M. M. Joglekar

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.

An Energy-Based Approach to Extract the Dynamic Instability Parameters of Dielectric Elastomer Actuators

An energy-based approach is presented to extract the thresholds on the transient dynamic response of step voltage driven dielectric elastomer actuators (DEAs). The proposed approach relies on establishing the energy balance at the point of maximum stretch in an oscillation cycle followed by the application of an instability condition to extract the dynamic instability parameters. Explicit expressions are developed for the critical values of maximum stretch and the corresponding nominal electric field, thus circumventing the need to perform iterative time-integrations of the equation of motion. The underlying principles of the approach are enunciated for the neo-Hookean material model and further extended to analyze relatively complex multiparameter hyperelastic models (Mooney–Rivlin and Ogden) that are employed prevalently for investigating the behavior of DEAs. The dynamic instability parameters predicted using the energy method are validated by examining the time-history response of the actuator in the vicinity of the dynamic instability. The development of dynamic instability parameters is complemented by energy-based extraction of static instability parameters to facilitate a quick comparison between the two. It is inferred quantitatively that the nominal electric field sufficient to cause the dynamic instability and the corresponding thickness stretch is lower than those corresponding to the static instability. A set of representative case studies for multiparameter material models is presented at the end, which can be used as an input for further experimental corroboration. The results of the present investigation can find their potential use in the design of DEAs subjected to transient loading.

Mitigation of residual oscillations in electrostatically actuated microbeams using a command-shaping approach

When electrostatically actuated microbeams are driven by an input-waveform comprising multiple voltage steps, the resulting response inherently contains residual oscillations, which may prove detrimental to the device performance and accuracy. In this article, we report the systematic development of a command shaping technique for mitigating such residual oscillations in electrostatically actuated microbeams and achieving fast switching between the successive equilibrium states. Invoking the force balance at a critical point in an oscillation cycle, the proposed technique relies on bringing the actuator to a stagnation state by applying an additional voltage signal of specific amplitude at a predetermined time. The underlying principle of the technique is enunciated for the lumped parallel-plates model of the microactuator, and further extended to the cases of microbeams. The electromechanical model of the microbeam incorporates the effects of full-order electrostatic nonlinearity, moderately large deflections, viscous energy dissipation, and fringing fields. The modal superposition method is employed to obtain the dynamic response of microbeams. Based on a single-mode assumption, the proposed technique lends itself to a simple multistep waveform, which is attractive from the implementation point of view. The applicability of the proposed technique is demonstrated by considering a wide range of parameters involving variations in the extent of geometric nonlinearity, damping, and equilibrium sequences. The impact of higher modes on the stabilized response is exposited, and a command shaping approach based on the multi-mode response of the actuator is suggested. In particular, such an approach is shown to be effective in controlling the motion of the beam in the vicinity of the static pull-in displacement, which is associated with strong electrostatic nonlinearity. The present investigation can find its potential use in the development of an open-loop controller for electrostatically actuated microbeams.

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.

DC dynamic pull-in instability of a dielectric elastomer balloon: an energy-based approach

This paper reports an energy-based method for the dynamic pull-in instability analysis of a spherical dielectric elastomer (DE) balloon subjected to a quasi-statically applied inflation pressure and a Heaviside step voltage across the balloon wall. The proposed technique relies on establishing the energy balance at the point of maximum stretch in an oscillation cycle, followed by the imposition of an instability condition for extracting the threshold parameters. The material models of the Ogden family are employed for describing the hyperelasticity of the balloon. The accuracy of the critical dynamic pull-in parameters is established by examining the saddle-node bifurcation in the transient response of the balloon obtained by integrating numerically the equation of motion, derived using the Euler–Lagrange equation. The parametric study brings out the effect of inflation pressure on the onset of the pull-in instability in the DE balloon. A quantitative comparison between the static and dynamic pull-in parameters at four different levels of the inflation pressure is presented. The results indicate that the dynamic pull-in instability gets triggered at electric fields that are lower than those corresponding to the static instability. The results of the present investigation can find potential use in the design and development of the balloon actuators subjected to transient loading. The method developed is versatile and can be used in the dynamic instability analysis of other conservative systems of interest.

NUMERICAL IMPLEMENTATION OF POROUS COMPOSITE ELECTRODE–DEGRADATION MODEL TO STUDY THE CYCLE LIFE OF LI-ION CELL

A numerical study is performed on the cyclic capacity degradation of a lithium manganese oxide (LMO) cell, under 21 different combinations of temperature and state of charge (SOC), based on the phenomenological model developed earlier. Out of the 21 sets, six are used for fitting in order to establish the degradation parameters of the model and the rest could be predicted with an average accuracy of about 90%. Two optimization algorithms (Genetic and Nelder Mead) are used and the consistency of the convergence is verified. The discussion includes sensitivity analysis of a selected set of degradation parameters. In addition, an analysis of the evolution of solid electrolyte interphase (SEI) and isolation (islanding) mechanisms under varying conditions of SOC and temperatures is performed which brings out the relative contribution of each mechanism to the overall capacity fade.