Abstract In this work we demonstrate how one can improve the angular rate sensitivity of ring/disk resonating gyroscopes by tailoring their nonlinear behavior by systematic shaping of the gyroscope body and electrodes, and by the tuning of bias voltages on segmented electrodes. Of specific interest are the drive and sense mode Duffing nonlinearities, which limit their dynamic ranges, and the intermodal dispersive coupling between these modes that provides parametric amplification of the sense mode output signal. These two effects have the same physical origins and are in competition in terms of system performance, which naturally calls for optimization considerations. The present analysis is based on a systematic modeling of the nonlinear response of these devices by which we explore ways in which one can optimize the angular rate sensitivity by manipulating the mechanical and electrostatic contributions to the nonlinearities. In particular, non-uniform modifications of the gyroscope body thickness are employed to affect the mechanical contributions to these parameters, while the electrostatic components are manipulated via shaping of the resonator-electrode gap and by applying non-uniform bias voltages among segmented electrodes around the gyroscope body. These models predict that such relatively simple alterations can achieve improvements in gain by about an order of magnitude when compared to devices with uniform layouts.
more »
« less
Strong internal resonance in a nonlinear, asymmetric microbeam resonator
Abstract Exploiting nonlinear characteristics in micro/nanosystems has been a subject of increasing interest in the last decade. Among others, vigorous intermodal coupling through internal resonance (IR) has drawn much attention because it can suggest new strategies to steer energy within a micro/nanomechanical resonator. However, a challenge in utilizing IR in practical applications is imposing the required frequency commensurability between vibrational modes of a nonlinear micro/nanoresonator. Here, we experimentally and analytically investigate the 1:2 and 2:1 IR in a clamped–clamped beam resonator to provide insights into the detailed mechanism of IR. It is demonstrated that the intermodal coupling between the second and third flexural modes in an asymmetric structure (e.g., nonprismatic beam) provides an optimal condition to easily implement a strong IR with high energy transfer to the internally resonated mode. In this case, the quadratic coupling between these flexural modes, originating from the stretching effect, is the dominant nonlinear mechanism over other types of geometric nonlinearity. The design strategies proposed in this paper can be integrated into a typical micro/nanoelectromechanical system (M/NEMS) via a simple modification of the geometric parameters of resonators, and thus, we expect this study to stimulate further research and boost paradigm-shifting applications exploring the various benefits of IR in micro/nanosystems.
more »
« less
- Award ID(s):
- 1738723
- NSF-PAR ID:
- 10227986
- Date Published:
- Journal Name:
- Microsystems & Nanoengineering
- Volume:
- 7
- Issue:
- 1
- ISSN:
- 2055-7434
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Metal-mediated cross-coupling reactions offer organic chemists a wide array of stereo- and chemically-selective reactions with broad applications in fine chemical and pharmaceutical synthesis.1 Current batch-based synthesis methods are beginning to be replaced with flow chemistry strategies to take advantage of the improved consistency and process control methods offered by continuous flow systems.2,3 Most cross-coupling chemistries still encounter several issues in flow using homogeneous catalysis, including expensive catalyst recovery and air sensitivity due to the chemical nature of the catalyst ligands.1 To mitigate some of these issues, a ligand-free heterogeneous catalysis reaction was developed using palladium (Pd) loaded into a polymeric network of a silicone elastomer, poly(hydromethylsiloxane) (PHMS), that is not air sensitive and can be used with mild reaction solvents (ethanol and water).4 In this work we present a novel method of producing soft catalytic microparticles using a multiphase flow-focusing microreactor and demonstrate their application for continuous Suzuki-Miyaura cross-coupling reactions. The catalytic microparticles are produced in a coaxial glass capillary-based 3D flow-focusing microreactor. The microreactor consists of two precursors, a cross-linking catalyst in toluene and a mixture of the PHMS polymer and a divinyl cross-linker. The dispersed phase containing the polymer, cross-linker, and cross-linking catalyst is continuously mixed and then formed into microdroplets by the continuous phase of water and surfactant (sodium dodecyl sulfate) introduced in a counter-flow configuration. Elastomeric microdroplets with a diameter ranging between 50 to 300 micron are produced at 25 to 250 Hz with a size polydispersity less than 3% in single stream production. The physicochemical properties of the elastomeric microparticles such as particle swelling/softness can be tuned using the ratio of cross-linker to polymer as well as the ratio of polymer mixture to solvent during the particle formation. Swelling in toluene can be tuned up to 400% of the initial particle volume by reducing the concentration of cross-linker in the mixture and increasing the ratio of polymer to solvent during production.5 After the particles are produced and collected, they are transferred into toluene containing palladium acetate, allowing the particles to incorporate the palladium into the polymer network and then reduce the palladium to Pd0 with the Si-H functionality present on the PHMS backbones. After the reduction, the Pd-loaded particles can be washed and dried for storage or switched into an ethanol/water solution for loading into a micro-packed bed reactor (µ-PBR) for continuous organic synthesis. The in-situ reduction of Pd within the PHMS microparticles was confirmed using energy dispersive X-ray spectroscopy (EDS), X-ray photoelectron spectroscopy (XPS) and focused ion beam-SEM, and TEM techniques. In the next step, we used the developed µ-PBR to conduct continuous organic synthesis of 4-phenyltoluene by Suzuki-Miyaura cross-coupling of 4-iodotoluene and phenylboronic acid using potassium carbonate as the base. Catalyst leaching was determined to only occur at sub ppm concentrations even at high solvent flow rates after 24 h of continuous run using inductively coupled plasma mass spectrometry (ICP-MS). The developed µ-PBR using the elastomeric microparticles is an important initial step towards the development of highly-efficient and green continuous manufacturing technologies in the pharma industry. In addition, the developed elastomeric microparticle synthesis technique can be utilized for the development of a library of other chemically cross-linkable polymer/cross-linker pairs for applications in organic synthesis, targeted drug delivery, cell encapsulation, or biomedical imaging. References 1. Ruiz-Castillo P, Buchwald SL. Applications of Palladium-Catalyzed C-N Cross-Coupling Reactions. Chem Rev. 2016;116(19):12564-12649. 2. Adamo A, Beingessner RL, Behnam M, et al. On-demand continuous-flow production of pharmaceuticals in a compact, reconfigurable system. Science. 2016;352(6281):61 LP-67. 3. Jensen KF. Flow Chemistry — Microreaction Technology Comes of Age. 2017;63(3). 4. Stibingerova I, Voltrova S, Kocova S, Lindale M, Srogl J. Modular Approach to Heterogenous Catalysis. Manipulation of Cross-Coupling Catalyst Activity. Org Lett. 2016;18(2):312-315. 5. Bennett JA, Kristof AJ, Vasudevan V, Genzer J, Srogl J, Abolhasani M. Microfluidic synthesis of elastomeric microparticles: A case study in catalysis of palladium-mediated cross-coupling. AIChE J. 2018;0(0):1-10.more » « less
-
A single micro-electromechanical (MEMS) resonator can be shown to exhibit behaviors unexpected in a simple resonant structure. For small driving forces, the resonator displays typical simple harmonic oscillator re- sponse. As the driving force is increased, the resonator shows the slightly more complex, but well understood, Duffing response. Rather unexpected response behavior can appear when the resonator frequency is detuned by nonlinear- ity to where two oscillatory modes of the resonator begin to interact through nonlinear coupling due to an internal resonance. The paper focuses on how the resonator response changes as the internal resonance is approached in the operating parameter space and how that behavior is conveniently represented in a bifurcation diagram. This behavior is accurately captured by a generic mathematical model. We describe an analysis of the model which shows how this coupled response varies with the system and drive parameters, especially focusing on the nonlinear coupling strength between the two modes.more » « less
-
more » « less
Resonant enhancement of nonlinear photonic processes is critical for the scalability of applications such as long-distance entanglement generation. To implement nonlinear resonant enhancement, multiple resonator modes must be individually tuned onto a precise set of process wavelengths, which requires multiple linearly-independent tuning methods. Using coupled auxiliary resonators to indirectly tune modes in a multi-resonant nonlinear cavity is particularly attractive because it allows the extension of a single physical tuning mechanism, such as thermal tuning, to provide the required independent controls. Here we model and simulate the performance and tradeoffs of a coupled-resonator tuning scheme which uses auxiliary resonators to tune specific modes of a multi-resonant nonlinear process. Our analysis determines the tuning bandwidth for steady-state mode field intensity can significantly exceed the inter-cavity coupling rate
g if the total quality factor of the auxiliary resonator is higher than the multi-mode main resonator. Consequently, over-coupling a nonlinear resonator mode to improve the maximum efficiency of a frequency conversion process will simultaneously expand the auxiliary resonator tuning bandwidth for that mode, indicating a natural compatibility with this tuning scheme. We apply the model to an existing small-diameter triply-resonant ring resonator design and find that a tuning bandwidth of 136 GHz ≈ 1.1 nm can be attained for a mode in the telecom band while limiting excess scattering losses to a quality factor of 106. Such range would span the distribution of inhomogeneously broadened quantum emitter ensembles as well as resonator fabrication variations, indicating the potential for the auxiliary resonators to enable not only low-loss telecom conversion but also the generation of indistinguishable photons in a quantum network. -
A locally resonant meta-surface for preferential excitation of a guided mode in a hollow pipe can improve ultrasonic guided wave inspection of pipelines. The proposed meta-surface comprises a periodic arrangement of bonded prismatic rod-like resonators in the circumferential and axial directions of the pipe. We demonstrate the presence of bandgaps for the low-frequency axisymmetric longitudinal modes L(0,1) and L(0,2) and the torsional mode T(0,1). The generated bandgaps can be used to filter the higher harmonics associated with the system nonlinearity to improve nonlinear ultrasonic measurements on pipes. These bandgaps exist even for the non-axisymmetric flexural modes but with their hybridized dispersion curves exhibiting mode-coupling for higher circumferential orders. Moreover, a “partial” bandgap is obtained where preferential transmission of the L(0,2) mode over L(0,1) is possible. We discuss the potential advantages of this partial bandgap to improve pipeline inspections using the L(0,2) mode. Time-domain finite element analyses are used to validate the presence of these bandgaps under radial, circumferential, and axial excitation that mimics the excitation using a ring of piezoelectric transducers. Finally, we discuss the influence of resonator spacing, filling fraction, and the number of resonator rings on the bandgaps for an informed meta-surface design.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1038/s41378-020-00230-1
