Design methods of MEMS switches are typically based on deterministic approaches, where the parameters such as geometrical and physical properties as well as the operating conditions that characterize the behavior of systems are assumed to be known precisely. However, in practice, due to the batch-production processes used in MEMS fabrication as well as the micron-scale dimensions of the structural elements, consideration of uncertainties in system parameters and an understanding of their effects are warranted and should be investigated in order to improve the switch performance and reliability. The primary purpose of the present paper is to perform uncertainty quantification predictions for MEMS switches based on the transient dynamic response, in particular, the bouncing behavior. A suitable mathematical model that captures the bouncing dynamics and previously validated via experiments is employed for this purpose. In particular, quantification of performance in terms of second order statistics is performed to predict propagation of uncertainties in Young’s modulus, beam width, beam thickness as well as actuation voltage. The influence of these uncertainties on significant switch performance parameters such as initial bounce time as well as maximum bounce height have been quantified.
Effect of stochastic fluctuations in angular velocity on the stability of two degrees-of-freedom ring-type microelectromechanical systems (MEMS) gyroscopes is investigated. The governing stochastic differential equations (SDEs) are discretized using the higher-order Milstein scheme in order to numerically predict the system response assuming the fluctuations to be white noise. Simulations via Euler scheme as well as a measure of largest Lyapunov exponents (LLEs) are employed for validation purposes due to lack of similar analytical or experimental data. The response of the gyroscope under different noise fluctuation magnitudes has been computed to ascertain the stability behavior of the system. External noise that affect the gyroscope dynamic behavior typically results from environment factors and the nature of the system operation can be exerted on the system at any frequency range depending on the source. Hence, a parametric study is performed to assess the noise intensity stability threshold for a number of damping ratio values. The stability investigation predicts the form of threshold fluctuation intensity dependence on damping ratio. Under typical gyroscope operating conditions, nominal input angular velocity magnitude and mass mismatch appear to have minimal influence on system stability.
The influence of stochastic fluctuations in the input angular rate of a class of single axis mass-spring microelectromechanical (MEM) gyroscopes on the system stability is investigated. A white noise fluctuation is introduced in the coupled 2-DOF model that represents the system dynamics for the purposes of stability prediction. Numerical simulations are performed employing the resulting set of stochastic differential equations (SDEs) that govern the system dynamics. The SDEs are discretized using the higher-order Milstein scheme for numerical computations. Simulations via the Euler scheme, as well as the measure of the largest Lyapunov exponent are employed for validation purposes due to a lack of similar analytical solutions or experimental data. Responses have been predicted under different noise fluctuation magnitudes and different input angular rates for stability investigations. A parametric study is performed to estimate the noise intensity stability threshold for a range of quality factor values at different input angular rates. The predicted results show a nonlinear dependence of the threshold on the quality factors for different input rates. Under typical gyroscope operating conditions, a realistic frequency mismatch appears to have insignificant influence on system stability. It is envisaged that the present quantitative predictions will aid improvements in performance, reliability, and the design process for this class of devices.
Batch fabrication processes used to produce micro-electro-mechanical systems (MEMS) are prone to uncertainties in the system geometrical and contact parameters as well as material properties. However, since the common design method for these systems is typically based on precise deterministic assumptions, it is necessary to get more insight into their variations. To this end, understanding the influences of uncertainties accompanied by these processes on the system performance and reliability is warranted. The present paper focuses on predictions of uncertainty measures for MEMS switches based on the transient dynamic response, in particular, the bouncing behavior. To understand and quantify the influence of pertinent parameters on the bouncing effects, suitable mathematical model that captures the bouncing dynamics as well as the forces that are dominant at this micron scale are employed. Measure of performance in terms of second-order statistics is performed, particularly for the beam as well as beam tip parameters since excessive tip bounce is known to degrade switch performance. Thus, the present study focusses on the influence of uncertainties in the beam tip geometry parameters such as beam tip length/width as well as contact asperity variables such as the area asperity density and the radius of asperities. In addition to beam tip parameters, this study quantifies the effects of uncertainties in Young's modulus, beam thickness as well as actuation voltage. These influences on significant switch performance parameters such as initial contact time and maximum bounce height have been quantified in the presence of interactive system nonlinearities.
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