Jeffrey F. Rhoads

The nonlinear response of resonant microbeam systems with purely-parametric electrostatic actuation

Electrostatically-actuated resonant microbeam devices have garnered significant attention due to their geometric simplicity and broad applicability. Recently, some of this focus has turned to comb-driven microresonators with purely-parametric excitation, as such systems not only exhibit the inherent benefits of MEMS devices, but also a general improvement in sensitivity, stopband attenuation and noise rejection. This work attempts to combine each of these areas by proposing a microbeam device which couples the inherent benefits of a resonator with purely-parametric excitation with the simple geometry of a microbeam. Theoretical analysis reveals that the proposed device exhibits desirable response characteristics, but also quite complex dynamics. Of particular note is the fact that the devices nonlinear frequency response is found to be qualitatively dependent on the systems ac excitation amplitude. While this flexibility can be desirable in certain contexts, it introduces additional design and operating limitations. While the principal focus of this work is the proposed systems nonlinear response, the work also contains details pertaining to model development and device design.

Tunable Microelectromechanical Filters that Exploit Parametric Resonance

Background: This paper describes an analytical study of a bandpass filter that is based on the dynamic response of electrostatically-driven MEMS oscillators. Method of Approach: Unlike most mechanical and electrical filters that rely on direct linear resonance for filtering, the MEM filter presented in this work employs parametric resonance. Results: While the use of parametric resonance improves some filtering characteristics, the

Linear and Nonlinear Tuning of Parametrically Excited MEMS Oscillators

Microelectromechanical oscillators utilizing noninterdigitated combdrive actuators have the ability to be parametrically excited, which leads to distinct advantages over harmonically driven oscillators. Theory predicts that this type of actuator, when dc voltage is applied, can also be used for tuning the effective linear and nonlinear stiffnesses of an oscillator. For instance, the parametric instability region can be rotated by using a previously developed linear tuning scheme. This can be accomplished by implementing two sets of noninterdigitated combdrives, choosing the correct geometry and alignment for each, and applying ac excitation voltages to one set and proportional dc tuning voltages to the other set. Such an oscillator can also be tuned to display a desired nonlinear behavior: softening, hardening, or mixed nonlinearity. Nonlinear tuning is attained by carefully designing combdrive geometry, flexure geometry, and applying the correct dc voltages to the second set of actuators. Here, two oscillators have been designed, fabricated, and tested to prove these tuning concepts experimentally

Parametrically Excited MEMS-Based Filters

In this paper we describe the dynamics of MEMS oscillators that can be used as frequency filters. The unique feature of these devices is that they use parametric resonance, as opposed to the usual linear resonance, for frequency selection. However, their response in the parametric resonance zone has some undesirable features from the standpoint of filter performance, most notably that their bandwidth depends on the amplitude of the input and the nonlinear nature of the response. Here we provide a brief background on filters, a MEMS oscillator that overcomes some of the deficiencies, and we offer a description of how one might utilize a pair of these MEMS oscillators to build a band-pass filter with nearly ideal stopband rejection. These designs are made possible by the fact that MEMS devices are highly tunable, which allows one to build in system features to achieve desired performance.

Modeling of parametrically excited microelectromechanical oscillator dynamics with application to filtering

A model for the dynamics of an emerging class of electrostatically driven microelectromechanical oscillators, parametrically excited MEM oscillators, has been developed. The equation of motion for these devices is a nonlinear version of the Mathieu equation, which gives rise to rich dynamics. A standard perturbation analysis, averaging, has been adopted to analyze this complicated system. Numerical bifurcation analysis was employed and successfully verified these analytical results. Using the analytical and numerical tools developed for this model, along with the experimental results for such a device, parameters for the system are identified. This model is a pivotal design tool for the development of parametrically excited MEM filters

NONLINEAR RESPONSE OF PARAMETRICALLY-EXCITED MEMS

Due to the position-dependent nature of electrostatic forces, many microelectromechanical (MEM) oscillators inherently feature parametric excitation. This work considers the nonlinear response of one such oscillator, which is electrostatically actuated via non-interdigitated comb drives. Unlike other parametricallyexcited systems, which feature only linear parametric excitation in their equation of motion, the oscillator in question here exhibits parametric excitation in both its linear and nonlinear terms. This complication proves to significantly enrich the system’s dynamics. Amongst the interesting consequences is the fact that the system’s nonlinear response proves to be qualitatively dependent on the system’s excitation amplitude. This paper includes an introduction to the equation of motion of interest, a brief, yet systematic, analysis of the equation’s nonlinear response, and experimental evidence of the predicted behavior as measured from an actual MEM oscillator.

Mechanical Domain Parametric Amplification

Though utilized for more than fifty years in a variety of power and communication systems, parametric amplification, the process of amplifying a harmonic signal with a parametric pump, has received very little attention in the mechanical engineering community. In fact, only within the past fifteen to twenty years has the technique been implemented in micromechanical systems as a means of amplifying the output of resonant micro-transducers. While the vast potential of parametric amplification has been demonstrated, to date, in a number of micro- and nano-mechanical systems (as well as a number electrical systems), few, if any, macroscale mechanical amplifiers have been reported. Given that these amplifiers are easily realizable using larger-scale mechanical systems, the present work seeks to address this void by examining a simple, representative example: a cantilevered beam with longitudinal and transverse base excitations. The work begins with the systematic formulation of a representative system model, which is used to derive a number of pertinent metrics. A series of experimental results, which validate the work’s analytical findings, are subsequently examined, and the work concludes with a brief look at some plausible applications of parametric amplification in macroscale mechanical systems.Copyright

A SISO, Multi-Analyte Sensor Based on a Coupled Microresonator Array

This work details a preliminary analytical and experimental investigation of a new class of resonant, single input - single output (SISO) microsensors, which are capable of detecting multiple analytes. The key feature of these sensors is that they exploit vibration localization in a set of N microbeams, coupled indirectly through a common shuttle mass, to allow for the detection of N distinct resonance shifts (induced by the presence of up to N distinct analytes) using solely the shuttle mass’ response. The work includes a brief overview of the proposed sensor design, the formulation and subsequent analysis of a representative lumpedmass model of the sensor, and details of a recently-completed simulated mass detection experiment, which verified the feasibility of the proposed sensor design. Where appropriate, practical design issues, essential to sensor development, are described.