes the interpretation of inspection results extremely difficult. The main objective of the current work is to obtain a numerical model able to convert a displacement on the surface of a structure into a voltage signal received by the transducer and vice versa, as well as to quantify the contribution of the symmetric- S0 and antisymmetric-A0 zero order modes of a Lamb wave to the total voltage output obtained in a piezoelectric transducer. The proposed method is based on the conversion of the displacement history in a point on the surface of a structure into a voltage signal, by means of the piezoelectric constitutive equations that define the electro-mechanical coupling behavior. In the first place, a measurement of the displacement field is obtained by means of numerical simulation or experimental based methods. The voltage signal for a given point in the structure (for example in the position of a virtual transducer) is rebuild from those measurements and the electro-mechanical coupling relationship. Finally, the voltage signal is decomposed, based on the physical interpretation of the extensional Lamb wave mode S0 and the flexural mode A0, into the S0 and A0 mode contributions.