Shear lag solution for tuning ultrasonic piezoelectric wafer active sensors with applications to Lamb wave array imaging

An analytical investigation of the interaction between piezoelectric wafer active sensor (PWAS), guided Lamb waves, and host structure is presented in this paper, supported with application examples. The analytical investigation assumes a PWAS transducer bonded to the upper surface of an isotropic flat plate. Shear lag transfer of tractions and strains is assumed, and an analytical solution using the space-wise Fourier transform is reviewed, closed-form solutions are presented for the case of both ideal bonding (i.e., load transfer mechanism localized at the PWAS boundary) and not ideal bonding (i.e., load transfer mechanism localized close the PWAS boundary). The analytical solutions are used to derive Lamb wave mode tuning curves which indicate that frequencies exist at which the A0 mode or the S0 mode can be either suppressed or enhanced. The paper further shows that the capability to excite only one desired Lamb wave mode is critical for practical structural health monitoring applications such as PWAS phased array technique (e.g., the embedded ultrasonics structural radar, EUSR) and the sparse array imaging. Extensive experimental tests that verify the tuning mechanism and prediction curves are reported. Examples of correctly tuned EUSR images vs. detuned cases illustrate the paramount importance of Lamb wave mode tuning for the success of PWAS based damage detection.