Study of radial bending vibration and excitation of piezoelectric rings

Piezoelectric ring transducer is one of the most common underwater transducers, and its radial vibration,bending vibration in-plane and out-of-plane have been widely studied. However, the current research onthe bending vibration in the plane of the ring is insufficient, although it may have a noticeable influence onthe applicability of the underwater transducers. In this study, mechanical analysis and related mathematicalcalculations of the bending vibrations in the plane are carried out by using the thin-shell theory. Herein,the following three aspects are studied: 1) free vibration theory solution, 2) forced vibration: multi-order modalexcitation theory, and 3) related finite element calculations and experimental verification. In this study, thebending vibration equations under electrical short and electric open condition are derived, and the multi-orderresonance frequency prediction formulas and shape functions for both conditions are obtained by analyticalsolution and function fitting. Using the finite element method, the influence of piezoelectric effect and the rangeof applicability of these two electrical conditions are analyzed. The non-homogeneous equations under forcedvibration are solved. By utilizing the orthogonal completeness of the vibration mode function, an integraltransformation with the vibration mode function can be defined as the basis vector, so that the equation issolved in a simple positive space, and the results reveal the relationship between the coefficients of the modes ofdifferent orders and the voltage distribution. By modal theory, the effects of electrical excitation conditions onthe multistep bending vibration modes are investigated, and effective methods such as unimodal excitation,partial excitation and single-ended excitation acting on several different target modes are obtained. Theproposed piezoelectric ring unimodal excitation and single-ended excitation methods successfully excite thetarget modes in the experiments: the unimodal excited ring excites only one of its corresponding bending modes,while the single-ended excitation method excites all the bending modes of the first five orders, and its modalstrength characteristics are in accordance with the theoretical predictions. This study involves finite elementsimulation, experimental and theoretical comparative verification, which are in good agreement. The relevantconclusions can provide a theoretical basis for identifying the vibration modes of piezoelectric ring and the finetuning of modal excitation