Finite element analysis of phased plano-concave multi-layer transducers

Phased multi-layer transducers offer the potential for yielding very high (multiple octave) usable bandwidth. The null normally encountered at the second harmonic is avoided and replaced with a resonant peak. However, the resulting spectrum exhibits a number of ´bumps´ that result in an undesirable ´tail´ in the time-domain impulse response. In this paper we present new results obtained using finite element analysis of modified multi-layer transducers in which the elements have diverse thickness so as to smooth out the associated spectral response. In this example we use dual-layer plano-concave elements. 3D finite element analysis is well suited to these complex 3D devices since they can include finite dimension effects in all three directions and properly account for the irregular geometry. Fortunately both the PZFlex finite element analysis technique and the materials of interest (PZT-5H type material) are very well characterized at this time and thereby enable reliable, accurate virtual design and test. In this paper we explore some of the design variables (e.g. maximum ratio of the thickness dimensions along the PZT bar element) and determine the practical extent of achievable bandwidth consistent with a smooth spectral characteristic, relatively uniform thickness vibrational motion and a lack of spurious lateral wave activity