Order Resonance Research Articles

Pervasive nonlinear vibrations due to rod-obstacle contact

Simple mechanical contact between a deformable body and a rigid obstacle can lead to rich nonlinear behavior even when the equations governing the body’s motion are otherwise linear. We study the nonlinear dynamics of contact both numerically and analytically in a model problem of an Euler–Bernoulli beam and a flat substrate. This problem is relevant to microelectromechanical systems (MEMS) and marine structures. We show the nonlinearity to be dominantly quadratic, thereby giving rise to superharmonic and combination resonances of order two. We then demonstrate that similar nonlinear dynamics can in fact arise in far more general circumstances with nonlinear rods in contact with curved surfaces.

Overview on second & third order resonant switch mode power converter for variable input voltage applications

DC-DC converters have wide applications in the field of battery charger, distributed generation, power supplies and so on. There are various isolated and non-isolated topologies available which has to be chosen based on the size, cost , weight, application, power range and duty of the converter. Due to increasing applicability of DC-DC converters, it is essential to enhance the efficiency, controllability and output regulation to a step ahead. Resonant converters at high frequency has gained attention in the market to a large scale due to its low size and weight. With the developing enthusiasm for this subject, it is essential to have a detailed review to sum up and update a unique reference about the soft switching configurations for better performance of the converter. The paper provides a brief overview in two and three element soft switching configurations. Moreover, The current technologies evolved in the field of resonant converters are also briefed for wide input voltage applications.

L- and X-Band Dual-Frequency Synthesizer Utilizing Lithium Niobate RF-MEMS and Open-Loop Frequency Dividers.

This article presents an 8.6-GHz oscillator utilizing the third-order antisymmetric overtone ( A3 ) in a lithium niobate (LiNbO3) radio frequency microelectromechanical systems (RF-MEMS) resonator. The oscillator consists of an acoustic resonator in a closed loop with cascaded RF tuned amplifiers (TAs) built on Taiwan Semiconductor Manufacturing Company (TSMC) RF general purpose (GP) 65-nm complementary metal-oxide semiconductor (CMOS). The TAs bandpass response, set by on-chip inductors, satisfies Barkhausen's oscillation conditions for A3 while suppressing the fundamental and higher order resonances. Two circuit variations are implemented. The first is an 8.6-GHz standalone oscillator with a source-follower buffer for direct 50- Ω -based measurements. The second is an oscillator-divider chain using an on-chip three-stage divide-by-two frequency divider for a ~1.1-GHz output. The standalone oscillator achieves a measured phase noise of -56, -113, and -135 dBc/Hz at 1 kHz, 100 kHz, and 1 MHz offsets from an 8.6-GHz output while consuming 10.2 mW of dc power. The oscillator also attains a figure-of-merit of 201.6 dB at 100-kHz offset, surpassing the state-of-the-art (SoA) oscillators-based electromagnetic (EM) and RF-MEMS. The oscillator-divider chain produces a phase noise of -69.4 and -147 dBc/Hz at 1 kHz and 1 MHz offsets from a 1075-MHz output while consuming 12 mW of dc power. Its phase noise performance also surpasses the SoA L -band phase-locked loops (PLLs). With further optimization, this work can enable low-power multistandard wireless transceivers featuring high speed, high sensitivity, and high selectivity in small-form factors.

Design of Multimodal Absorption in the Mid-IR: A Metal Dielectric Metal Approach.

Specific control on the mid-infrared (mid-IR) emission properties is attracting increasing attention for thermal camouflage and passive cooling applications. Metal–dielectric–metal (MDM) structures are well known to support strong magnetic polariton resonances in the optical and near-infrared range. We extend the current understanding of such an MDM structure by specifically designing Au disc arrays on top of ZnS–Au–Si substrates and pushing their resonances to the mid-IR regime. Therefore, we combine fabrication via lift-off photolithography with the finite element method and an inductance–capacitance model. With this combination of techniques, we demonstrate that the magnetic polariton resonance of the first order strongly depends on the individual disc diameter. Furthermore, the fabrication of multiple discs within one unit cell allows a linear combination of the fundamental resonances to conceive broadband absorptance. Quite importantly, even in mixed resonator cases, the absorptance spectra can be fully described by a superposition of the individual disc properties. Our contribution provides rational guidance to deterministically design mid-IR emitting materials with specific narrow- or broadband properties.

Analysis of Influence of Scale Factor and Design on Performance Characteristics and Stress Strain State of Micro Sensing Element

A new type of semitoroidal type sensing element is discussed in this scientific article. In the study, possible modes of vibration were identified and a working one was selected. A dynamic analysis was carried out and it was established what force is necessary to excite the resonator in order to ensure both the vibration amplitude that is convenient for reading, and the strength of the resonator. The study of the influence of the scale factor on the performance characteristics and stress strain state of the micro SE was carried out. The SE sizes were changed proportionally. The simulation was carried out with seven options concerning sizes, the calculation was performed with the help of the finite element method, for each individual case, and the results were tabulated. Based on the results obtained, graphs were plotted and conclusions were drawn concerning the influence of the scale factor on the performance characteristics and stress strain state of the device. After that, tasks were identified for further study of micro SE, as an advanced model. Finally, the references including eight sources were given.

Experimental study on modal characteristics of flame tube in a can type combustor in aero-engine

The flame tube is a key component in the combustor of the gas turbine engine. It is important to understand the structure dynamic characteristics of the tube. The present paper used both FEM and experiment modal method to examine the vibrating modal characteristics of a flame tube in a can type combustor. Its first six orders' modal parameters such as frequency and mode were obtained, respectively. The calculated results show that the flame tube vibrates along x- and y-directions. The tangential vibration with several circumferential waves and few horizontal half waves was observed. The tube's lower order resonant frequencies vary from 145 to 600 Hz, and its higher order frequencies are about 1000 Hz. The first three orders' frequencies of the tube in experiment are lower by about 30% than those by FEM method, but the calculated last three orders' frequencies are consistent with the experimental ones.

Placement of multiple low order resonance frequencies due to rigid coupling of a rigid and small subsystem to a main system

Placement of multiple low order resonance frequencies due to rigid coupling of a rigid and small subsystem to a main system

Efficient single-photon pair generation by spontaneous parametric down-conversion in nonlinear plasmonic metasurfaces.

Spontaneous parametric down-conversion (SPDC) is one of the most versatile nonlinear optical techniques for the generation of entangled and correlated single-photon pairs. However, it suffers from very poor efficiency leading to extremely weak photon generation rates. Here we propose a plasmonic metasurface design based on silver nanostripes combined with a bulk lithium niobate (LiNbO3) crystal to realize a new scalable, ultrathin, and efficient SPDC source. By coinciding fundamental and higher order resonances of the metasurface with the generated signal and idler frequencies, respectively, the electric field in the nonlinear media is significantly boosted. This leads to a substantial enhancement in the SPDC process which, subsequently, by using the quantum-classical correspondence principle, translates to very high photon-pair generation rates. The emitted radiation is highly directional and perpendicular to the metasurface in contrast to relevant dielectric structures. The incorporation of circular polarized excitation further increases the photon-pair generation efficiency. The presented work will lead to the design of new efficient ultrathin SPDC single-photon nanophotonic sources working at room temperature that are expected to be critical components in free-space quantum optical communications. In a more general context, our findings can have various applications in the emerging field of quantum plasmonics.

Optimal design and experiment study of the double spherical rotor of the MSCSG.

The magnetically suspended control and sense gyroscope (MSCSG) integrates spacecraft attitude measurement and control function; this paper proposes a double spherical rotor (DSR) for MSCSG. The DSR realizes the five degrees of freedom (DOFs) full active control and full channel magnetic path decoupling by the following design: the spherical axial/radial reluctance magnetic bearings are adopted to control the 3DOFs translation of rotor in the range of double spherical envelope, Lorentz force magnetic bearing (LFMB) is used to precisely drive the 2DOFs universal deflection of rotor. The optimization model is established based on the structural mechanical analysis, taking the deviation between rotor centroid and shape center as the optimization objective, choosing the first order resonance frequency, maximum equivalent stress, rigid body displacement, polar moment of inertia and inertia ratio as constraints. Then the DSR is optimized and simulated by the finite element, the MSCSG principle prototype based on DSR is successfully developed, the online dynamic balance experiment and modal test of the DSR are conducted, where the vibration amount of the DSR decreases from 20 μm before the experiment to 0.14 μm after the experiment, which decreases by 99.3%, the first test modal is 2881 Hz which is 5% different from the finite element simulation value of 3034 Hz. The results show that the DSR has the good mechanical properties and magnetic circuit decoupling characteristics.

Design of a High-Sensitivity Microstrip Patch Sensor Antenna Loaded with a Defected Ground Structure Based on a Complementary Split Ring Resonator.

A comparative study to determine the most highly sensitive resonant frequency among the first four resonant frequencies of a conventional patch antenna and defected ground structure (DGS)-loaded patch antennas using commonly used DGS geometries in the literature, such as a rectangular slit, single-ring complementary split ring resonators (CSRRs) with different split positions, and double-ring CSRRs (DR-CSRRs) with different locations below the patch, for relative permittivity measurement of planar materials was conducted. The sensitivity performance for placing the DGS on two different locations, a center and a radiating edge of the patch, was also compared. Finally, the effect of scaling down the patch size of the DGS-loaded patch antenna was investigated in order to enhance the sensitivities of the higher order resonant frequencies. It was found that the second resonant frequency of the DR-CSRR DGS-loaded patch antenna aligned on a radiating edge with a half scaled-down patch size shows the highest sensitivity when varying the relative permittivity of the material under test from 1 to 10. In order to validate the simulated performance of the proposed antenna, the conventional and the proposed patch antennas were fabricated on 0.76-mm-thick RF-35 substrate, and they were used to measure their sensitivity when several standard dielectric substrate samples with dielectric constants ranging from 2.17 to 10.2 were loaded. The measured sensitivity of the second resonant frequency for the proposed DGS-loaded patch antenna was 4.91 to 7.72 times higher than the first resonant frequency of the conventional patch antenna, and the measured performance is also slightly better compared to the patch antenna loaded with a meander-line slot on the patch.

Suppression of spurious harmonic responses in superconducting microstrip spiral filters using gold overlay and stagger tuning

The higher order resonances of microwave superconducting filters with spiral resonators were suppressed, giving a very wide stop-band. In one filter spirals were modified to have equal fundamental resonances, but different higher order resonances, by adding stubs and using non-uniform line width. The higher resonances were reduced to −39 dB, in a stop band up to 4.3 times the pass band centre. In another filter, parasitic resistive resonators were added, suppressing the responses to −57 dB. The resistance is provided by patterning the 200 nm gold overlay already required for the external contacts. The increase in pass band loss is not measurable. Measurements of a single spiral resonator with a gold-YBCO bi-layer (200 and 600 nm respectively) suggest that the resistivity of the gold layer at 15 K is the order of 22 times that of bulk gold, a slight advantage for the present application. At 100 K, it is about double.

Design of Mechanical Multi-Sensor for Contaminated Water Filter Applications

Effect of addition (salts, soil and bacteria) on piezoelectric detecting a signal of a specific liquid like water has been inspected here in the project. Identifying signals (piezoelectric) categorized and accomplished by usage of transducer that conducts a mechanical signal in the direction of the water liquid cell, and then the receptor collects the weakened indications. The quartz cell (contains water solution) embedded between the two piezo crystals and piezo crystals with silver (Ag) nanowire thin film prepared using hydrothermal method. It is clear that the formation of the yield is rope-similar and close to be uniform in width (60 ± 10 nm) whereas the extent is in a moderately wide range (from 0.2 to 4 μm) with an average at 2.5 μm. Four peaks can be recognized in XRD results, it is clear according to the ASTM cards that the film is polycrystalline at which (111), (200) and (220) silver (Ag) respectively. The range of functioning frequencies was (400 kHz - 40MHz), for all specimens, the measurement outcomes that involved reporting the first order resonance frequencies. The data presented shifting the resonance frequency to the higher order frequency for addititive cases (salts+soil+bacteria) of water.

Label-free biosensor array comprised of Vernier microring resonator and 3 × 3 optical coupler

A 3 × 3 linearly distributed optical coupler was used in a Vernier -based SOI microring resonator in order to design a label-free biosensor takes advantage of low loss and fully isolated reference unit from the measurand. The coupled mode theory was used to drive the optical transfer function of the system. The electric field propagation through the sensor’s waveguides and the normalized light transmission versus the wavelength spectrum were studied using variational finite-difference time domain (varFDTD) method. The sensor performance was characterized based on the refractive index variation of the optical waveguide superstrate by applying different concentrations of glucose and NaCl solutions. Then, three types of cancer cells, including MCF7, MDA-MB-231 and Hella cell line, were detected based on the antibody–antigen reaction. The sensitivity and the detection limit of the proposed sensor were measured to be 578 nm/RIU and 2.8 × 10−5 RIU, respectively. Results show the capability of the proposed sensor as a high-performance device for label-free sensing. The proposed sensor can potentially be used for measuring the sucrose concentration in food industries and accurate determination of seawater salinity.

Broadband optical absorption using graphene-wrapped cross-hair/nano-rod combination

In this paper, an assembly of substrate mediated graphene-coated cylindrical nano-rods is proposed as an efficient broadband absorber. Initially, a square lattice of isolated graphene-based particles is considered and a single-band perfect optical absorber is obtained. Then, the possibility of absorption spectrum modulation using the lattice periodicity is illustrated. Moreover, it is exhibited that the performance is stable concerning any polarization state and incident angle up to around 60°. The absorption mechanism relies on the excitation of localized surface plasmon resonances (LSPRs) of various orders on the different sections of the unit cell. Later, the particles are connected through optimized bridges to enhance the operating bandwidth. The bridges also offer the opportunity for the real-time tunability of the absorption spectrum by the electrostatic scheme. The attained absorption band regarding the efficiency of 90% is extended to a 15.43 THz span (18.57–34 THz) using a geometrically simple structure.

Coplanar waveguide low pass filter based on square complementary split ring resonator with wide rejection

In this paper, we present a novel coplanar waveguide low pass filter (LPF) structure based on the use of square complementary split ring resonators (CSRRs) in order to enhance the performances of a low pass filter. Especially, to enlarge the bandwidth of the LPF, the insertion losses and to increase the rejection of the LPF. The CSRRs are optimised and inserted periodically along the center conductor of the CPW line with a CPW ground integrating stubs permitting to enlarge the bandwidth. The simulation results of this filter show a -3 dB cut-off frequency equal to fc = 5.28 GHz. The designed filter has a good rejection in the stop band which below -20 dB and presents a good insertion loss in the bandwidth. The proposed filter has been fabricated and tested which give a good agreement between simulation and measurement results, the whole dimensions of the validated filter are 35.48x21.16 mm2. The originality of this work is the wide rejection band and the miniature dimensions. © 2020, Universitas Ahmad Dahlan.

High dimensional nonlinear spring characteristic modelling and vibration analyses of subharmonic resonance of a dual-rotor system based on energy tracks

The subharmonic resonance is a typical nonlinear vibration that occurs in a nonlinear rotor system. In this paper, expressions of the potential energy of rotor systems are derived systematically, and the high dimensional nonlinear spring characteristic modelling is revealed firstly through the potential energy with nonlinear variation characteristics. A novel nonlinear dual-rotor model considering nonlinear spring characteristics is proposed to reveal the inducing mechanism of subharmonic resonances of rotors and to study vibration characteristics of subharmonic resonances of the dual-rotor system. The new concepts such as energy tracks, the energy-phase plane and energy-spectrum analyses are presented to analyze nonlinear variation characteristics of the potential energy of rotors, and results show that different nonlinear coefficients correspond to subharmonic resonances of different orders, respectively. The resonance responses in the vicinities of critical speeds of subharmonic resonances of orders 1/2 and 1/3 to be obtained by numerical simulations and theoretical analyses are discussed comprehensively. It is found that a group of independent branching solutions in the solution space appears corresponding to subharmonic resonances in the vicinity of coupling subharmonic critical speeds. In addition, analysis results of numerical simulations based on energy concepts are consistent with results of theoretical analyses about the potential energy of rotors. This study is beneficial to understand the inducing mechanism of subharmonic resonances of rotors, and verifies the correctness of the high dimensional nonlinear spring characteristic modelling and the proposed nonlinear dynamic model of the dual-rotor system.

Trimodal structure of Hercules stream explained by originating from bar resonances

ABSTRACT Gaia Data Release 2 revealed detailed structures of nearby stars in phase space. These include the Hercules stream, whose origin is still debated. Most of the previous numerical studies conjectured that the observed structures originate from orbits in resonance with the bar, based on static potential models for the Milky Way. We, in contrast, approach the problem via a self-consistent, dynamic, and morphologically well-resolved model, namely a full N-body simulation of the Milky Way. Our simulation comprises about 5.1 billion particles in the galactic stellar bulge, bar, disc, and dark-matter halo and is evolved to 10 Gyr. Our model’s disc component is composed of 200 million particles, and its simulation snapshots are stored every 10 Myr, enabling us to resolve and classify resonant orbits of representative samples of stars. After choosing the Sun’s position in the simulation, we compare the distribution of stars in its neighbourhood with Gaia’s astrometric data, thereby establishing the role of identified resonantly trapped stars in the formation of Hercules-like structures. From our orbital spectral-analysis, we identify multiple, especially higher order resonances. Our results suggest that the Hercules stream is dominated by the 4:1 and 5:1 outer Lindblad and corotation resonances. In total, this yields a trimodal structure of the Hercules stream. From the relation between resonances and ridges in phase space, our model favoured a slow pattern speed of the Milky-Way bar (40–45 $\mathrm{km \, s^{-1} \, kpc^{-1}}$).

Constraining protoplanetary discs with exoplanetary dynamics: Kepler-419 as an example

ABSTRACT We investigate the origins of Kepler-419, a peculiar system hosting two nearly coplanar and highly eccentric gas giants with apsidal orientations liberating around anti-alignment, and use this system to place constraints on the properties of their birth protoplanetary disc. We follow the proposal by Petrovich, Wu, & Ali-Dib that these planets have been placed on these orbits as a natural result of the precessional effects of a dissipating massive disc and extend it by using direct N-body simulations and models for the evolution of the gas discs, including photoevaporation. Based on a parameter space exploration, we find that in order to reproduce the system the initial disc mass had to be at least 95 MJup and dissipate on a time-scale of at least 104 yr. This mass is consistent with the upper end of the observed disc masses distribution, and the dissipation time-scale is consistent with photoevaporation models. We study the properties of such discs using simplified 1D thin-disc models and show that they are gravitationally stable, indicating that the two planets must have formed via core accretion and thus prone to disc migration. We hence finally investigate the sensitivity of this mechanism to the outer planet’s semimajor axis, and find that the nearby 7:1, 8:1, and 9:1 mean-motion resonances can completely quench this mechanism, while even higher order resonances can also significantly affect the system. Assuming the two planets avoid these high-order resonances and close encounters, the dynamics seems to be rather insensitive to planet c semimajor axis, and thus orbital migration driven by the disc.

Universal generation of devil's staircases near Hopf bifurcations via modulated forcing of nonlinear systems

The discrete circle map is the archetypical example of a driven periodic system, showing a complex resonance structure under a change of the forcing frequency known as the devil's staircase. Adler's equation can be seen as the direct continuous equivalent of the circle map, describing locking effects in periodic systems with continuous forcing. This type of locking produces a single fundamental resonance tongue without higher-order resonances, and a devil's staircase is not observed. We show that, with harmonically modulated forcing, nonlinear oscillations close to a Hopf bifurcation generically reproduce the devil's staircase even in the continuous case. Experimental results on a semiconductor laser driven by a modulated optical signal show excellent agreement with our theoretical predictions. The locking appears as a modulation of the oscillation amplitude as well as the angular oscillation frequency. Our results show that by proper implementation of an external drive, additional regions of stable frequency locking can be introduced in systems which originally show only a single Adler-type resonance tongue. The induced resonances can be precisely controlled via the modulation parameters.

Transfers of energy through fast diffusion channels in some resonant PDEs on the circle

<p style='text-indent:20px;'>In this paper we consider two classes of resonant Hamiltonian PDEs on the circle with non-convex (respect to actions) first order resonant Hamiltonian. We show that, for appropriate choices of the nonlinearities we can find time-independent linear potentials that enable the construction of solutions that undergo a prescribed growth in the Sobolev norms. The solutions that we provide follow closely the orbits of a nonlinear resonant model, which is a good approximation of the full equation. The non-convexity of the resonant Hamiltonian allows the existence of <i>fast diffusion channels</i> along which the orbits of the resonant model experience a large drift in the actions in the optimal time. This phenomenon induces a transfer of energy among the Fourier modes of the solutions, which in turn is responsible for the growth of higher order Sobolev norms.</p>