Radial modes of laterally stiffened piezoelectric disc transducers for ultrasonic collimated beam generation

We numerically investigate the resonance and vibration characteristics of radial modes of laterally stiffened piezoelectric disc transducers. Lateral stiffening is modelled using a spring and vibration characteristics of the piezo-disc are investigated with increasing lateral stiffness. It is found that the resonant frequency response of the radial modes follows an asymptotic behaviour approaching that of a clamped disc with increasing lateral stiffness. The radial mode vibration pattern of the discs is also found to be affected by lateral stiffness. While the vibration pattern of a free disc corresponds to a Bessel function, laterally stiffened discs show edge-effects where they depart from the Bessel-like behaviour. In addition, a fully clamped piezo-disc is found to have an extra side-lobe when compared to a free disc. Ultrasonic beam profiles generated from radial modes of laterally stiffened discs are numerically investigated. It is found that the free piezo-disc generates a Bessel beam that has multiple side-lobes. Increasing the lateral stiffness results in a significant reduction of side-lobes in the beam profile. This technique of generating a collimated beam with side-lobe reduction finds significant applications in imaging through concrete, drilling mud, and other highly attenuating materials.