Electrostatic MEMS switches have become prevalent because of low power consumption and ease of integration in
micro-fabrication technology. The equations governing their dynamic response obtained by energy methods are
nonlinear differential equations. Even the unit-step response of these devices requires numerical computation.
Depending on the magnitude of the applied step voltage and the presence of dielectric in the actuator, the
response could be recurring or non-recurring. Estimating the period time and the switching time in these cases
proves to be hard because one has to solve the energy equation numerically which could be time consuming or
difficult to converge if it is not posed properly. Elata et al. have developed excellent methods to obtain these
times on a logarithmic scale of voltage more easily for the undamped case. This paper extends their work for
the case when the bottom plate is covered with a dielectric layer. The stagnation time occurring before dynamic
pull-in, and the switching time thereafter are first shown as nonlinear graphs with the dielectric permittivity as
a parameter. They are also linearized on an exponential scale and made useful for quick look up and convenience
Performance of electrostatic actuators used in MEMS devices is severely limited by the stability considerations
that are related to the pull-in parameters. The static and dynamic responses of electrostatic actuators driven
by single as well as multiple voltage excitations are studied with an aim of estimating these pull-in voltage
and distance parameters. A normalized Hamiltonian formulation is adopted and the resulting equations are
solved analytically and also numerically using an iterative scheme. Recently a numerical α-line method has been
proposed to extract the pull-in parameters. Scanning along the α-lines by voltage and displacement iteration
schemes were studied. Estimating the intersection of the α-lines with the pull-in hypersurface indicates maximal
voltage variable. We revisit these two iteration schemes and propose few insights to improve the convergence.
Convergence of the parameters to the theoretical values is found to be smooth. This approach helps us to
generalize the technique for more complicated geometries.
Due to the increased complexity demands and precision requirements of microelectromechanical systems (MEMS), there is a need for reliable and accurate simulation methods to model physical behavior involved. In particular, the design of improved MEMS transducers can be facilitated by simulating the interaction between the electrostatic and structural domains associated with these devices. In this work, several computational mechanics issues involving electrostatic and structural coupling for MEMS are presented and discussed, including the trade-off between cost and accuracy. Several uncoupled finite element (FE) models are presented and simulated to optimize the design and fabrication of a combdrive based electrostatic microactuator. The benefits and limitations of these uncoupled FE models are then discussed. The asymmetric structural response of the combdrive actuator is further analyzed and a simplified closed-form analytical model is presented for a basis of comparison for the FE results. Based on differences between FE and analytically calculated values, the contribution of fringing electrostatic fields to the mechanical forces produced in the combdrive are discussed.
An SMA material model for use with finite element analysis is presented. Experimental results conducted to demonstrate and verify the concept closely matched the results obtained from FEA. Both one-dimensional and three-dimensional variations of the material models were used in the FE analysis. The one- dimensional SMA model was used to model the active twisting of a beam while the three-dimensional model was used to investigate stresses developed in a SMA reinforced smart composite plate. Surface-to-surface contact algorithms, nonlinear kinematics and nonlinear material model of SMA were used in FE analysis. A two-step approach was developed in order to analyze behavior of smart composite plates reinforced by SMA wires. Results from the analysis of changing the shape of wing prototype are also presented.
This paper shows how shape memory alloy (SMA) wires can be used to actively twist a beam or other long slender structural members. This is accomplished by attaching to the beam, a pre- strained SMA strip in its martensite state. The strip is wrapped around the beam in a helical pattern. When heated, the SMA wire transforms into from it martensite state to its austenite state. This causes the wire to shorten in length but since it is attached to the beam it induces a force on the beam that causes the beam to twist. A nonlinear finite element model that incorporates the thermo-structural coupling is used to analyze and study the phenomenon. Results from experiments and finite element analysis are presented and they show that this method can produce large twist angles. This twist can be maintained and reversed without causing any damage to the underlying structure. Several issues involving the method of attachment of the SMA strip to the beam are addressed including a method that allows the SMA wire to 'slide' along the beam. This concept can be used to control the angle of twist of blades of rotor equipment and thereby improve their performance or change their vibratory response.
The blades of helicopter rotors and turbine blades can be modeled as pretwisted beams/plates or shells. The angle of pretwist can affect the performance of these turbo-machinery systems. Being able to actively change the angle of pretwist even moderately can enhance or optimize these systems for various modes of operation. To actively change the angle of pretwist, a torque has to be introduced to the pretwist member that will cause it to either increase or decrease the existing pretwist angle of the blade. By building piezoelectric layers into the blade/plate and applying a controlled voltage the shape and or position of the cross- section can be changed. Due to the coupling of both bending modes and the extensional and torsional modes in pretwisted members a piezoelectric materials that can induce extension in the plate can also be used to twist or bend the shape of the plate. In this study a cantilevered pretwisted plates bonded to two piezoelectric layers on the outside is modeled using 3D linear elastic finite element approach with the pretwist built into the formulation. The static response of the pretwisted plate to a uniform voltage applied to the piezoelectric layers is investigated. Twisting and bending of the plate is accomplished through coupling of the bending modes and extensional-torsional coupling. The piezoelectric layer itself is not isotropic and so introduces additional coupling into the system.