A fast computational method for modeling and simulation of large projector arrays is presented. The method is based on the array equations that account for the acoustic interaction among the projector elements as well as the individual characteristics of each projector. Unlike the existing solution method in which the acoustic interaction must be known a priori in the form of interaction impedance matrix Z, the present method seeks the solution of modified array equations through iterations without explicitly evaluating the Z matrix. This significantly speeds up the analysis of complex arrays with surrounding structures, where the evaluation of the Z matrix may require a large number of time-consuming finite element computations. The method is compared with the traditional Z-matrix method for the case of a cylindrical array of 72 × 8 Tonpilz transducers. For the same level of accuracy, the iterative method is shown to be up to 2 orders-of-magnitude faster than the Z-matrix method. The method can be used for rapid design and analysis of active sonar arrays and medical ultrasonic transducers, often made of hundreds and even thousands of elements.

Parametric array (PA) loudspeakers generate directional audible sound via the PA effect, which can make private listening possible. The practical applications of PA loudspeakers include information technology devices that require large power efficiency transducers with a wide frequency bandwidth. Piezoelectric micromachined ultrasonic transducers (PMUTs) are compact and efficient units for PA sources [Je, Lee, and Moon, Ultrasonics 53, 1124-1134 (2013)]. This study investigated the use of an array of PMUTs to make a PA loudspeaker with high power efficiency and wide bandwidth. The achievable maximum radiation bandwidth of the driver was calculated, and an array of PMUTs with two distinct resonance frequencies (f1 = 100 kHz, f2 = 110 kHz) was designed. Out-of-phase driving was used with the dual-resonance transducer array to increase the bandwidth. The fabricated PMUT array exhibited an efficiency of up to 71%, together with a ±3-dB bandwidth of 17 kHz for directly radiated primary waves, and 19.5 kHz (500 Hz to 20 kHz) for the difference frequency waves (with equalization).

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The Helmholtz-Kirchhoff integral (HKI) for the radiation problem from a finite source with a vibrating surface is a method of calculating the acoustic pressure at any position in the three-dimensional space using the velocity conditions of the radiating surface. Previous studies predicted the acoustic pressure from the radiator based on the HKI. However, the acoustic pressure should be evaluated first on the radiation surface in order to calculate the acoustic pressure in the space. Nonetheless, it is difficult to evaluate the acoustic pressure on the radiation surface accurately if there are non-smooth points. Because the exact HKI is not easily found to be applicable for the evaluation, in this study, we investigated the HKI from the beginning. Through the process of deriving the formula, we proposed the form of the HKI that can be used for calculating the acoustic pressure at both smooth and non-smooth points of the radiation surface. The proposed formula is also proved mathematically. As a result, the acoustic pressures calculated by the proposed formula are compared to those using a FEM. The results yield that the overall relative errors are less than 2% even on the radiator surface including vertices. [Work supported by Samsung Display Corporation.]

A free-flooded ring (FFR) transducer can generate low-frequency sound in a small device and has a wide operating frequency bandwidth. Many studies have been performed that can predict the characteristics of an FFR transducer using analytical techniques and an equivalent circuit model (ECM), and methods to predict properties using numerical simulations have recently been developed. However, an ECM, a type of lumped parameter model (LPM), is still widely used to interpret the properties of such transducers in the design process. In this study, the authors investigated an ECM of an FFR transducer. The ECM consists of three parts: the piezoelectric ring, the cylindrical cavity, and the radiation load. Moreover, it can be included readily in a circuit to drive an FFR transducer. Additionally, an LPM was proposed, considering the mutual radiation loads, to improve the accuracy of the model. Each model was tested in comparisons with the finite element method; it was confirmed that an LPM could predict the properties of an FFR transducer with much better accuracy than an ECM. The LPM developed can save much time in designing FFR transducers.