SUMMARY

Acoustic transducer arrays composed of a large number of flexural membranes are found in a diversity of applications such as underwater acoustics, medical therapeutics, and medical imaging. By coupling the vibration of electromechanical layers to the flexural motion of low-impedance membrane structures, these transducers can achieve large bandwidths in immersion without the complexity of matching and backing layers associated with traditional piezoelectric designs. Accurate simulation of array behavior is computationally challenging due to the large number of membranes, complicated by the acoustic interaction between the membranes which has been shown to degrade the frequency and directional characteristics. The acoustic interactions are a result of evanescent standing waves above the fluid-solid interface with resonant behavior related to the geometric layout of the array, the location of the array boundaries, and the individual membrane resonances. Modeling approaches such as finite element analysis (FEA) and boundary element methods (BEM) are computationally difficult due to mesh sizes which become prohibitively large as the number and size of the membranes increase. In this proposed work, we develop a framework for the efficient simulation of fluid-structure coupling for large membrane-type transducer arrays. The simulation is based on a BEM model with improved computational efficiency through the application of a multi-level fast multipole algorithm (ML-FMA). By leveraging truncated multipole expansions for distant membrane pairs, the resulting algorithm improves the theoretical asymptotic space and time complexity from 𝑂(𝑁^2) and 𝑂(4/3𝑁^3), respectively, to 𝑂(𝑁𝑙𝑜𝑔𝑁) in both cases. We verify the model with FEA and direct BEM solutions. The accurate modeling of large transducer arrays is particularly relevant to emerging technologies such as capacitive (CMUTs) and piezoelectric micromachined ultrasonic transducers (PMUTs). We use this framework to investigate the performance of novel large CMUT array designs for near-field and far-field imaging applications in the ultrasonic regime.