Mechanical analysis of a tunable capacitive ultrasound transducer using higher order gradient theory

•Mathematical modeling of a capacitive ultrasound transducer (CMUT) using higher order gradient theory is presented.•The equivalent circuit model of a CMUT is presented.•The coupling coefficient of a CMUT is investigated.•The frequency responses, the static and dynamic pull-in voltage of the CMUT are studied. 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.