Dnyanesh N. Pawaskar

Closed-form empirical relations to predict the dynamic pull-in parameters of electrostatically actuated tapered microcantilevers

We develop novel closed-form empirical relations to estimate the dynamic pull-in parameters of electrostatically actuated linearly tapered microcantilever beams driven by a step-function voltage. A computationally efficient single degree-of-freedom model is employed in the setting of an energy-based technique to characterize the dynamic pull-in of the distributed electromechanical model that takes into account the effects of fringing field capacitance. The model exploits the fundamental mode shape of the respective nonprismatic geometry obtained using the differential transform technique. A unique surface fitting model is proposed to characterize the variations of both pull-in displacement and pull-in voltage over a realistically wide range of system parameters. Optimum coefficients of the proposed surface fitting model are obtained using nonlinear regression analysis. The empirical estimates of dynamic pull-in parameters are validated against 3D finite element simulations and available data in the literature. Excellent agreement indicates that the proposed relationships are sufficiently accurate to be safely used for the preliminary design of tapered microcantilever beams.

Pull-In Dynamics of Variable-Width Electrostatic Microactuators

Determination of pull-in parameters is vital in the design of electrostatically actuated microdevices. Moreover, it is important to devise some means to gain a control over the pull-in parameters in order to establish the customized microactuator design practice. In this paper, we analyze the influence of the beam geometry on the dynamic pull-in parameters of electrostatically actuated microbeams. Novel width functions are proposed for the microcantilever and the fixed-fixed beam, which smoothly vary the width of the microbeam along its length. We demonstrate the use of these width-functions by comparing six different microbeam geometries, three for cantilevered beam and three for fixed-fixed beam along with their constant width rectangular counterparts. All configurations are analyzed using an energy technique which gives an upper bound on the critical amplitude of the microbeam displacement, which is subsequently used to extract a lower bound on the applied voltage at the point of dynamic pull-in instability. For every case, a comparison is made between the static and the dynamic pull-in parameters. Results indicate a greater pull-in range for concave beam geometries, while the convex geometries exhibit a reduction in the pull-in range. Actuation voltage requirement is found to be proportional to the increase in the travel range. In all cases, the dynamic pull-in displacement is found to be greater than the static pull-in displacement, while the dynamic pull-in voltage is found to be less than the static pull-in voltage.Copyright

Optimization of static and dynamic travel range of electrostatically driven microbeams using particle swarm optimization

Abstract This paper examines the enhancement of static and dynamic travel range of electrostatically driven microbeams using shape optimization approach. Continuous functions of width and thickness are used for optimizing the geometry of both cantilever and fixed–fixed microbeams. Rayleigh–Ritz energy method is employed to compute the static and dynamic pull-in parameters. Particle swarm optimization and hybrid simulated annealing are used for shape optimization of microbeams. Constraints on design variables are imposed using penalty approach. Enhanced pull-in parameters obtained for variable geometry microbeams have been validated using 3-D finite element analysis. Optimized shapes of microbeams show significant improvement in static and dynamic travel range. Pull-in displacement is increased up to 54.92% for cantilever microbeam and 40.79% for fixed–fixed microbeam with hybrid simulated annealing. Effectiveness of particle swarm optimization is brought out through representative test cases. The convergence of the particle swarm optimization is approximately five times faster as compared to the hybrid simulated annealing, while maintaining the same level of accuracy.

Shape optimization of electrostatically driven microcantilevers using simulated annealing to enhance static travel range

The objective of this paper is to present a systematic development of the generic shape optimization of elec- trostatically actuated microcantilever beams for extending their static travel range. Electrostatic actuators are widely used in micro electro mechanical system (MEMS) devices because of low power density and ease of fab- rication. However, their useful travel range is often restricted by a phenomenon known as pull-in instability. The Rayleigh- Ritz energy method is used for computation of pull-in parameters which includes electrostatic potential and fringing field effect. Appropriate width function and linear thickness functions are employed along the length of the non-prismatic beam to achieve enhanced travel range. Parameters used for varying the thick- ness and width functions are optimized using simulated annealing with pattern search method towards the end to refine the results. Appropriate penalties are imposed on the violation of volume, width, thickness and area constraints. Nine test cases are considered for demonstration of the said optimization method. Our results indicate that around 26% increase in the travel range of a non-prismatic beam can be achieved after optimiza- tion compared to that in a prismatic beam having the same volume. Our results also show an improvement in the pull-in displacement of around 5% compared to that of a variable width constant thickness actuator. We show that simulated annealing is an effective and flexible method to carry out design optimization of structural elements under electrostatic loading.

Static and Dynamic Analysis of Electrostatically Actuated Microcantilevers Using the Spectral Element Method

The objective of this paper is to present the Spectral Element Method (SEM) as an accurate and efficient design tool for static and dynamic simulations of cantilever based MEMS devices. The microcantilever under consideration is modeled as a Timoshenko beam and discretized using the spectral element formulation that accounts for fringing field and the nonlinearity arising from the electrostatic driving force. The static analysis has been carried out using Picard’s iteration method and the static pull-in displacement and voltage have been calculated. An eigenvalue analysis of this beam is also carried out to determine its natural frequencies. In addition, the dynamics of this cantilever is studied using the explicit Newmark predictor-corrector method to generate the time history. In all cases, the results have been compared to the one-dimensional Finite Element Method and three-dimensional finite element method (implemented through the commercial package COMSOL Multiphysics) to examine the accuracy and computational speed of the proposed SEM. The results of the simulations were also compared to those obtained by experiments in the existing scientific literature.These comparisons lead to the inference that the SEM is able to reproduce the static and dynamic response of the beam to a high degree of accuracy. It was also found that several numerical features inherent in the SEM lead to a significantly faster computation than the corresponding finite element method for equivalent degrees of freedom. This advantage was verified by using the SEM to carry out static and dynamic simulations of variable width microcantilevers.We therefore propose that the SEM is a viable tool for the MEMS community to accurately and quickly determine the static and dynamic pull-in parameters, frequency eigenvalues, and static and dynamic behavior at the design stage.Copyright

Design Method to Achieve High Frequency Stability of Electrostatically Actuated Doubly-Clamped Nano-Oscillators

Frequency stability is a desirable property for micro- and nanoelectromechanical system oscillators used in reference and timing applications. In case of doubly-clamped oscillators, resonant frequencies are highly sensitive to the operating temperature because of development of internal stresses due to thermal expansion under the restraint of fixed boundary conditions. In this paper, we present a design procedure to reduce the variation of resonant frequency with respect to change in operating temperature, in other words improve the frequency stability, by exploiting the interaction between electrostatic and geometric nonlinearities in electrostatically actuated doubly-clamped nano-oscillators. We have modeled the nano-oscillators using Euler-Bernoulli beam theory and Galerkin based reduced order modeling technique. We have examined first natural frequency variation due to temperature change for different carbon nanotube oscillators and an optimization based design procedure has been devised for improving the frequency stability.© 2014 ASME

An Efficient Numerical Scheme to Determine the Pull-In Parameters of an Electrostatic Micro-Actuator With Contact Type Nonlinearity

In this article, we present an efficient numerical scheme based on the Rayleigh-Ritz method to determine the pull-in parameters of electrostatically actuated microbeams exploiting contact type nonlinearity. A case of an electrostatically actuated cantilevered microbeam is first analyzed using the Rayleigh-Ritz energy technique. The deflection of the microbeam is approximated by a polynomial trial function. The principle of the stationary potential energy leads to a highly nonlinear algebraic equation, which is solved to determine the deflected shape of the microbeam. A novel voltage iteration algorithm is implemented to determine the critical voltage at which the pull-in occurs. The analysis is then extended to the case of cantilever beam making use of the contact type nonlinearity to exhibit an extended travel range. The present case consists of a compression spring getting engaged at the cantilever tip at the critical point where the pull-in occurs. An increase in both travel range and pull-in voltage is observed with the introduction of the compression spring. A performance index is suggested, which combines the gain in the travel range together with the concomitant increase in the pull-in voltage. This index is used to determine the critical bound for the choice of the stiffness of the newly introduced compression member.Copyright