First-order Resonance Research Articles

Highly sensitive trace gas detection based on a miniaturized 3D-printed Y-type resonant photoacoustic cell.

We report, what we believe to be, a novel miniaturized 3D-printed Y-type resonant photoacoustic cell (YRPAC) consisting of a frustum of cone-type buffer chamber and a cylindrical resonant chamber. The volume of the designed YRPAC is about 7.0 cm3, which is only about a half of the T-resonant photoacoustic cell (TRPAC). The finite element simulation of the sound field distribution of the TRPAC and YRPAC based on COMSOL shows that the photoacoustic signal is enhanced with the shape of the buffer chamber changing from the traditional cylinder to a frustum of cone. The photoacoustic spectroscopy (PAS) system, utilizing the YRPAC and TRPAC as the photoacoustic reaction units, a 1653.7 nm distributed feedback (DFB) laser as the excitation light source, a cantilever beam acoustic sensor as the acoustic sensing unit, and a high-speed spectrometer as the demodulation unit, has been successfully developed for high-sensitivity trace CH4 sensing. When the CH4 concentration is 1000 ppm, the 2f signal of YRPAC in the first-order resonance mode is 2.3 nm, which is 1.7 times higher than the 2f signal amplitude of TRPAC. The detection sensitivity and minimum detection limit for the PAS system are 2.29 pm/ppm and 52.8 parts per billion (ppb) at 100 s of averaging time. The reported YRPAC has higher sensitivity, smaller size, and faster response time compared to the conventional TRPAC, which can provide a new solution for PAS development.

Performance analysis of nonlinear piezoelectric energy harvesting system under bidirectional excitations

In this paper, a cantilever beam piezoelectric energy harvester model of nonlinear partial differential equation based on Hamilton's Principle is established. A piezoelectric device using a bimorph cantilever beam with a fixed is subjected to horizontal and vertical excitation. Based on the Euler-Bernoulli thin beam model assumptions and inextensible deformation, the analysis further includes the effects of geometric nonlinearity and damping nonlinearity. The reduced-order nonlinear partial differential equations of motion with electro-mechanical coupling distributed parameter are derived by using Galerkin method. By using the method of multiple scales and solving the equations of motion, the energy harvester in its fundamental first-order resonance response is analyzed and the amplitudes of fundamental transverse deflection, output voltage and output power are determined. The major influence aspects of excitation amplitude, linear damping coefficient, nonlinear damping coefficient, impedance, nonlinear electro-mechanical coupling coefficient on transverse deflection, voltage and power are analyzed. The result shows that the linear damping coefficient and resistance affect the initial threshold of parametric excitation. The combination of parametric excitation and direct excitation gives full play to the advantages of parametric excitation and improve the energy conversion efficiency of the energy harvesting system.

A Six-planet Resonance Chain in K2-138?

The K2-138 system hosts six planets and presents an interesting case study due to its distinctive dynamical structure. Its five inner planets are near a chain of 3/2 two-body mean-motion resonances, while the outermost body (planet g) is significantly detached, having a mean-motion ratio of n f/n g ∼ 3.3 with its closest neighbor. We show that the orbit of m g is actually consistent with the first-order three-planet resonance (3P-MMR) characterized by the relation 2n e − 4n f + 3n g = 0 and is the first time a pure first-order 3P-MMR has been found in a multiplanet system and tied to its current dynamical structure. Adequate values for the masses allow one to trace the dynamical history of the system from an initial capture in a six-planet chain (with n f/n g in a 3/1 resonance) up to its current configuration due to tidal interactions over the age of the star. The increase in resonance offset with semimajor axis, as well as its large value for n f/n g, can be explained by the slopes of the pure three-planet resonances in the mean-motion ratio plane. The triplets slide outward over these curves when the innermost pair is pulled apart by tidal effects, in a pantograph-like manner. The capture into the 3P-MMR is found to be surprisingly robust given similar masses for m g and m f, and it is possible that the same effect may also be found in other compact planetary systems.

Low-frequency Resonant Photoacoustic Gas Sensor by Employing Hollow Core Fiber-Based O-Shaped Multipass Cells.

A low-frequency flexible resonant photoacoustic (PA) gas sensor using an O-shaped multipass cell is demonstrated. The PA sensor employed a flexible gradually tapered leaky hollow core fiber (LHCF). The LHCF was bent to be an end-to-end structure to make full use of the incident light. Additionally, the two ends of the LHCF were put inside a single buffer chamber, yielding an equivalent H-type acoustic resonator. The geometric size was reduced thanks to the bending structure. The geometric length of the LHCF was 500 mm. A micro-electro-mechanical-systems electrical microphone was installed at the center of the resonant tube to detect the PA signal. The proposed PA gas sensor exhibited a first-order longitudinal resonance frequency of 408 Hz. Trace acetylene (C2H2) was used as the target gas. The minimum detectable limit was calculated to be 25.8 parts-per-billion (ppb) with an average time of 400 s, which was 1.93 times higher than that of a single-pass PA gas sensor. The normalized noise-equivalent absorption coefficient and the PA cell constant were calculated to be 9.6 × 10-9 W·cm-1·Hz-1/2 and 8295 Pa/W·cm-1, respectively. The PA gas sensor owns a low resonance frequency and can be used for detection of most of the polar gaseous molecules, especially suitable for gas molecules with a long V-T relation time, such as carbon monoxide and carbon dioxide.

Development and Application of Eddy Current Damping-Based Tuned Mass Damper for Wind-Induced Vibration Control of Transmission Tower

To reduce the low-order vibrations of high-voltage transmission towers in response to strong winds, a tuned mass damper (TMD) that uses eddy current damping (ECD) with omnidirectional damping function (ECD-TMD) is proposed here. Compared with previous similar devices, the outstanding advantage of the proposed ECD-TMD lies in its use of non-contact ECD, structural simplicity, lack of internal friction, ability to sense micro-vibrations, and in the asymmetric cantilever pendulum structure that enables omnidirectional vibration suppression. Aero-elastic model wind tunnel test and field measurements were used for analyzing and validating the vibration responses of a 50-m-tall transmission tower with and without the proposed ECD-TMD. The results demonstrated that the proposed ECD-TMD reduced transmission tower’s first-order bending vibrations along and across the direction of transmission line. For the mass ratio of approximately 2%, approximately 18–27% reduction of acceleration and 10–25% reduction of displacement occurred. Because the first-order resonance of the tower body in response to wind accounts for a small fraction of the background response, the addition of a TMD device suppresses structural wind vibrations in a limiter manner but can significantly increase the first-order bending damping ratio of the tower.

Optically transparent and mechanically stretchable fractal-structured wave-absorbing metamaterial in low frequency range

Development of microwave absorption technology triggers higher requirements for the multi-function of microwave absorbing materials. An optically transparent and mechanically stretchable wave-absorbing metamaterial based on fractal structure has been proposed numerically and experimentally in the microwave low frequency range. It is designed to possess two spectrally overlapped resonances located at 4.42 GHz and 7.02 GHz, which originate from the first-order cross resonance and the second-order cross resonance, respectively. Microwave absorbing mechanisms are elaborated by normalized impedance, surface current and power loss density. Moreover, the optical transmittance of the designed wave-absorbing metamaterial is higher than 70 % in the visible region. By stretching the absorber, the frequencies of two resonant peaks occur remarkable red shift with a adjustable frequency band range of 0.64 GHz. The corresponding relationship between the variation of substrate thickness and square resistance and the shift of peak absorption frequencies is discussed. Ultimately, the wave-absorbing performance of the proposed wave-absorbing metamaterial are illustrated at different incident angles for both TE and TM waves. Research results could provide and enrich instructive guidances for realizing optically transparent and mechanically stretchable metamaterial absorber.

Measurement of Air Layer Thickness under Multi-Angle Incidence Conditions Based on Ultrasonic Resonance Reflection Theory for Flange Fasteners

During the servicing of flange fasteners, the sealing gasket and the flange cover interface are prone to separation and air contamination due to factors such as stress, corrosion, and vibration. In the detection process, there are two main issues: firstly, the conventional ultrasonic measurement methods based on the theory of acoustic elasticity are not applicable due to the small thickness of the air layer; secondly, the use of conventional vertical incidence detection methods is difficult to ensure due to the influence of the actual structure. To address these issues, this paper first establishes a mathematical model of ultrasonic resonance reflection, and then calculates the corresponding relationship between the air layer thickness and the resonance frequency under vertical incidence conditions. However, this model is difficult to use to calculate the resonance frequency under different incidence angles. To meet the requirements of different working conditions, a finite element simulation model is further established. By comparing the calculation results of the two models under vertical incidence, the reliability of the established finite element model is verified. The reflection and transmission pressure acoustic field distribution under different incidence angles and air layer thicknesses is simulated, and the function relationship between the incidence angle, air layer thickness, and the corresponding first-order resonance frequency is derived. This enables the measurement of the air layer thickness at any incidence angle, providing technical and theoretical support for practical industrial applications.

Parametric excitation analysis for system performance of piezoelectric energy harvesters

Capitalizing on the advantages of parametric excitation and real-life low frequency vibration, the steady-state response of piezoelectric energy harvesting system composing of a cantilever beam with a tip mass and horizontal excitation at the fixed end is investigated. By applying Hamilton's principle, the nonlinear partial differential equation of a cantilever bimorph piezoelectric energy harvesting system with an additional tip mass is derived and analyzed. The cantilever is modeled as an axially non-elongated Euler Bernoulli beam with geometric and damping nonlinearities. By using the Galerkin method, the nonlinear partial differential equation is reduced to an electromechanical coupling system that governs a cantilever piezoelectric energy harvesting system with a tip mass under parametric excitation. The first-order resonance response of this harvesting system is studied by using the method of multiple scales. The analytical response expressions and first-order amplitude functions for vertical displacement, output voltage and output power are derived and analyzed. The influence of different impedance and tip mass on the piezoelectric energy harvesting system performance is summarized and concluded. For the parametric excitation system, the load resistance shows significant influence on the initial threshold of the piezoelectric energy harvesters under parametric excitation. For a short circuit, the initial threshold increases with increasing load resistance. For an open circuit, the initial threshold decreases with increasing load resistance. For an open circuit resistance or a short circuit resistance under parametric excitation, an increase in the end block mass effectively reduces the resonance frequency of the piezoelectric energy harvesters. Consequently, the energy harvesting bandwidth is increased, and the harvesting effect of the piezoelectric energy harvesters is enhanced. In this paper, a more accurate and practical theoretical model is established to predict the electromechanical coupling behavior of cantilever piezoelectric energy harvester under parametric excitation. Using this approach, it is possible to complement parametric and direct excitation such that the advantages of parametric excitation can be achieved. It is also significant to improve the energy conversion efficiency of energy harvesting system.

Dynamics and Origins of the Near-resonant Kepler Planets

Short-period super-Earths and mini-Neptunes encircle more than ∼50% of Sun-like stars and are relatively amenable to direct observational characterization. Despite this, environments in which these planets accrete are difficult to probe directly. Nevertheless, pairs of planets that are close to orbital resonances provide a unique window into the inner regions of protoplanetary disks, as they preserve the conditions of their formation, as well as the early evolution of their orbital architectures. In this work, we present a novel approach toward quantifying transit timing variations within multiplanetary systems and examine the near-resonant dynamics of over 100 planet pairs detected by Kepler. Using an integrable model for first-order resonances, we find a clear transition from libration to circulation of the resonant angle at a period ratio of ≈0.6% wide of exact resonance. The orbital properties of these systems indicate that they systematically lie far away from the resonant forced equilibrium. Cumulatively, our modeling indicates that while orbital architectures shaped by strong disk damping or tidal dissipation are inconsistent with observations, a scenario where stochastic stirring by turbulent eddies augments the dissipative effects of protoplanetary disks reproduces several features of the data.

Investigation of the do minant Rossiter modal tones at the locked-on state

Rossiter resonance noise, which is flow driven cavity noise involving fluid dynamics processes, was investigated in a low-speed wind tunnel. The experiments include near-field and far-field acoustic field measurements of the rectangular cavity at different depths as well as velocity measurements of the shear layer. The rectangular cavity geometry was also designed to enable the Rossiter mode to interact with the first-order depth resonant mode in a locked-on state. The experimental results showed the variation of frequency and overall sound pressure level (OASPL) when the self-sustained oscillation was in the locked-on state. When the self-sustained oscillatory mode is in the unlocked state, the frequency of the self-sustained oscillatory mode can be predicted well by using the Rossiter formula, whereas the frequency of the dominant Rossiter mode in the locked-on state will be predicted inconsistently. Moreover, the corresponding selection of the dominant mode also depends on the resonant mode, and there are local variations in the OASPL. The results indicate that the ratio of the resonant mode frequency to the self-sustained oscillatory fundamental frequency, Rd, plays a key role in the locked-on state. In this paper, the Rossiter model is modified using the parameter Rd for the prediction of the dominant mode frequency in the locked-on state. The difference between the current formula and previous studies is that the variation of the phase delay coefficient γ with velocity is considered, and γ is related to Rd. Finally, the accuracy of the formulation is verified with experimental data from different models.

The effect of 1H offset and flip-angle on heteronuclear decoupling efficiency in ROSPAC pulsed sequence: A Floquet description.

A new heteronuclear decoupling sequence for solid-state NMR and magic angle spinning faster than 60kHz was recently introduced [Simion et al., J. Chem. Phys. 157, 014202 (2022)]. It was dubbed ROtor-Synchronized Phase-Alternated Cycles (ROSPAC), and it offers robustness for a large range of chemical shifts and low radio-frequency (RF) powers and is almost independent of the radio-frequency power. Here, we theoretically explore the robustness of the ROSPAC sequence toward 1H offset and RF field inhomogeneities, as well as the spacing effect of the π pulses on the decoupling efficiency. We use a generalized theoretical framework based on the Floquet theory to assess these parameters. The optimum decoupling conditions, where the magnitude of the second-order cross-terms and first-order resonance conditions are small, were identified.

Nonzero-Order Resonances in Single-Beam Spin-Exchange Relaxation-Free Magnetometers

Zero-field optically pumped magnetometers operating in the spin-exchange relaxation-free (SERF) regime have been extensively studied, and usually depend on zeroth-order parametric resonance to measure the magnetic field. However, the studies conducted on this topic lack thorough analyses and in-depth discussion of nonzero-order magnetic resonances in single-beam SERF magnetometers. In this paper, we analyzed the nonzero-order resonance, especially the first-order resonance, based on a single-beam SERF magnetometer, and discussed its various applications. A comprehensive theoretical analysis and experiments were conducted with respect to multiple functions, including nonzero finite magnetic field measurements, spin polarization measurement, and in situ coil constant calibration. The results showed that first-order resonance can be utilized for nonzerofinite magnetic field measurements, and the spin polarization of alkali-metal atoms can be determined by measuring the slowing-down factor using the resonance condition. Furthermore, acquiring the first-order resonance point at an equivalent zero pump light power through fitting offers an approach for quick and precise in situ coil constant calibration. This study contributes to the applications of SERF magnetometers in nonzero finite magnetic fields.

When, where, and how many planets end up in first-order resonances?

ABSTRACTThe theory of Type I migration has been widely used in many studies. Transiting multiplanet systems offer us the opportunity to examine the consistency between observation and theory, especially for those systems harbouring planets in Mean Motion Resonance (MMR). The displacement these resonant pairs show from exact commensurability provides us with information on their migration and eccentricity-damping histories. Here, we adopt a probabilistic approach, characterized by two distributions – appropriate for either the resonant or non-resonant planets – to fit the observed planet period ratio distribution. With the Markov chain Monte Carlo (MCMC) method, we find that ${\approx }15{{\ \rm per\ cent}}$ of exoplanets are in first-order (j + 1: j) MMRs, the ratio of eccentricity-to-semimajor axis damping is too high to allow overstable librations, and that the results are by-and-large consistent with Type-I migration theory. In addition, our modelling finds that a small fraction of resonant pairs is captured into resonance during migration, implying late planet formation (gas-poor). Most of the resonant pairs park themselves at the migration barrier, indicating early planet formation (gas-rich). Furthermore, after improving the criterion on two-body resonant trapping, we obtain an upper limit of the disc surface density at the time the planets are locked in resonance.

Object Identification With Minimal Precomputed Library Using Physical Aspect of Singularity Expansion Method

In this letter, we propose a method for estimating the circumferential length of metal objects without any <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> information regarding object shape and dimension. Object type can also be determined using this method with a reduced precomputed library consisting of the quality factor of fundamental natural resonance frequency and the ratio of second-order to first-order damped resonance frequency for each object type. The proposed method is applied to identify different canonical objects. Natural resonance frequencies, extracted using the matrix pencil method of singularity expansion from the scattered field from different metal objects, have been validated with physical reasoning. Simple methods for predicting the resonance frequency of triangular plates and discs have been proposed.

Dissipative Capture of Planets into First-order Mean-motion Resonances

The emergence of orbital resonances among planets is a natural consequence of the early dynamical evolution of planetary systems. While it is well established that convergent migration is necessary for mean-motion commensurabilities to emerge, recent numerical experiments have shown that the existing adiabatic theory of resonant capture provides an incomplete description of the relevant physics, leading to an erroneous mass scaling in the regime of strong dissipation. In this work, we develop a new model for resonance capture that self-consistently accounts for migration and circularization of planetary orbits, and derive an analytic criterion based upon stability analysis that describes the conditions necessary for the formation of mean-motion resonances. We subsequently test our results against numerical simulations and find satisfactory agreement. Our results elucidate the critical role played by adiabaticity and resonant stability in shaping the orbital architectures of planetary systems during the nebular epoch, and provide a valuable tool for understanding their primordial dynamical evolution.

Highly vibration-resistant sub-Hertz ultra-stable laser passing over 1700 km transport test

We present a compact ultra-stable laser at 1550 nm with a line-width of 0.57 Hz, achieved using a 50-mm length cubic optical cavity. With the help of elaborate investigation of the vibration behavior of the cavity in three directions, its physical structure was optimized for significantly improved insensitivity to vibration by increasing the first-order resonance frequency almost twice that of the previous setup. The anti-vibration capability of the ultra-stable laser was then verified in the long-distance highway transport test over more than 1700 km, which shows nearly unchanged performance compared to that before transport. A fractional frequency instability of ∼ 2.6 × 10−15 was observed at 1–10 s, approaching the thermal noise floor. To our knowledge, this is the longest-distance transport vibration test for a practical transportable laser to date. The presented system will act as the local optical oscillator for high-precision remote optical frequency transfer, and the design strategy is valuable for space-borne laser applications.

Non-perturbative investigation of low-eccentricity exterior mean motion resonances

ABSTRACT Mean motion resonances are important in the analysis and understanding of the dynamics of planetary systems. While perturbative approaches have been dominant in many previous studies, recent non-perturbative approaches have revealed novel properties in the low-eccentricity regime for interior mean motion resonances of Jupiter in the fundamental model of the circular planar restricted three-body model. Here, we extend the non-perturbative investigation to exterior mean motion resonances in the low-eccentricity regime (up to about 0.1) and for perturber mass in the range of ∼5 × 10−5 to 1 × 10−3 (in units of the central mass). Our results demonstrate that first-order exterior resonances have two branches at low eccentricity as well as low-eccentricity bridges connecting neighbouring first-order resonances. With increasing perturber mass, higher order resonances dissolve into chaos, whereas low-order resonances persist with larger widths in their radial extent but smaller azimuthal widths. For low-order resonances, we also detect secondary resonances arising from small-integer commensurabilities between resonant librations and the synodic frequency. These secondary resonances contribute significantly to generating the chaotic sea that typically occurs near mean motion resonances of higher mass perturbers.

Resonance characteristics and energy losses of an ultra-high frequency ZnO nanowire resonator

An ultra-high frequency (UHF, 300 MHz∼3 GHz) nano mechanical resonator based on defect-free zinc oxide nanowire (ZnO NW) was fabricated through a top-down processing method. Using UHF detection technology based on a lock-in amplifier, through optimized measurement of high-performance equipment, it was detected at room temperature that the ZnO NW resonator could operate at a resonance frequency of nearly 650 MHz and a quality factor Q ≈ 1000∼2500, and its force sensitivity could reach 1 f N·Hz−1/2. The deformation, driving force and first-order resonance frequency of the resonator were calculated using the continuum model and compared with the experimental data. The resonance characteristics of ZnO NW resonators under piezoelectric excitation were analyzed and compared with that under electromagnetic excitation. The effects of various loss factors on the resonance characteristics were analyzed, with emphasis on the generation mechanism of piezoelectric loss, clamping loss and eddy current loss and their effects on quality factor and force sensitivity. The ZnO NWs used in this paper have piezoelectric effect, which is rare in other NWs, and are difficult to be fabricated in a bottom-up manner. And experiments show that for ZnO NWs resonators, piezoelectric excitation has obvious advantages in Q value compared with electromagnetic excitation. Unlike the bottom-up wet etch processing method, the resonant beam structure is well protected by the top-down processing method to reduce internal defects, and the top-down fabrication method is easier to integrate into the fabrication process of integrated circuits, which provides great potential for the applications of NW resonators, such as quantum electromechanical systems and high-frequency signal processing.

Vibration characteristics of multi-dimensional isolator based on 4-PUU parallel mechanism with joint clearance

For isolating multi-dimensional vibration experienced by vehicle-mounted precise facility, a multi-dimensional vibration isolator based on parallel mechanism with joint clearance is designed and analyzed. The main thrust of this work is establishing kinematic and dynamic equations of the isolator and exploring vibration isolation capability with joint clearance. Firstly, type synthesis of the parallel mechanism with three translations and one rotation is performed. The kinematic and dynamic equations of the isolator with joint clearance are deduced. Subsequently, vibration isolation performance is simulated with different values of joint clearance under harmonic and stochastic excitations in time and frequency domain, respectively. The simulating results demonstrate the proposed isolator with joint clearance inhibit multi-dimensional vibration effectively. The first-order resonance peak is sensitive to the increment in joint clearance. Finally, the proposed multi-dimensional vibration isolator is fabricated. The vibration isolation experiment is conducted. Through experimental results, the isolator reduces multi-dimensional vibration effectively in time and frequency domain. The vibration isolation capability degenerates as the counterweight of moving platform increases.

Analysis of Resonance Transition Periodic Orbits in the Circular Restricted Three-Body Problem

Resonance transition periodic orbits exist in the chaotic regions where the 1:1 resonance overlaps with nearby interior or exterior resonances in the circular restricted three-body problem (CRTBP). The resonance transition periodic orbits have important applications for tour missions between the interior and the exterior regions of the system. In this work, following the increase of the mass parameter μ in the CRTBP model, we investigate the breakup of the first-order resonant periodic families and their recombination with the resonance transition periodic families. In this process, we can describe in detail how the 1:1 resonance gradually overlaps with nearby first-order resonances with increasing strength of the secondary’s perturbation. Utilizing the continuation method, features of the resonance transition periodic families are discussed and characterized. Finally, an efficient approach to finding these orbits is proposed and some example resonance transition periodic orbits in the Sun–Jupiter system are presented.