Resonant Mode Interactions Research Articles

Mode selection in concentric jets: the steady–steady 1 : 2 resonant mode interaction with O(2) symmetry

The linear and nonlinear stability of two concentric jets separated by a duct wall is analysed by means of global linear stability and weakly nonlinear analysis. Three governing parameters are considered, the Reynolds number based on the inner jet, the inner-to-outer jet velocity ratio ( $\delta _u$ ) and the length of the duct wall ( $L$ ) separating the jet streams. Global linear stability analysis demonstrates the existence of unsteady modes of inherent convective nature, and symmetry-breaking modes that lead to a new non-axisymmetric steady state with a single or double helix. Additionally, we highlight the existence of multiple steady states, as a result of a series of saddle-node bifurcations and its connection to the changes in the topology of the flow. The neutral lines of stability have been computed for inner-to-outer velocity ratios within the range $0 < \delta _u < 2$ and duct wall distances in the interval $0.5 < L < 4$ . They reveal the existence of hysteresis, and mode switching between two symmetry-breaking modes with azimuthal wavenumbers $1:2$ . Finally, the mode interaction is analysed, highlighting the presence of travelling waves emerging from the resonant interaction of the two steady states, and the existence of robust heteroclinic cycles that are asymptotically stable.

Resonant Mode Coupling in δ Scuti Stars

Delta Scuti (δ Sct) variables are intermediate-mass stars that lie at the intersection of the main sequence and the instability strip on the Hertzsprung–Russell diagram. Various lines of evidence indicate that nonlinear mode interactions shape their oscillation spectra, including the particularly compelling detection of resonantly interacting mode triplets in the δ Sct star KIC 8054146. Motivated by these observations, we use the theory of three-mode coupling to study the strength and prevalence of nonlinear mode interactions in 14 δ Sct models that span the instability strip. For each model, we calculate the frequency detunings and nonlinear coupling strengths of ∼104 unique combinations of mode triplets. We find that all the models contain at least ∼100 well-coupled triplets whose detunings and coupling strengths are consistent with the triplets identified in KIC 8054146. Our results suggest that resonant mode interactions can be significant in δ Sct stars and may explain why many exhibit rapid changes in amplitude and oscillation period.

Spectrally Selective Optical Loss in Fibers With High-Index Rods Embedded Into Silica Cladding

In this work, we perform a detailed study of a novel type of optical fiber for spectral filtering, which is based on a step-index core with high-index rods embedded into silica cladding. Recently, it was theoretically predicted that such a structure could demonstrate a very sharp stopband due to the resonant core mode interaction with the eigen high-index rod mode. In the current paper, we realize the proposed structure and experimentally confirm its applicability for spectral filtering. In our experiments, we show the possibility of creating a very sharp shortpass fiber spectral filter. In particular, we demonstrate a change in the optical loss of the core mode by two orders of magnitude (from less than 0.1 dB/m to more than 10 dB/m) for a 12 nm wavelength shift (from 1008 nm to 1020 nm) and by more than 3 orders of magnitude (from 0.02 dB/m to 60 dB/m) for a 70 nm wavelength shift (from 980 to 1050 nm). Possible applications of the realized fiber design are discussed. Mechanisms of optical loss in the fabricated structure are studied, and the presence of an additional mechanism, which is not related to absorption in the high-index rods, is revealed.

K2 Photometry on Oscillation Mode Variability: The New Pulsating Hot B Subdwarf Star EPIC 220422705

We present an analysis of oscillation mode variability in the hot B subdwarf star EPIC 220422705, a new pulsator discovered from ∼78 days of K2 photometry. The high-quality light curves provide a detection of 66 significant independent frequencies, from which we identified nine incomplete potential triplets and three quintuplets. Those g- and p-multiplets give rotation periods of ∼36 and 29 days in the core and at the surface, respectively, potentially suggesting a slightly differential rotation. We derived a period spacing of 268.5 s and 159.4 s for the sequence of dipole and quadrupole modes, respectively. We characterized the precise patterns of amplitude and frequency modulations (AM and FM) of 22 frequencies with high enough amplitude for our science. Many of them exhibit intrinsic and periodic patterns of AM and FM, with periods on a timescale of months as derived by the best fitting and Markov Chain Monte Carlo test. The nonlinear resonant mode interactions could be a natural interpretation for such AMs and FMs after other mechanisms are ruled out. Our results are the first step to building a bridge between mode variability from K2 photometry and the nonlinear perturbation theory of stellar oscillation.

Metasurface absorber for ultra-broadband sound via over-damped modes coupling

Highly efficient absorption of broadband low-frequency sound with a slim subwavelength meta-structure promises extensive applications in acoustic engineering, which remains a major challenge due to the weak coupling of strong scattering resonant modes. Here, we formulate the interaction of resonant modes in different damping states on the basis of a coupled-mode theory and draw the conclusion that couplings between over-damped modes demonstrate superiority to under-damped or critically coupled states in sound absorption. Furthermore, we theoretically propose and experimentally demonstrate an ultra-broadband sound absorber by hybridizing multi-order Helmholtz resonators, which support a series of over-damped modes in a single element with flexible key acoustic parameters, including operating frequencies and loss and leakage factors decorated at will. Due to the intense coupling between these elaborated over-damped modes, the designed absorber demonstrates 81% average absorptance for airborne sound ranging from 100 to 1000 Hz (exceeding three octaves) with a thickness down to 1/18.8 of wavelength at the lower-limit frequency. We envision the design methodology to push forward more versatile functional devices.

Nonlinear Resonant Responses, Mode Interactions, and Multitime Periodic and Chaotic Oscillations of a Cantilevered Pipe Conveying Pulsating Fluid under External Harmonic Force

The nonlinear resonant responses, mode interactions, and multitime periodic and chaotic oscillations of the cantilevered pipe conveying pulsating fluid are studied under the harmonic external force in this research. According to the nonlinear dynamic model of the cantilevered beam derived using Hamilton’s principle under the uniformly distributed external harmonic excitation, we combine Galerkin technique and the method of multiple scales together to obtain the average equation of the cantilevered pipe conveying pulsating fluid under 1 : 3 internal resonance and principal parametric resonance. Based on the average equation in the polar form, several amplitude-frequency response curves are obtained corresponding to the certain parameters. It is found that there exist the hardening-spring type behaviors and jumping phenomena in the cantilevered pipe conveying pulsating fluid. The nonlinear oscillations of the cantilevered pipe conveying pulsating fluid can be excited more easily with the increase of the flow velocity, external excitation, and coupling degree of two order modes. Numerical simulations are performed to study the chaos of the cantilevered pipe conveying pulsating fluid with the external harmonic excitation. The simulation results exhibit the existence of the period, multiperiod, and chaotic responses with the variations of the fluid velocity or excitation. It is found that, in the cantilevered pipe conveying pulsating fluid, there are the multitime nonlinear vibrations around the left-mode and the right-mode positions, respectively. We also observe that there exist alternately the periodic and chaotic vibrations of the cantilevered pipe conveying pulsating fluid in the certain range.

A dual modal formulation for multiple flexural subsystems connected at a junction in energy-based models

Abstract Statistical energy methods in vibroacoustics, like the statistical energy analysis (SEA) or the statistical modal energy distribution analysis (SmEdA), rely on specific modal coupling assumptions (MCAs) between subsystem modes. These methods assume that the behavior of subsystem mode amplitudes mimic that of oscillators, that the modes within a subsystem are uncoupled, and that the coupling between two different subsystems only takes place through the interaction of resonant modes. In the case of more than two subsystems being connected at a junction, however, it becomes difficult to establish a modal interaction scheme for them. In SEA, the problem is avoided by resorting to the travelling wave approach instead of the modal one. Nevertheless, there is a need for other energy-based methods, like SmEdA, to deal with such a situation. In this work it is proposed to extend the displacement-stress dual formulation, originally intended for two subsystems, to the case of multiple flexural waveguides connected at a junction. Numerical results are presented for a test case consisting of a floor coupled to two walls at right angle. The fulfillment of the MCAs by the dual modal formulation is examined in terms of the impedance mismatch between the floor and the walls.

Vibrational Signatures of Electronic Properties in Oxidized Water: Unraveling the Anomalous Spectrum of the Water Dimer Cation.

The water dimer cation, (H2O)2+, has long served as a prototypical reference system for water oxidation chemistry. In spite of this status, a definitive explanation for the anomalous—and dominant—features in the experimental vibrational spectrum [Gardenier, G. H.; Johnson, M. A.; McCoy, A. B. J. Phys. Chem. A, 2009, 113, 4772–4779] has not been determined, and harmonic analyses qualitatively fail to reproduce these features. In this computational study, accurate quantum chemistry methods are combined with a fully coupled, six-dimensional anharmonic model to show that the unassigned bands are the result of resonant mode interactions and strong anharmonic coupling. Such coupling is fundamentally due to the unique electronic structure of this open-shell ion and the manner in which auxiliary modes affect the natural charge-transfer properties of the shared-proton stretch. These unique vibrational signatures provide a key reference point for modern spectroscopic and mechanistic analyses of water-oxidation catalysts.

Fano resonance in MIM waveguide structure with oblique rectangular cavity and its application in sensor

In this paper, an asymmetric plasmonic waveguide structure is designed with a MIM waveguide and an oblique rectangular cavity, and its double Fano resonance characteristics and transmission properties are numerically investigated by the finite element method. The results show that double Fano resonances appear in the transmission spectra when the oblique rectangular cavity has different rotation angular θ. The double Fano resonances derive from different mechanisms, one of Fano resonances is induced by the interaction of horizontal and vertical resonance modes in the rectangular cavity, and the other is derived from rotating the rectangular cavity. So the Fano resonances can be easily tuned by the changing angle of rotation θ and structure parameters of rectangular cavity. Moreover, when the rectangular cavity is rotated to a certain angle, three Fano resonant peaks are appeared in the transmission spectra. The asymmetric plasmonic structure is also to detect the refractive index changes of the filled media inside of rectangular cavity and waveguide, which reveals a potential sensors application of the MIM waveguide with oblique rectangular cavity.

Theoretical research on quartz enhanced photoacoustic spectroscopy base on the resonance in an elliptical cavity

As a new optical detection technique,quartz enhanced photoacoustic spectroscopy (QEPAS) has been widely used in the field of trace gas detection,which has an outstanding performance because of its advantages of extremely high sensitivity,high selectivity and compact absorption detection module.The most important factor of the detection sensitivity for QEPAS sensor is the acoustic wave enhancement.For increasing the acoustic enhancement,great effort has been devoted to the investigations by increasing laser power,employing tube resonators and using custom-made acoustic transducers.However,less attention has been paid to the elliptical cavity enhancement photoacoustic spectroscopy.In this work,novel quartz enhanced photoacoustic spectroscopy based on an elliptical cavity is proposed,which employs two quartz tuning forks and an elliptical cavity to further enhance the acoustic wave.The analysis and optimization of the elliptical cavity are also demonstrated. For the elliptical cavity QEPAS sensor,the acoustic enhancement properties can be influenced by resonant modes, coupling between laser and acoustic wave,and dimension of the cavity.Based on the Helmholtz wave equation,the acoustic modes and corresponding resonance frequency can be quantized.To further investigate the acoustic wave resonance inside the cavity,the model of the cavity is established in Comsol Multiphysics software with finite element method.The acoustic pressure,quality factor can be obtained numerically by the software.With the model,parameters of the spectrophone are investigated,including the resonant modes,laser incidence angle and dimension of the elliptical cavity.As a result,the (2,1) resonant mode is selected as the enhancement mode in the cavity,in which the maximum acoustic pressure is achieved at the ends of the long axis.By changing the incidence angle of the laser beam from 0 to 90,the performance of the sensor is analyzed,which indicates that the laser incidence angle has little influence on acoustic properties except for 30.This is due to the interaction of other resonant modes at this incidence angle.With the length of half-long axis varying from 4.8 mm to 5.2 mm,eccentricity from 0.5 to 0.8 and the cavity height from 0.4 mm to 0.8 mm,the resonance frequency,acoustic pressure and quality factor are studied.It reveals that there is an optimal length of half-long axis for a fixed eccentricity,and a relative large height is beneficial to enhancing the acoustic pressure.On the whole,a set of parameters is identified for the optimal sensor performance. By optimizing and designing the spectrophone,the experiment is conducted,in which a laser (1578 nm) and H2S as the sample gas are used.The detection limit of H2S gas of 6.3 ppm is achieved and the corresponding Normalized noise equivalent absorption coefficient (NNEA) is 2.0210-9cm-1W/Hz1/2.Finally,several H2S detection results of other QEPAS methods are listed and compared for demonstrating the high detection sensitivity of the sensor.This work may contribute to the research of high sensitivity photoacoustic detection.

Cooperative optical trapping in asymmetric plasmon nanocavity arrays.

We propose a scheme using cooperative interaction of antiphase resonance modes to enhance optical trapping in plasmonic nanostructures. This is implemented with a subwavelength array of asymmetric binary nanogrooves (e.g. different depths) in metal. When damping and inter-coupling of antiphase fields in the nanogrooves are mediated satisfying a critical condition, light can be cooperatively trapped in the nanogrooves, demonstrating perfect absorption at nearly the intrinsic resonance frequency of the deeper nanogrooves. A harmonic oscillator model is developed to interpret the cooperative interaction processes. The phenomenon has been also implemented in asymmetric ternary nanogroove arrays. In terms of compositions and intra-coupling mechanisms, the asymmetric binary/ternary plasmonic nanostructure arrays are crystalline molecular-metamaterials, analogous to electronic crystals composed of covalence-bond molecules.

A mode parabolic equation method in the case of the resonant mode interaction

A mode parabolic equation method for resonantly interacting modes has been developed. The method ensures acoustic energy flux conservation in accord with multiple scaled analysis accuracy. We carried out testing calculations for the ASA wedge benchmark, that showed excellent agreement with the COUPLE program.

Nonlinear Mode Interactions in the Wake of a Medium Height Roughness Element

The present study is devoted to nonlinear (resonant) mode interactions in the wake of a medium height, cylindrical roughness element, which is placed in a laminar, airfoil boundary layer. The roughness element causes a considerable mean flow distortion in the near wake centerline region and two counter-rotating vortex pairs arise in the outer spanwise domain. In the streamwise evolution the mean flow stabilizes and a spanwise uniform flow is recovered in the far wake. Upstream of the roughness controlled, low-amplitude Tollmien-Schlichting (TS) wave modes are excited in the upper branch unstable region. The interference of the excited, 2D fundamental modes with the roughness results in the excitation of oblique modes in a broad spanwise wave number range. Nonlinear interactions in-between the (oblique) fundamental modes in the destabilized near wake lead to the generation of primary, low-frequency modes at the difference frequencies of the fundamental modes, before the fundamental modes can recover linear stability characteristics in the far wake. In contrast, the primary, subharmonic-type modes experience a nonlinear growth, which is a result of frequency and spanwise wave number detuned resonant mode interactions with the 2D fundamental modes. The resonant growth of the primary interaction modes initiates a symmetrization of the spectrum in the low-frequency, subharmonic range. That is, symmetric subharmonic-type (secondary) modes are resonantly amplified in the far wake. Therefore, although the fundamental modes recover linear stability characteristics with the stabilization of the mean flow, resonant mode interactions in the low-frequency, subharmonic range initiate the onset of boundary layer transition in the far wake of the medium height roughness element.

Oscillating multidromion excitations in higher-dimensional nonlinear lattice with intersite and external on-site potentials using symbolic computation

We show by an extensive method of quasi-discrete multiple-scale approximation that nonlinear multi-dimensional lattice waves subjected to intersite and external on-site potentials are found to be governed by (N + 1)-dimensional nonlinear Schrödinger (NLS) equation. In particular, the resonant mode interaction of (2+1)-dimensional NLS equation has been identified and the theory allows the inclusion of transverse effect. We apply the exponential function method to the (2+1)-dimensional NLS equation and obtain the class of soliton solutions with a purely algebraic computational method. Notably, we discuss in detail the effects of the external on-site potentials on the explicit form of the soliton solution generated recursively. Under the action of the external on-site potentials, the model presents a rich variety of oscillating multidromion patterns propagating in the system.

Gapless surface states in a lattice of coupled cavities: A photonic analog of topological crystalline insulators

We show that a tetragonal lattice of weakly interacting cavities with uniaxial electromagnetic response is the photonic counterpart of topological crystalline insulators, a new topological phase of atomic band insulators. Namely, the frequency band structure stemming from the interaction of resonant modes of the individual cavities exhibits an omnidirectional band gap within which gapless surface states emerge for finite slabs of the lattice. Due to the equivalence of a topological crystalline insulator with its photonic-crystal analog, the frequency band structure of the latter can be characterized by a ${Z}_{2}$ topological invariant. Such a topological photonic crystal can be realized in the microwave regime as a three-dimensional lattice of dielectric particles embedded within a continuous network of thin metallic wires.

Apport de la convolution non linéaire à la caractérisation de l'endommagement des matériaux hétérogènes en résonance

Implementation of nonlinear convolution method, usually called Synchronous Swept Sine, is presented in the frame of damage characterisation of heterogeneous materials. The estimation of higher order frequency responses, the used approach allows detection of new resonance modes created during the interaction of classical resonance modes with damage. The created modes made possible the definition of new nonlinear parameters whose sensitivity to the presence of damage as well as its propagation is likely to go beyond structural health monitoring applications by offering a better understanding of the physics corresponding to hysteretic non linear materials. MOTS-CLES : resonance non lineaire, comportement non lineaire hysteretique, composites, endommagement, identification des systemes non lineaires, structure de hammerstein generalisee.

Time and resonance patterns in chaotic piece-wise linear systems

The aim of this paper is to characterize time and resonant behavior in a class of piece-wise linear systems evolving chaotically. To this end, statistical methods are used to reveal interactions of different parts of the system. The system under study comprises a continuous time subsystem and a switching rule that induces an oscillatory path by switching alternately between stable and unstable conditions. Since the system is not continuous, the principal oscillation frequency depends on the switching regime and linear subsystem parameters; therefore, many time and resonant patterns can be observed. It is shown that the system may display resonance produced by the action of a external signal (switching law), as well as internal and combinational resonance. The effect of system parameters on time evolution and resonance is studied. It is shown that the nature of subsystems eigenvalues plays a crucial role in the type of resonance observed, producing in some cases complex interaction of resonance modes.

Control of non-axisymmetric magnetic fields for plasma enhanced performances: The RFX contribution

Active control of non-axisymmetric magnetic fields has been developed to increase the plasma performances in Tokamaks and RFPs. In the past at RFX, the effect of non-axisymmetric fields, static and rotating, with m = 0, n > 0, was studied. Through a plasma non linear coupling, the internal tearing modes coupled with the external m = 0 fields are dragged into rotation. The results have encouraged to realize a dedicated system for the generation of non-axisymmetric magnetic field by using ad hoc saddle coil arrays. One hundred and Ninety-two uniformly distributed saddle coils, each fed through switching power supply have been installed for the generation of m = 0 and 1 magnetic fields in a range n = 1–24. Each coil will be operated in a frequency range from dc to 300 Hz and will produce a maximum field intensity of 50 mT dc at the plasma surface. The resulting configuration of coils, power supplies, measurements and real time control equipment gives nowadays the most versatile system for studies of non-axisymmetric field effect on plasma. The experiments will be focused to increase the present understanding in the control of Resistive Wall Modes (RWMs) and to analyse the resonant and non-resonant MHD mode interaction with external magnetic fields, common issues for present Tokamaks and RFPs.The paper reviews the state-of-art of MHD control performed with non-axisymmetric external magnetic fields on Tokamaks and RFPs, with reference to the RWMs and field errors. The RFX contribution to the MHD mode control by external fields is discussed.

Influence of the viscosity of a nonlinearly vibrating charged liquid drop on the positions of internal resonances

An asymptotic analytical expression for the generatrix of a viscous charged liquid drop is for the first time derived in the second order of smallness in the axisymmetric initial deformation of the drop. The expression is represented as an infinite series in the roots of the dispersion relation and a finite sum of the numbers of modes specifying the initial deformation. In some of the terms of the analytical expression, the denominators involve the differences between the mode frequencies. These differences may become small under certain values of the charge, causing internal nonlinear resonant mode interaction. Analytical and numerical investigations of the effect of viscosity on the vibrating frequency show that the resonant values of the self-charge of the drop tend to increase with increasing viscosity. The viscosity of the liquid does not affect the spectrum of modes excited via nonlinear mode interaction.

Averaging and Benjamin–Feir instabilities in a parametrically forced nonlinear Schrödinger equation

We study small amplitude solutions of a parametrically forced nonlinear Schrödinger equation, and give exact expressions for the quartic resonant mode interactions by analyzing the corresponding Diophantine equations. We use this information to find some classes of periodic orbits of the averaged equation and characterize the linearly unstable directions of Stokes wave solutions.