Analysis of Pull-In Instability of Geometrically Nonlinear Microbeam Using Radial Basis Artificial Neural Network Based on Couple Stress Theory

The static pull-in instability of beam-type microelectromechanical systems (MEMS) is theoretically investigated. Two engineering cases including cantilever and double cantilever microbeam are considered. Considering the midplane stretching as the source of the nonlinearity in the beam behavior, a nonlinear size-dependent Euler-Bernoulli beam model is used based on a modified couple stress theory, capable of capturing the size effect. By selecting a range of geometric parameters such as beam lengths, width, thickness, gaps, and size effect, we identify the static pull-in instability voltage. A MAPLE package is employed to solve the nonlinear differential governing equations to obtain the static pull-in instability voltage of microbeams. Radial basis function artificial neural network with two functions has been used for modeling the static pull-in instability of microcantilever beam. The network has four inputs of length, width, gap, and the ratio of height to scale parameter of beam as the independent process variables, and the output is static pull-in voltage of microbeam. Numerical data, employed for training the network, and capabilities of the model have been verified in predicting the pull-in instability behavior. The output obtained from neural network model is compared with numerical results, and the amount of relative error has been calculated. Based on this verification error, it is shown that the radial basis function of neural network has the average error of 4.55% in predicting pull-in voltage of cantilever microbeam. Further analysis of pull-in instability of beam under different input conditions has been investigated and comparison results of modeling with numerical considerations shows a good agreement, which also proves the feasibility and effectiveness of the adopted approach. The results reveal significant influences of size effect and geometric parameters on the static pull-in instability voltage of MEMS.

Modeling the Effects of the PCB Motion on the Response of Microstructures Under Mechanical Shock

Microelectromechanical systems (MEMS) are often used in portable electronic devices that are vulnerable to mechanical shock or impact, such as that induced due to accidental drops on the ground. This work presents a modeling and simulation effort to investigate the effect of the vibration of a printed circuit board (PCB) on the dynamics of MEMS microstructures when subjected to shock. Two models are investigated. In the first model, the PCB is modeled as an Euler-Bernoulli beam to which a lumped model of a MEMS device is attached. In the second model, a special case of a cantilever microbeam is studied and modeled as a distributed-parameter system, which is attached to the PCB. These lumped-distributed and distributed-distributed models are discretized into ordinary differential equations, using the Galerkin method, which are then integrated numerically over time to simulate the dynamic response. Results of the two models are compared against each other for the case of a cantilever microbeam and also compared to the predictions of a finite-element model using the software ANSYS. The influence of the higher order vibration modes of the PCB, the location of the MEMS device on the PCB, the electrostatic forces, damping, and shock pulse duration are presented. It is found that neglecting the effects of the higher order modes of the PCB and the location of the MEMS device can cause incorrect predictions of the response of the microstructure and may lead to failure of the device. It is noted also that, for some PCB designs, the response of the microstructure can be amplified significantly causing early dynamic pull-in and hence possibly failure of the device.

Electromechanical Coupling Study on the Pull-in Parameters of Electrostatic Cantilever Microbeam

In this paper, the coupling electromechanical model is proposed for a cantilever microbeam in microelectromechanical system (MEMS). Based on mechanics of plate and theories of electrostatic field, the coupling electromechanical behavior of the cantilever microbeam is investigated. The pull-in voltage is accomplished using the increment-iterative method. The effectiveness of the proposed method is verified by comparing numerical results with that in the literature. The numerical results show that the pull-in voltage decreases with the improvement of the ratio of the width of micro beam to the initial gap between the electrodes.