Investigation of Squeeze Film Effect on Dynamic Characteristics of Electrically Actuated Fully Clamped Micro-Beam

In this article a clamped-clamped type micro beam has been considered in an interaction with a thin film of air underneath the beam and its dynamic characteristics such as natural frequency and damping ratio have been discussed. Most important priority is to solve the dynamic motion of the beam due to electrical actuation considering pressure distribution of air within the gap. So a distributed model for both flexural deflection and pressure distribution has bean considered using Euler-Bernoulli beam model and ideal gas Reynolds equation. In that way a set of coupled nonlinear partial differential equations have been obtained that must be solved simultaneously. Because there is no analytic solution for any of equations some simplifications have been considered to make both of them linear. Assuming the actuation voltage to be compound of a finite DC component and an infinitesimally low AC component the quasi static conditions took place and the equations became linear. Application of Galerkin based reduced order model mass, spring and damping matrixes has been found so root locus, frequency and damping ratio diagrams of the system have been plotted and discussed in terms of some defined dimensionless parameters that are very reasonable and useful in design of MEMS

Pull-in Phenomena and Dynamic Response of a Capacitive Nano-beam Switch

In this paper static and dynamic responses of a nano-beam subjected to the electrostatic force have been studied. For this purpose, the governing nonlinear equations for static and dynamic behavior of a nano-beam have been obtained. Due to the nonlinearity of electrostatic, van der Waals (vdW) and Casimir forces, the governing differential equation for static analysis has been linearized using step by step linearization method (SSLM) and the developed linearized equation has been discretized using Galerkin weighted residual method. Dynamic responses have also been studied using linearized form of the Galerkin based reduced order model. In this model, nonlinear force terms have been taken into account using an iteration procedure. Using this model, dynamic response of a nano-switch to a stepwise DC voltage excitation at the presence of Casimir and vdW forces has also been studied. The results show that the Casimir force for some orders of geometric properties has more effect on the static pull-in voltage than the vdW force; and therefore the effect of the vdW force, in some cases can be ignored. The results also show that un-damped dynamic pull-in voltage at the presence of Casimir and vdW forces is 89 % of the static pull-in voltage, whereas, this ratio rises to 90.8 % when the effect of these forces has been ignored. By considering damping effects, pull-in voltage increases up to a definite value of DC voltage. At this level, the nano beam tends to be critically damped and the dynamic pull-in voltage approaches the static pull-in voltage limit

Modeling of a Bio Sensor Based on Detection of Antigens Concentration Using an Electrically Actuated Micro Cantilever

Nano molecular adsorption of bio particles made it possible to design and produces of some micro sensors that can sense some vital characteristics of a patient. In this paper, electromechanical characteristics of such a device are investigated and a novel suggestion is made to increase its sensitivity. The device is a micro-cantilever beam submerged in blood that it has been proven that by applying an electrical potential difference between the beam and a supplemented substrate it will work more precisely. In order to investigate the electromechanical behavior of its structure, the well-known Euler-Bernoulli beam theory and differentially parallel capacitor assumption is hired. Due to the nonlinearity of governing differential equations, there is no known explicit solution, so in order to gain an approximate solution, Galerkin based step by step linearization method (SSLM) (for static deflection) is used then the equation of dynamic motion is linearized about an electrostatically deflected position so mode summation method is implemented. In addition some sensing methods including capacitive, resonance frequency shifting method have been investigated