The active structural component of a capacitive micromachined ultrasonic transducer (CMUT) is the top plate which vibrates under the influence of a time-varying electrostatic force thereby producing ultrasound waves of the desired frequency in the surrounding medium. Analysis of MEMS devices which rely on electrostatic actuation is complicated due to the fact that the structural deformations alter the electrostatic forces, which redistribute and modify the applied loads. Hence, it becomes imperative to consider the electrostatics-structure coupling aspect in the design of these devices. This paper presents an approximate analytical solution for the static deflection of a thin, clamped circular plate caused by electrostatic forces which are inherently nonlinear. Traditionally, finite element simulations using some commercial software such as ANSYS are employed to determine the structural deflections caused by electrostatic forces. Since the structural deformation alters the electrostatic field, a coupled-field simulation is required wherein the electrostatic mesh is continuously updated to coincide with the deflection of the structure. Such simulations are extremely time consuming, in addition to being nontransparent and somewhat hard to implement. We employ the classical thin-plate theory which is adequate when the ratio of the diameter to thickness of the plate is very large, a situation commonly prevalent in many MEMS devices, especially the CMUTs. We solve the thin-plate electrostatic-elastic equation using the Galerkin-weighted residual technique, under the assumption that the deflections are small in comparison to the thickness of the plate. The evaluation of the electrostatic force between the two plates is simplified due to the fact that the electrostatic gap is much smaller than the lateral dimensions of the device. The results obtained are compared to those found from ANSYS simulations and an excellent agreement is observed between the two. The pull-in voltage predicted by our model is close to the value predicted by ANSYS simulations.Index Terms-Capacitive micromachined ultrasonic transducer (CMUT), capacitive sensors, electrostatic forces, MEMS, pull-in voltage, thin plate, ultrasonic transducers.

This paper aims to examine the Darcy–Brinkman flow over a stretching sheet in the presence of frictional heating and porous dissipation. The governing equations are modeled and simplified under boundary layer approximations, which are then transformed into system of self-similar equations using appropriate transformations. The resulting system of nonlinear equations was solved numerically under velocity and thermal slip conditions, by fourth-order Runge–Kutta method and built-in routine bvp4c in Matlab. Under special conditions, the obtained results were compared with the results available in the literature. An excellent agreement was observed. The variation of parameters was studied for different flow quantities of interest and results are presented in the form of tables and graphs.

The present study offers mathematical calculations of the roll-coating procedure lubricated with an upper-convected Maxwell fluid. An incompressible isothermal viscoelastic fluid was considered, with both the roll and the porous web having uniform velocities. By using the lubrication approximation theory, the desired equations of motion for the fluid applied to the porous web were modelled and analyzed. The suction rate on the web and the injection rate at the roll surface were proportionately anticipated. Results for the velocity profile and pressure gradient were received analytically. Fluid parameters of industrial significance (i.e., detachment point, pressure, sheet/roll separating force, power contribution, and coating thickness) were also calculated numerically. A substantial and monotonic increase was witnessed in these quantities with the increase of flow parameters.

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This article describes the development of a mathematical model of forward roll coating of a thin film of a non-Newtonian material when it passes through a small gap between the two counter-rotating rolls. The conservation equations of mass, momentum, and energy in the light of LAT (lubrication approximation theory) are non-dimensionalized and solutions for the velocity profile, flow rate, pressure distribution, pressure, forces, stresses, power input to the roller, and temperature distribution are calculated analytically. It is found that by changing (increasing/decreasing) the value of material parameters, one can really control the engineering parameters like, stress and the most important the coating thickness and is a quick reference for the engineer working in coating industries. Some results are shown graphically. From the present study, it has been established that the material parameter is a device to control flow rate, coating thickness, separation points, and pressure distribution.