Past, present and future of nonlinear system identification in structural dynamics

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

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

Inthe last decadewe havewitnessed excitingtechnologicaladvancesin the fabricationand control of microelectromechanical and nanoelectromechanical systems (MEMS& NEMS) [1–5]. Such systems are being developed for a host of nanotechnologicalapplications,suchashighly-sensitivemass[6–8],spin[9],andchargedetectors[10,11],aswellasforbasicresearchinthemesoscopicphysicsofphonons[12],andthegeneralstudy of the behavior of mechanical degrees of freedom at the interface between thequantum and the classical worlds [13,14]. Surprisingly, MEMS & NEMS have alsoopenedup a whole new experimentalwindowinto the study of the nonlineardynamicsof discrete systems in the form of nonlinear micromechanical and nanomechanicaloscillators and resonators.Thepurposeofthisreviewisto providean introductionto thenonlineardynamicsofmicromechanical and nanomechanical resonators that starts from the basics, but alsotouches upon some of the advanced topics that are relevant for current experimentswith MEMS & NEMS devices. We begin in this section with a general motivation,explaining why nonlinearities are so often observed in NEMS & MEMS devices. In§ 1.2 we describe the dynamics of one of the simplest nonlinear devices—the Dufﬁngresonator—while giving a tutorial in secular perturbation theory as we calculate itsresponse to an external drive. We continue to use the same analytical tools in § 1.3 todiscuss the dynamics of a parametrically-excited Dufﬁng resonator, building up to thedescription of the dynamicsof an array of coupled parametrically-excitedDufﬁng res-onatorsin § 1.4. We conclude in § 1.5 by giving an amplitude equation description forthe array of coupled Dufﬁng resonators, allowing us to extend our analytic capabilitiesin predicting and explaining the nature of its dynamics.

/pdf/nonlinear-dynamics-of-nanomechanical-and-micromechanical-4cn87cp3vp.pdf

Nonlinear Dynamics of Nanomechanical and Micromechanical Resonators

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

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

Tunable Microelectromechanical Filters that Exploit Parametric Resonance

The authors demonstrate the fabrication of different architectures of carbon nanotubes on conducting substrates via contact transfer of nanotubes using low temperature solders. Lithographically patterned multiwalled carbon nanotube arrays grown on silica substrates by chemical vapor deposition methods are transferred onto solder coated substrates. Both negative and positive patterns can be obtained by changing the printing parameters. Good wetting and electrical contacts are confirmed by measuring their field emission properties. This method can be used to construct nanotube structures of different shapes and dimensions over large areas on substrates of choice and could be a feasible process to integrate nanotubes into various devices.

Contact transfer of aligned carbon nanotube arrays onto conducting substrates

Recent discovery of substrate-selective growth of carbon nanotubes on SiO2 in exclusion to Si, has opened up the possibility of organizing nanotubes on Si/SiO2 patterns in premeditated configurations for building devices. Here, we report the strong dependence of nanotube growth on the SiO2 layer thickness, and the utility of this feature to build three-dimensional architectures. Our results show that there is no detectable nanotube growth on SiO2 layers with thickness (TSiO2) less than ∼5–6 nm. For 6 nm 50 nm. We grew nanotubes with multiple lengths at close proximity in a single step by using substrates with regions of different TSiO2. Such processing strategies would be attractive for creating nanotube mesoscale architectures for device applications.

Silicon oxide thickness-dependent growth of carbon nanotubes

Controlled vibration selectively propels multiple microliter-sized drops along microstructured tracks, leading to simple microfluidic systems that rectify oscillations of the three-phase contact line into asymmetric pinning forces that propel each drop in the direction of higher pinning.

Rajashree Baskaran

Papers

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

Tunable Microelectromechanical Filters that Exploit Parametric Resonance

Contact transfer of aligned carbon nanotube arrays onto conducting substrates

Silicon oxide thickness-dependent growth of carbon nanotubes

Controlling liquid drops with texture ratchets.