RESUMEN
Recently, capacitive micromachined ultrasound transducers (CMUTs) with long rectangular membranes have demonstrated performance advantages over conventional piezoelectric transducers; however, modeling these CMUT geometries has been limited to computationally burdensome numerical methods. Improved fast modeling methods, such as equivalent circuit models, could help achieve designs with even better performance. The primary obstacle in developing such methods is the lack of tractable methods for computing the radiation impedance of clamped rectangular radiators. This paper presents a method that approximates the velocity profile using a polynomial shape model to rapidly and accurately estimate radiation impedance. The validity of the approximate velocity profile and corresponding radiation impedance calculation was assessed using finite element simulations for a variety of membrane aspect ratios and bias voltages. Our method was evaluated for rectangular radiators with width:length ratios from 1:1 up to 1:25. At all aspect ratios, the radiation resistance was closely modeled. However, when calculating the radiation reactance, our initial approach was only accurate for low aspect ratios. This motivated us to consider an alternative shape model for high aspect ratios, which was more accurate when compared with FEM. To facilitate the development of future rectangular CMUTs, we provide a MATLAB script that quickly calculates radiation impedance using both methods.
RESUMEN
Nonlinear ultrasound has been proven to be a useful nondestructive testing tool for micro-damage inspection of materials and structures operating in harsh environment. When measuring the nonlinear second harmonic wave in a solid specimen in the pulse-echo (PE) testing mode, the stress-free boundary characteristics brings the received second harmonic component close to zero. Therefore, the PE method has never been employed to measure the so-called "nonlinear parameter (ß)", which is used to quantify the degree of micro-damage. When there are stress-free boundaries, a focused beam is known to improve the PE reception of the second harmonic wave, so phased-array (PA) transducers can be used to generate the focused beam. For the practical application of PE nonlinear ultrasonic testing, however, it is necessary to develop a new type of PA transducer that is completely different from conventional ones. In this paper, we propose a new annular PA transducer capable of measuring ß with improved second harmonic reception in the PE mode. Basically, the annular PA transducer (APAT) consists of four external ring transmitters and an internal disk receiver at the center. The focused beam properties of the transducers are analyzed using a nonlinear sound beam model which incorporates the effects of beam diffraction, material attenuation, and boundary reflection. The optimal design of the APAT is performed in terms of the maximum second harmonic reception and the total correction close to one, and the results are presented in detail.