Clinical studies using a capacitive micromachined ultrasound transducer (CMUT) at a high rang of frequency in ultrasonic imaging have encouraged researchers to delve into all aspects of this new technology. CMUTs are used as energy converters between electrical and mechanical domains. So, in this paper, the equivalent circuit model of a capacitive micromachined ultrasound transducer is analyzed in order to explore the coupling coefficient and frequency of the structure. To produce images with a high resolution, we require a high-frequency ultrasound transducer and that needs a structure like plates in microscale using a microelectromechanical system. Higher order gradient theory by introducing a new term and considering the effects of higher gradients of deformation on strain energy density, explains that the material length scale value to the plate thickness ratio (as in Couple Stress Theory) can play an important role in bending of thin plates, as well as material length scale value to the plate radius (as in nonlocal elasticity theory). However, these effects have not been considered simultaneously in existing classical and non-classical theories that have been used in literature for modeling of CMUTs. Hence, in this study, to predict the mechanical behavior of a microscale system accurately, the static and dynamic properties of a micro circular plate in terms of deflection, pull-in instability, phase plane, frequency response, time history, and mechanical shock wave are studied based on the higher order gradient theory by using Galerkin solution method. A fully clamped micro circular plate which can vibrate and is the main mechanical component of a CMUT is investigated to show the size effect. The developed model is solved numerically using a MATLAB script. The obtained results show that the size effect is indeed important in the mechanical behavior of a CMUT. The investigated model is studied structure is indeed a feasible, simple, general and accurate technique to be applied for devices which vastly are used in medical applications.

在超声成像中使用高频电容式微机械超声换能器 (CMUT) 的临床研究鼓励研究人员深入研究这项新技术的各个方面。CMUT 用作电气和机械领域之间的能量转换器。因此，本文对电容式微机械超声换能器的等效电路模型进行了分析，以探讨该结构的耦合系数和频率。为了产生高分辨率的图像，我们需要一个高频超声换能器，并且需要一个使用微机电系统的微型板结构。高阶梯度理论通过引入一个新术语并考虑更高的变形梯度对应变能密度的影响，解释了材料长度尺度值与板厚比值（如在耦合应力理论中）以及材料长度尺度值与板半径之比（如在非局部弹性理论中）可以在薄板弯曲中发挥重要作用。然而，在文献中用于 CMUT 建模的现有经典和非经典理论中并未同时考虑这些影响。因此，在本研究中，为了准确预测微尺度系统的机械行为，微圆板在挠度、拉入不稳定性、相平面、频率响应、时程和机械冲击波方面的静态和动态特性基于高阶梯度理论，采用伽辽金解法进行研究。研究了可振动且是 CMUT 主要机械部件的完全夹紧的微圆板，以显示尺寸效应。开发的模型使用 MATLAB 脚本进行数值求解。获得的结果表明，尺寸效应在 CMUT 的机械性能中确实很重要。所研究的模型研究结构确实是一种可行的、简单的、通用的和准确的技术，可应用于广泛用于医疗应用的设备。