Bandwidth extension of the Tonpilz transducer using high-order longitudinal vibrations

Tonpilz transducers mainly work near the first-order longitudinal resonance. Until now, the cognition, research, and application of third-order resonance and above are still inadequate. By coupling the first-order resonance with other high-order resonances, it is possible to extend the bandwidth of the Tonpilz transducer to more than two octaves. Three difficulties hinder the achievement of the ultra-wideband, including how to activate consecutive high-order resonances, how to eliminate the response notches between resonances, and how to control the response values of resonances to reduce band fluctuation. This paper addresses these key issues. The results show that the number, position, length, and applied voltage of the drive-stack all significantly affect the band. We finally propose a drive-stack design principle that can activate the first four longitudinal resonances with close response values to be coupled to form the ultra-wideband. When applying this principle to the Tonpilz transducer, many variables need to be optimized. To solve this problem, an efficient and accurate optimization technology is proposed, consisting of simulated annealing initial optimization and finite element re-optimization, through which an ultra-wideband covering the frequency range of 19.5-90 kHz is obtained, verifying the effectiveness of the proposed principle. The designed transducer has three drive-stacks, and the band contains four longitudinal resonances.