http://liberzon.csl.illinois.edu/research/autom-impulsive-iss.pdf

Lyapunov conditions for input-to-state stability of impulsive systems

A nonlinear Timoshenko beam formulation based on the modified couple stress theory

We use Anderson or vibration localization in coupled microcantilevers as an extremely sensitive method to detect the added mass of a target analyte. We focus on the resonance frequencies and eigenstates of two nearly identical coupled gold-foil microcantilevers. Theoretical and experimental results indicate that the relative changes in the eigenstates due to the added mass can be orders of magnitude greater than the relative changes in resonance frequencies. Moreover this sensing paradigm possesses intrinsic common mode rejection characteristics thus providing an alternate way to achieve ultrasensitive mass detection under ambient conditions.

/pdf/ultrasensitive-mass-sensing-using-mode-localization-in-y13lktqqww.pdf

Ultrasensitive mass sensing using mode localization in coupled microcantilevers

Any polarizable body placed in an inhomogeneous electric field experiences a dielectric force. This phenomenon is well known from the macroscopic world: a water jet is deflected when approached by a charged object. This fundamental mechanism is exploited in a variety of contexts-for example, trapping microscopic particles in an optical tweezer, where the trapping force is controlled via the intensity of a laser beam, or dielectrophoresis, where electric fields are used to manipulate particles in liquids. Here we extend the underlying concept to the rapidly evolving field of nanoelectromechanical systems (NEMS). A broad range of possible applications are anticipated for these systems, but drive and detection schemes for nanomechanical motion still need to be optimized. Our approach is based on the application of dielectric gradient forces for the controlled and local transduction of NEMS. Using a set of on-chip electrodes to create an electric field gradient, we polarize a dielectric resonator and subject it to an attractive force that can be modulated at high frequencies. This universal actuation scheme is efficient, broadband and scalable. It also separates the driving scheme from the driven mechanical element, allowing for arbitrary polarizable materials and thus potentially ultralow dissipation NEMS. In addition, it enables simple voltage tuning of the mechanical resonance over a wide frequency range, because the dielectric force depends strongly on the resonator-electrode separation. We use the modulation of the resonance frequency to demonstrate parametric actuation. Moreover, we reverse the actuation principle to realize dielectric detection, thus allowing universal transduction of NEMS. We expect this combination to be useful both in the study of fundamental principles and in applications such as signal processing and sensing.

/pdf/universal-transduction-scheme-for-nanomechanical-systems-27sm3ylbze.pdf

Universal transduction scheme for nanomechanical systems based on dielectric forces

Parametric resonance has been well established in many areas of science, including the stability of ships, the forced motion of a swing and Faraday surface wave patterns on water. We have previously investigated a linear parametrically driven torsional oscillator and along with other groups have mentioned applications including mass sensing, parametric amplification, and others. Here, we thoroughly investigate the design of a highly sensitive mass sensor. The device we use to carry out this study is an in-plane parametrically resonant oscillator. We show that in this configuration, the nonlinearities (electrostatic and mechanical) have a large impact on the dynamic response of the structure. This result is not unique to this oscillator—many MEMS oscillators display nonlinearities of equal importance (including the very common parallel plate actuator). We report the effects of nonlinearity on the behavior of parametric resonance of a micro-machined oscillator. A nonlinear Mathieu equation is used to model this problem. Analytical results show that nonlinearity significantly changes the stability characteristics of parametric resonance. Experimental frequency response around the first parametric resonance is well validated by theoretical analysis. Unlike parametric resonance in the linear case, the jumps (very critical for mass sensor application) from large response to zero happen at additional frequencies other than at the boundary of instability area. The instability area of the first parametric resonance is experimentally mapped. Some important parameters, such as damping co-efficient, cubic stiffness and linear electrostatic stiffness are extracted from the nonlinear response of parametric resonance and agree very well with normal methods.

Effect of cubic nonlinearity on auto-parametrically amplified resonant MEMS mass sensor

A mass sensing concept based on parametric resonance amplification is proposed and experimentally investigated using a non-interdigitated comb-finger driven micro-oscillator. Mass change can be detected by measuring frequency shift at the boundary of the first order parametric resonance ‘tongue’. Both platinum deposition using focused ion beam (FIB) and water vapor desorption and absorption are used to change the mass of a prototype sensor. Due to the sharp transition in amplitude caused by parametric resonance, the sensitivity is 1–2 order of magnitude higher than the same oscillator working at Simple Harmonic Resonance (SHR) mode in air. Picogram (10 −12  g) level mass change can be easily detected in the sensor with mass about 30 ng and resonance frequency less than 100 kHz. Damping effects and noise processes on sensor dynamics and sensing performance are also investigated and damping has no significant effect on sensor noise floor and sensitivity. Higher sensitivity is expected when the oscillator design is optimized and dimensions are scaled.

Application of parametric resonance amplification in a single-crystal silicon micro-oscillator based mass sensor

Generalized parametric resonance in electrostatically actuated microelectromechanical oscillators

We describe how to significantly change the dynamic behavior of parametric resonance in a micromechanical oscillator. By varying the voltage amplitude of applied electrical signal, the frequency response of the first order parametric resonance changes dramatically. We attribute this variation to the tuning of effective cubic stiffness of the oscillator, which is a contribution of both structural and electrical cubic stiffness. This phenomenon is well explained by the first-order perturbation analysis of nonlinear Mathieu equation.

Tuning the dynamic behavior of parametric resonance in a micromechanical oscillator

The use of tightly packed arrays of probes can achieve the much desirable goal of increasing the throughput of scanning probe devices. However the proximity of the probes induces coupling in their dynamics, which increases the complexity of the overall device. In this paper we analyze and model the behavior of a pair of electrostatically and mechanically coupled microcantilevers. For the common case of periodic driving voltage, we show that the underlying linearized dynamics are governed by a pair of coupled Mathieu equations. We provide experimental evidence that confirms the validity of the mathematical model proposed, which is verified by finite element simulations as well. The coefficients of electrostatic and mechanical coupling are estimated respectively by frequency identification methods and noise analysis. Finally, we discuss parametric resonance for coupled oscillators and include a mapping of the first order coupled parametric resonance region.

/pdf/characterization-of-electrostatically-coupled-50v2cl192w.pdf

Wenhua Zhang

Papers

Effect of cubic nonlinearity on auto-parametrically amplified resonant MEMS mass sensor

Application of parametric resonance amplification in a single-crystal silicon micro-oscillator based mass sensor

Generalized parametric resonance in electrostatically actuated microelectromechanical oscillators

Tuning the dynamic behavior of parametric resonance in a micromechanical oscillator

Characterization of electrostatically coupled microcantilevers