Resonant Beam Research Articles

Passive Location Estimation via Resonant Beam

High-accuracy indoor positioning is a demanding but challenging technology. In the Internet of Things applications, the existing indoor positioning schemes face the following challenges: 1) for the active positioning schemes, e.g., WiFi, Bluetooth, etc., the targets need power supply to emit signals; and 2) for the passive positioning schemes, e.g., Radar, Lidar, etc., the base station usually needs beam-steering control to aim at the targets for receiving sufficient reflective signals. Here, we propose a passive 3-dimensional monocular positioning scheme, resonant beam based positioning (RBP), which adopts a resonant beam for angle-of-arrival estimation and a time-of-flight module for distance estimation. We present the principle of the proposed scheme and establish analytical models and simulation tools for evaluating the impacting factors on the positioning accuracy including sensing noises, signal power, etc. To verify the RBP performance, we also present a testbed. Both numerical analysis and experimental measurements demonstrate that the positioning accuracy can be less than 1cm over 2m distance in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$15^{\circ }$</tex-math></inline-formula> field of view. With RBP, high-accuracy and monocular without computation and high complexity positioning can be achieved while the target needs no power supply and the base station needs no beam-steering control. RBP is an important candidate for providing location-aware services in the Internet of everything and the proposed simulation models provide guidelines for system analysis and design.

Particle-in-cell simulations – ion beam instabilities and the generation of Alfvén and whistler waves in low β plasma

ABSTRACT Ion beam-driven instabilities in a collisionless space plasma with low β, i.e. low plasma and magnetic pressure ratio, are investigated using particle-in-cell (PIC) simulations. Specifically, the effects of different ion drift velocities on the development of Buneman and resonant electromagnetic (EM) right-handed (RH) ion beam instabilities are studied. Our simulations reveal that both instabilities can be driven when the ion beam drift exceeds the theoretical thresholds. The Buneman instability, which is weakly triggered initially, dissipates only a small fraction of the kinetic energy of the ion beam while causing significant electron heating, owing to the small electron-ion mass ratio. However, we find that the ion beam-driven Buneman instability is quenched effectively by the resonant EM RH ion beam instability. Instead, the resonant EM RH ion beam instability dominates when the ion drift velocity is larger than the Alfvén speed, leading to the generation of RH Alfvén waves and RH whistler waves. We find that the intensity of Alfvén waves decreases with decrease of ion beam drift velocity, while the intensity of whistler waves increases. Our results provide new insights into the complex interplay between ion beams and plasma instabilities in low β collisionless space plasmas.

Dynamic gravitational excitation of structural resonances in the hertz regime using two rotating bars

With the planning of new ambitious gravitational wave observatories, fully controlled laboratory experiments on dynamic gravitation become more and more important. Such experiments can provide new insights in potential dynamic effects such as gravitational shielding or energy flow and might contribute to bringing light into the mystery still surrounding gravity. Here we present a laboratory-based transmitter-detector experiment using two rotating bars as transmitter and a 42 Hz, high-Q bending beam resonator as detector. Using a precise phase control to synchronize the rotating bars, a dynamic gravitational field emerges that excites the bending motion with amplitudes up to 100 nm/s or 370 pm, which is a factor of 500 above the thermal noise. The two-bar design enables the investigation of different transmitter configurations. The detector movement is measured optically, using three commercial interferometers. Acoustical, mechanical, and electrical isolation, a temperature-stable environment, and lock-in detection are central elements of the setup. The moving load response of the detector is numerically calculated based on Newton’s law of gravitation via discrete volume integration, showing excellent agreement between measurement and theory both in amplitude and phase. The near field gravitational energy transfer is 1025 times larger than the one of the propagating gravitational wave component.

The Method for Determining Conditions to Vibrations Suppression of Bridge Beams

The paper deals with the problem of obtaining a given dynamic behavior of simply supported bridge beams from the impact of rolling stock. Resonant vibrations of beams become a reality at high speeds if the train is formed of identical cars, which is typical for passenger trains. The phenomenon of suppression of beam vibrations by a train, known from publications, is possible only with an exact ratio of the length of the car and the beam. This significantly reduces the possibilities of choosing the necessary spans of beams. Consideration of issues of interaction in the “bridge–track—train” system for security purposes requires the involvement of a rather complex mathematical apparatus and appropriate software. The paper proposes a new method for determining the specified dynamic behavior of bridge beams, suitable for any spans and available to engineers at the stage of pre-design assignment of dynamic parameters of beams. The requirements that are necessary and sufficient conditions for preventing the resonance of bridge beams on the HSR are determined. At the same time, it does not require the involvement of software based on a complex mathematical technique.

Quasi-periodic solutions for quintic completely resonant derivative beam equations on T2

In the present paper, we consider two dimensional completely resonant, derivative, quintic nonlinear beam equations with reversible structure. Because of this reversible system without external parameters or potentials, Birkhoff normal form reduction is necessary before applying Kolmogorov–Arnold–Moser (KAM) theorem. As application of KAM theorem, the existence of partially hyperbolic, small amplitude, quasi-periodic solutions of the reversible system is proved in this paper.

Simulation analyses and configuration optimizations of an LD pumped 3.1 µm Co/Er:PbF2 MIR laser

The demand for mid-infrared physics technology is increasing, and it is still a difficult process from growing excellent laser crystals to performing laser experiments. In this paper, we consider the energy transfer process between Co2+ and Er3+, and present the theoretical simulation results of the output power of the 3.1 µm Co/Er:PbF2 MIR laser. Based on the setup of a LD pulse pumped laser system, the effects of beam waist radius, resonator parameters and crystal length on the output are discussed in detail. The calculation results show that under good cavity mirror conditions, we can obtain a 3.1 µm laser with an output slope efficiency of 43.4%, whose output energy reaches 2.19 mJ at an input of 5 mJ. This provides guidance include the cavity mirror parameters and crystal parameters for laser experiments.

The Low-Frequency Vibration Control Mechanism of a Finite Locally Resonant Beam with Elastic Supports

The Low-Frequency Vibration Control Mechanism of a Finite Locally Resonant Beam with Elastic Supports

Angular magnetic field dependence of a doubly clamped magnetoelectric resonator

Angular dependence of magnetic field response of fully suspended resonant microelectromechanical double-clamped magnetoelectric beams was investigated as the basis for a vector magnetometer utilizing the magnetically induced change in fundamental resonance frequency. Strain-coupled magnetostrictive iron cobalt (FeCo) and piezoelectric aluminum nitride layers together constitute a magnetoelectric heterostructure with a high magnetic field sensitivity of 70 Hz/mT along the beam axis and a transfer function of 47 V/T at 10 Hz. The fundamental frequency shift to an external magnetic field is found to be strongly anisotropic with a relative variation of more than 3% between perpendicular and parallel field orientations with respect to the long axis of the beam at a field of 100 mT. This design can form the basis for an on-chip high sensitivity vector magnetometer operating with ultra-low power when multiplexed with two or more resonators.

Analysis of the Thermally Induced Packaging Effects on the Frequency Drift of Micro-Electromechanical System Resonant Accelerometer.

Due to the working principle of MEMS resonant accelerometers, their thermally induced frequency drift is an inevitable practical issue for their extensive application. This paper is focused on reducing the thermally induced packaging effects on the frequency drift. A leadless ceramic chip carrier package with a stress-buffering layer was proposed for a MEMS resonant accelerometer, and the influences of packaging structure parameters on the frequency drift were investigated through finite element simulations and verified experimentally. Because of the thermal mismatch between dissimilar materials, the thermo-mechanical stress within the resonant beam leads to a change in the effective stiffness and causes the frequency drift to decrease linearly with increasing temperature. Furthermore, our investigations reveal that increasing the stress-buffering layer thickness and reducing the solder layer thickness can significantly minimize the thermo-mechanical stress within the resonant beam. As the neutral plane approaches the horizontal symmetry plane of the resonant beam when optimizing the packaging structure, the effects of the compressive and tensile stresses on the effective stiffness of the resonant beam will cancel each other out, which can dramatically reduce the frequency drift. These findings provide guidelines for packaging design through which to improve the temperature stability of MEMS resonant accelerometers.

Auto-parametric resonance of flexible viscoelastic beams under interaction between longitudinal and transverse modes

For a system encompassing subsystems, dynamic modal interaction may experience unanticipated vibrations among subsystems that are excited indirectly. This paper focuses attention to a nonlinear auto-parametric resonance phenomenon of a flexible beam introduced via modal coupling of longitudinal forced resonance and transverse parametric resonance under longitudinal pulsatile excitation. The coupled resonance equations are first modeled based on the Euler-Bernoulli beam theory by incorporating nonlinear curvature, von Kármán's nonlinear strain-displacement relationship and the flexible beam model characterizing nonlinear inertia and displacement interaction. The Galerkin truncation-incremental harmonic balance method (IHBM) is then introduced to obtain both the stability boundary and amplitude-frequency bifurcation maps. Through the corresponding relationship between stability boundary and bifurcation diagram, the energy exchange between two modes is identified as well as the instability region and bifurcation topology can be tuned. It is found that the modal interaction greatly widens the instability region with at most two resonance bands of lateral resonance. By tuning structural and foundation damping, resonance can be controlled to occur only in one frequency band of the pair as desired. This research provides guidance to design broadband energy harvesting or vibration suppression equipment with tunable working frequency band for using the strategy of auto-parametric resonance.

The combined effects of temperature and relative humidity on resonant frequency and quality factor of MEMS beam resonators in atmospheric pressure and gas rarefaction

The combined effects of temperature and relative humidity on resonant frequency and quality factor of MEMS beam resonators in atmospheric pressure and gas rarefaction

Historical Review on Resonance and Cancellation of Simply Supported Beams Subjected to Moving Train Loads: From Theory to Practice

The advent of railways and especially highspeed railways marks great strides in human transportation history. To guarantee exclusive right-of-way, highspeed railways are often built on equal simply supported beams resting on piers. In this paper, a historical review will be given of the resonance and cancellation phenomena observed for simply supported beams traveled by a set of moving loads, as they are typical of highspeed railways. The phenomenon of resonance was observed by early investigators including Timoshenko, Bolotin, Frýba, Matsuura, etc. However, the phenomenon of cancellation was noted lately in 1997 by Yang et al. By letting the conditions of resonance and cancellation coincident, they proposed the optimal span length for suppressing the resonance of simple beams, which is equal to 1.5 times the car length. This 1.5 times rule has been verified and adopted in the design of some highspeed railways. In this article, the theoretical solution for the problem will be revisited for unveiling the key parameters such as the resonance speed (in temporal domain) and resonance wavelength (in spatial domain). Then a rather in-depth review will be given of existing works on the resonance and cancellation of railway bridges from the waves perspective. Some new developments along these lines will also be identified.

Synchronous mass detection based on 1:1:2 internal resonance of piezo-driven resonator

The bifurcation-based mass sensor can take advantage of amplitude jumps between multiple steady states to realize quantitative mass detection and mass warning. Compared with the classical detection based on the frequency shift induced by an added mass, sudden jumps in amplitude make the detection of a very small mass possible. Most research has been focused on the mass detection of a single analyte, but less research has been done on the detection of double analytes. In this study, the concept of synchronous mass detection for double analytes based on bifurcation induced by 1:1:2 internal resonance is first proposed and verified experimentally. Firstly, a piezo-driven three-degree-of-freedom (3-DOF) magnetic coupling resonant structure with the potential of 1:1:2 internal resonance is designed. Through driving the high-frequency resonant beam, the parametric vibration of two low-frequency resonant beams is realized, which causes the modal coupling vibration phenomenon in the three frequency intervals. The physical conditions of multi-mode coupling vibration are also deduced theoretically. Typically, by measuring the shifts of the upper and the lower critical bifurcation frequencies, the quantitative mass detection of the double analytes can be carried out simultaneously. Beside, a conceptual scheme with multiple mass warnings for double analytes is also creatively proposed. The experimental results show that with the increase of the adsorption mass, the resonant amplitude of the system obviously changes near the equilibrium point, accompanied by a bifurcation phenomenon. The research results provide a systematic framework for the development of resonant mass sensing devices based on multi-mode coupled vibration.

Frequency-dependent reflection of a misaligned beam by a Fabry–Pérot cavity

Gravitational-wave detectors, such as Virgo, LIGO, and KAGRA, are modified Michelson interferometers, with a system of coupled Fabry–Pérot cavities, to increase its sensitivity and bandwidth. In order to control the detector, several radio frequency sidebands, not resonant in the kilometric arm cavities but resonant in the central cavities of the interferometer, are added to the carrier frequency to extract longitudinal and alignment error signals. Misalignment of the laser in the Fabry–Pérot cavities causes sensitivity degradation through different mechanisms and results in non-superposition of carrier and sidebands. These relative misalignment between fields at different frequency contain clues to optimally align the interferometer, but the question of the direction of a reflected beam by a Fabry–Pérot cavity, as a function of the state of resonance of the incoming electromagnetic field, is neither straightforward nor intuitive. While numerical optical simulations used in the gravitational-wave detector community are able to answer the question, they do not give a qualitative and handy understanding of the observed phenomenon, useful for the commissioning and operation of the detectors. In this Letter, we present a model based on Gaussian beam first-order modal expansion to calculate analytically how misalignment on the input beam in a Fabry–Pérot cavity translates into misalignment of the reflected and circulating beams. We find a strong dependence not only on the beam resonance condition but also on the mirror geometry. Finally, we checked the consistency of our model by comparing its predictions with existing numerical simulators.

The bandgap characteristics of a flexural beam with periodic arrays of inertial amplification cantilever-type resonators

This paper presents the investigation of a metastructure, built with periodic arrays of inertial amplification (IA) cantilever-type resonators on a host beam, to improve its low-frequency flexural wave attenuation performance. The IA mechanism is composed of an additional mass and three rigid bars, which are connected by hinges and embedded on the host beam and cantilever-type resonators, respectively. The dynamical model of an IA cantilever-type resonant beam (IACRB) is established by the spectral element method, and its bandgap characteristics and vibration transmissibility are verified numerically and experimentally. The bandgaps of the lumped mass cantilever-type resonant beam are compared to those of the IACRB, showing that the latter has better low-frequency wave attenuation ability. To reveal the underlying physics, the effects of the amplification ratio, IA span, and length ratio of cantilever-type resonators on the band diagram of the IACRB are investigated. It is found that the variation of the amplification ratio results in the bandgap near-coupling phenomenon and the bandgap transposition phenomenon. The increase of IA span by changing position 1 weakens the coupling effect of local resonance and IA. However, the increase of IA span by changing position 2 creates the super-wide pseudo-bandgap as well, which is potential in engineering practices. The variation of the length ratio of cantilever-type resonators decreases its first bending modal frequency and shifts the IA bandgap to a lower frequency range slightly. The modal analysis results of the IACRB show that the proposed mechanism affects the modal distributions of the host structure. The modal frequencies existing in bandgaps are caused by the local vibration mode of the ends of the IACRB.

Multi-harmonic forced vibration and resonance of simple beams to moving vehicles

This study modeled the moving-vehicle-induced forcing excitation on a single-span prismatic bridge as a multiple frequency-multiplication harmonic load on the modal coordinates of a linear elastic simple Euler–Bernoulli beam, and investigated the forced modal oscillation and resonance behavior of this type of dynamic system. The forced modal responses consist of multiple frequency-multiplication steady-state harmonics and one damped mono-frequency complementary harmonic. The analysis revealed that a moving load induces high-harmonic forced resonance amplification when the moving speed is low. To verify the occurrence of high-harmonic forced resonance, numerical tests were conducted on single-span simple beams based on structural modeling using the finite element method (FEM) and a moving sprung-mass oscillator vehicle model. The forced resonance amplification characteristics of the fundamental mode for beam response estimation are presented with consideration to different end restraint conditions. The results reveal that the high-harmonic forced resonance may be significant for the investigated beams subjected to vehicle loads moving at specific low speeds. For the investigated single-span simple beams, the moving vehicle carriage heaving oscillation modulates the beam modal frequency, but does not induce notable variation of the modal oscillation harmonic structure for the cases that vehicle of small mass moves in low speed.

Resonant Beam SWIPT With Telescope and Second Harmonic

Simultaneous wireless information and power transfer (SWIPT) is a prospective technology that can handle the energy consumption and communication requirements in the Internet of Things. Resonant beam SWIPT (RB-SWIPT) scheme utilizes narrow optical beam as carrier and with spatially separated resonator structure, which can support high power and high rate SWIPT for mobile devices. However, the performance of original RB-SWIPT systems is limited by returning beam interference and transmission loss. In this paper, we propose a RB-SWIPT scheme for transmission-enhanced and anti-interference. The telescope internal modulator (TIM) and second harmonic generator (SHG) are adopted in the proposed system. The TIM can compress beams to reduce the transmission loss. The SHG can generate frequency-doubled beams to avoid interference. To evaluate the proposed system, we establish mathematical models to depict the beam transmission, energy conversion, electric power output and data receiving. Numerical results illustrate that the proposed system can achieve 18 bit/s/Hz spectral efficiency and deliver 8 W power over 100 m distance.

Terahertz Detectors Using Microelectromechanical System Resonators.

The doubly clamped microelectromechanical system (MEMS) beam resonators exhibit extremely high sensitivity to tiny changes in the resonance frequency owing to their high quality (Q-) factors, even at room temperature. Such a sensitive frequency-shift scheme is very attractive for fast and highly sensitive terahertz (THz) detection. The MEMS resonator absorbs THz radiation and induces a temperature rise, leading to a shift in its resonance frequency. This frequency shift is proportional to the amount of THz radiation absorbed by the resonator and can be detected and quantified, thereby allowing the THz radiation to be measured. In this review, we present an overview of the THz bolometer based on the doubly clamped MEMS beam resonators in the aspects of working principle, readout, detection speed, sensitivity, and attempts at improving the performance. This allows one to have a comprehensive view of such a novel THz detector.

Correlation between Q-Factor and Residual Stress in Epitaxial 3C-SiC Double-Clamped Beam Resonators

In this work, we investigate the correlation between tensile residual stress and Q-factor of double-clamped beams fabricated on epitaxial 3C-SiC layers grown on both &lt;100&gt; and &lt;111&gt; silicon substrates, using a completely optical measurement setup to measure the Q-factor of the resonators and the residual stress of the layers by means of purposely designed micromachined test structures. From the measurements, a clear correlation appears between the residual stress of the SiC layer and the Q-factor of the resonators, with Q-factor values above half a million for resonators fabricated on &lt;111&gt; substrates, showing residual stress around 1 GPa.

Adaptive Wireless Power Transfer via Resonant Laser Beam Over Large Dynamic Range

Wireless power transfer (WPT) via resonant laser beam from a spatially-distributed laser resonator not only benefits the instinct safety, but also has important potential of adaptive operation without positioning and aiming when retroreflectors are used to enable the alignment-free operation of the laser. Despite the intense theoretical modeling and experimental efforts with different laser schemes, the adaptive resonant beam WPT across large dynamic range -including both working distance and field of view (FoV) -has never been demonstrated, due to the absence of true alignment-free laser. In this work, we summarized the requirements on the dynamic range and discussed the optimization criteria of dynamic range and laser safety, including the telescope in the laser resonator, the resonator stability, coupled-resonator scheme, and influences of the optical aberrations. The analysis indicated that loss induced by optical aberrations is the main issue limits the dynamic range. In the experiment, alignment-free laser with large dynamic range for WPT application was demonstrated with improved resonator design and optical design to compensate the aberrations. Efficient multiwatt optical output was obtained across a working distance of 1-5 m, a receiver FoV of ±30∘, and a transmitter FoV of 4.6∘; and over 1.3 W electrical output was obtained via an InGaAs photovoltaic cell, with DC-DC WPT efficiency being 4%. Our work proved the feasibility of large-dynamic-range alignment-free laser with distributed-resonator, which paves the way for practical resonant beam charging and communication applications based on it for the internet of things devices.