Effect of subdicing on the dispersion and resonance behavior of elastic guided waves in 1D array ultrasound transducers

Abstract

1D array ultrasound subdicing is a common fabrication practice to avoid the presence of lateral modes near the center frequency of the transducer. The objective of this study is to theoretically analyze the effect of subdicing depth and width on the dispersion and resonance behavior of elastic guided wave propagation in 1D array transducers. The transducer is modeled as a periodic structure with the representative cell composed of one element. A semi-analytical finite-element (SAFE) method is derived to obtain the dispersion curves, group velocity and resonance mode shapes of a piezoelectric structure with arbitrary cross-section and periodic boundary conditions. Results indicate that resonant modes can occur at cutoff frequencies (wavenumber k = 0), where the phase velocity is infinite. Moreover, another interesting resonance behavior at zero-group-velocity (ZGV) points (wavenumber k ≠ 0) is observed where the phase velocity is finite. Theoretical results show that subdicing increases the number of waveguide modes, lowers the cut-off frequencies, increases the number of ZGV points and lowers the group velocities for flexural and extensional modes. Lower values of subdicing depth tend to increase the cut-off frequencies, but subdicing width has a minor effect on the dispersion curves. These important changes of the dispersion behavior are likely to influence the resonance characteristics and the bandwidth of the transducer. The analysis presented in this study provides a useful tool to optimize the design of 1D array ultrasound transducers and to gain better understanding of the complicated acoustic behavior of 1D array ultrasound transducers