Second-order Resonance Research Articles

BROADBAND EPSILON NEGATIVE TRANSMISSION LINE RESONANT ANTENNA WITH AIS LOADING

A metamaterial-based broadband antenna loaded with artificial impedance surface (AIS) is presented in this letter. Two metallic vias connect a Y-shaped patch to the ground plane. The patch, two metallic vias, and the AIS compose an epsilon negative (ENG) transmission line (TL). The asymmetry Y-shaped patch and the AIS bring about the first-order resonance (FOR) and second-order resonance (SOR) modes, which can be merged into one passband to yield a wideband property. The proposed ENG-TL resonant antenna has the advantages of compact size, wide bandwidth, and high gain, which can be applied to portable and handheld communication system.

制冷机房的隔振降噪设计

根据某大型写字楼制冷机房的噪声测试结果，为了降低振动影响，建立了具有中间质量块的双激励双输出二级隔振系统，通过调节隔振器中间质量块的重量调节二阶共振峰值的频率，达到增强隔振降噪效果的目的。经测试，制冷机房的噪声由92.3 dB (A)降低为68.7 dB (A)，而且楼板振动明显减小，取到了良好的减振降噪效果。 According to the noise test results of a large office building’s refrigeration room, a double in- centive dual output vibration isolation system is established with intermediate masses in order to reduce vibration. Second-order resonance peak frequency can be changed by adjusting the inter- mediate mass weight of the isolator, and then improve the vibration isolation effect. By noise testing, the noise value in the refrigeration room is reduced from 92.3 dB (A) to 68.7 dB (A). Furthermore, the floor vibration is significantly reduced which indicates the effect of vibration and noise reduction is good.

Water dynamics on ice and hydrate lattices studied by second-order central-line stimulated-echo oxygen-17 nuclear magnetic resonance.

Oxygen-17 stimulated-echo spectroscopy is a novel nuclear magnetic resonance (NMR) technique that allows one to investigate the time scale and geometry of ultraslow molecular motions in materials containing oxygen. The method is based on detecting orientationally encoded frequency changes within oxygen's central-transition NMR line that are caused by second-order quadrupolar interactions. In addition to the latter, the present theoretical analysis of various two-pulse echo and stimulated-echo pulse sequences takes also heteronuclear dipolar interactions into account. As an experimental example, the ultraslow water motion in polycrystals of tetrahydrofuran clathrate hydrate is studied via two-time oxygen-17 stimulated-echo correlation functions. The resulting correlation times and those of hexagonal ice are similar to those from previous deuteron NMR measurements. Calculations of the echo functions' final-state correlations for various motional models are compared with the experimental data of the clathrate hydrate. It is found that a six-site model including the oxygen-proton dipolar interaction describes the present results.

Anharmonic Effects on Vibrational Spectra Intensities: Infrared, Raman, Vibrational Circular Dichroism, and Raman Optical Activity.

The aim of this paper is 2-fold. First, we want to report the extension of our virtual multifrequency spectrometer (VMS) to anharmonic intensities for Raman optical activity (ROA) with the full inclusion of first- and second-order resonances for both frequencies and intensities in the framework of the generalized second-order vibrational perturbation theory (GVPT2) for all kinds of vibrational spectroscopies. Then, from a more general point of view, we want to present and validate the performance of VMS for the parallel analysis of different vibrational spectra for medium-sized molecules (IR, Raman, VCD, ROA) including both mechanical and electric/magnetic anharmonicity. For the well-known methyloxirane benchmark, careful selection of density functional, basis set, and resonance thresholds permitted us to reach qualitative and quantitative agreement between experimental and computed band positions and shapes. Next, the whole series of halogenated azetidinones is analyzed, showing that it is now possible to interpret different spectra in terms of mass, electronegativity, polarizability, and hindrance variation between closely related substituents, chiral spectroscopies being particular effective in this connection.

Detuned square ring resonators for multiple plasmon-induced transparencies in metal–insulator–metal waveguide

We propose a metal–insulator–metal (MIM) waveguide with two detuned square ring resonators to achieve on-chip multiple plasmon-induced transparencies (PITs). PITs can be explained by a well-defined phase coupling that can be established between detuned resonances. For third-order detuned resonances, there is one PIT window. For second-order detuned resonances, there are one, two, or three PIT windows, depending on the detuning degree between the two square ring resonators. Electromagnetic simulation based on the finite element method is carried out to calculate the PIT transmission spectrum and electromagnetic field distribution.

Nonlinear response of flapping beams to resonant excitations under nonlinear damping

The effect of excitation and damping parameters on the superharmonic and primary resonance responses of a slender cantilever beam undergoing flapping motion is investigated. The problem is cast into mathematical form using a nonlinear inextensible beam model which is subjected to time-dependent boundary conditions and linear or nonlinear damping forces. The flapping excitation is assumed to be non-harmonic, composed of two sine waves with different amplitudes. We employ a combination of Galerkin and perturbation methods to arrive at the frequency–response relationships associated with the second- and third-order superharmonic and primary resonances. The resonance solutions of the spatially discretized equation of motion, which involves both quadratic and cubic nonlinear terms, are constructed as first-order uniform asymptotic expansions via the method of multiple timescales. The effect of excitation and damping parameters on the steady-state resonance responses and their stability is described quantitatively using approximate analytical expressions. The critical excitation amplitudes leading to bistable solutions are identified. For the second-order superharmonic resonance, the critical excitation amplitude is determined to be dependent on the first-harmonic amplitude in the case of nonlinear damping. The third-order superharmonic resonance is determined to be independent of the second-harmonic excitation amplitude regardless of the damping types considered. The perturbation solutions are compared with numerical time-spectral solutions for different flapping amplitudes. The first-order perturbation solution is determined to be in very good agreement with the numerical solution up to 5° while above this amplitude differences in the two solutions develop, which are attributed to phase estimation accuracy.

The resonance overlap and Hill stability criteria revisited

We review the orbital stability of the planar circular restricted three-body problem in the case of massless particles initially located between both massive bodies. We present new estimates of the resonance overlap criterion and the Hill stability limit and compare their predictions with detailed dynamical maps constructed with N-body simulations. We show that the boundary between (Hill) stable and unstable orbits is not smooth but characterized by a rich structure generated by the superposition of different mean-motion resonances, which does not allow for a simple global expression for stability. We propose that, for a given perturbing mass $$m_1$$ and initial eccentricity e, there are actually two critical values of the semimajor axis. All values $$a < a_\mathrm{Hill}$$ are Hill-stable, while all values $$a > a_\mathrm{unstable}$$ are unstable in the Hill sense. The first limit is given by the Hill-stability criterion and is a function of the eccentricity. The second limit is virtually insensitive to the initial eccentricity and closely resembles a new resonance overlap condition (for circular orbits) developed in terms of the intersection between first- and second-order mean-motion resonances.

On Vibrodiagnostics of the Presence of a Closing Edge Crack in a Beam with Amplitude-Dependent Damping Capacity Under Superharmonic Resonance

The paper summarizes the results of approximate calculation of the influence of amplitudedependent damping capacity of a vibrating system on vibrodiagnostic parameters of the presence of a closing mode I edge crack in a cantilever beam of rectangular cross section for various methods of excitation of the second-order resonance in the lowest natural bending mode.

Electric and magnetic resonance in metal strip tetramer

We have numerically investigated the transmission and plasmon resonance properties of the metal strip tetramer. The results show that in the symmetric model there are three sharp transparent windows, the first and third peaks’ transmittance are more than 75%. When decreasing metal strips size or increasing gap distance, the transmission spectra blue-shift and intensities change. While introducing asymmetry, the transmission spectra and Plasmon resonance significantly change, whether to modify the size or the gap distance, a new dip exist on the second peak, and one or two new peaks exist on the third dip. Through analysis of the electric-magnetic properties, we find that the new dip results from asymmetric second-order magnetic resonance, while the peak is originated from the strong electric resonance. It is also demonstrated that the sensor sensitivity in this proposed system can reach of 380nm/RIU. The resonator design strategy opens up a rich pathway for the implementation of optimized optical properties for specific applications.

Fully nonlinear analysis of second-order sloshing resonance in a three-dimensional tank

The 3D boundary element method (BEM) based on the potential flow theory is developed to study the second-order resonance problems in rectangular sloshing tanks. Fully-nonlinear free-surface boundary conditions are considered. A local surface fitting method is used to calculate tangential derivatives. A shared-memory parallel procedure based on OpenMP is adopted for the efficiency improvement. Both 2D and 3D sloshing cases are studied. It is found that the second-order resonance may occur due to the interaction among natural frequencies and excitations frequencies. The second-order resonance becomes obvious after a sufficient long time length. After increasing the excitation amplitude, the second-order resonance emerges much earlier. For 3D situations, the second-order resonance in rectangular tanks with either equal or unequal length and width sides are investigated. The second-order resonances due to the interaction of two orthogonal plane waves in length and width directions are observed.

Evolutionary outcomes for pairs of planets undergoing orbital migration and circularization: second-order resonances and observed period ratios in Kepler's planetary systems

In order to study the origin of the architectures of low mass planetary systems, we perform numerical surveys of the evolution of pairs of coplanar planets in the mass range $(1-4)\ \rmn{M}_{\oplus}.$ These evolve for up to $2\times10^7 \rmn{yr}$ under a range of orbital migration torques and circularization rates assumed to arise through interaction with a protoplanetary disc. Near the inner disc boundary, significant variations of viscosity, interaction with density waves or with the stellar magnetic field could occur and halt migration, but allow ircularization to continue. This was modelled by modifying the migration and circularization rates. Runs terminated without an extended period of circularization in the absence of migration torques gave rise to either a collision, or a system close to a resonance. These were mostly first order with a few $\%$ terminating in second order resonances. Both planetary eccentricities were small $< 0.1$ and all resonant angles liberated. This type of survey produced only a limited range of period ratios and cannot reproduce Kepler observations. When circularization alone operates in the final stages, divergent migration occurs causing period ratios to increase. Depending on its strength the whole period ratio range between $1$ and $2$ can be obtained. A few systems close to second order commensurabilities also occur. In contrast to when arising through convergent migration, resonant trapping does not occur and resonant angles circulate. Thus the behaviour of the resonant angles may indicate the form of migration that led to near resonance.

RESONANCES, CHAOS, AND SHORT-TERM INTERACTIONS AMONG THE INNER URANIAN SATELLITES

The Portia group of Uranian satellites, representing 9 of the planet’s 13 tiny innermost moons, form a densely packed dynamical system. Hubble Space Telescope observations indicate that their orbits have changed significantly over two decades, and long-term numerical integrations show that their orbits are unstable over millions of years. To investigate the dynamical interactions of the Portia group satellites on the decade timescale over which orbital changes have been observed, we have performed a suite of 100–1000 yr N-body numerical integrations for a range of assumed satellite masses, which are at present not tightly constrained by observations. As first noted by Dawson et al. and recently investigated independently by Quillen and (Robert) French, the moons are configured in chains of interlinked first- and second-order eccentric resonances that contribute to chaotic behavior. We explore in detail several of the strongest of these interlinked resonances. The first such chain is a quintet of orbital resonances: Bianca is near a resonance with Cressida, which is itself near a resonance with Desdemona. Desdemona, in turn, is near a resonance with Portia, which is itself near a resonance with Juliet. The five participating resonances are: Cressida and Bianca (16:15), Desdemona and Cressida (47:46), Portia andmore » Desdemona (13:12), and Portia and Juliet (51:49). A second such chain is a set of two interlinked resonances: Cupid and Belinda (58:57) and Belinda and Perdita (44:43). We also report the new identification of a companion set of second-order inclination-type resonances (Cressida and Bianca (32:30), Desdemona and Cressida (94:92), Portia and Desdemona (26:24), Portia and Juliet (51:49), Cupid and Belinda (116:114), and Belinda and Perdita (88:86)), some of which result in quite strongly coupled variations in the inclinations of the interacting satellites. Using a robust formulation of orbital elements that accounts for the oblateness of Uranus, we probe the dynamical interactions among the moons in the time and frequency domains, and also in phase space, using numerical integrations of subsets of the inner moons, for a range of assumed masses. Several of the satellites are near mean-motion resonance with more than one neighbor, and undergo orbital variations at two nearly equal resonant frequencies. Such configurations of two interlinked resonances can result in chaotic behavior, associated with the transition of one resonant argument from circulation to libration. We demonstrate that, even on the short timescales investigated here, the dynamical interactions, onset of chaos, and associated Lyapunov times are highly sensitive to the masses of the interacting satellites.« less

Plasmon ruler with gold nanorod dimers: utilizing the second-order resonance.

The idea of utilizing the second-order plasmon resonance of gold nanorod π-dimers for plasmon rulers is introduced. We report on a qualitatively different dependence of the plasmon resonance shift on the interparticle distance for the first- and second-order longitudinal modes of the nanorods, extending the working range of plasmon rulers up to the distance values of approximately 400 nm.

Criteria for first- and second-order vibrational resonances and correct evaluation of the Darling-Dennison resonance coefficients using the canonical Van Vleck perturbation theory.

The second-order vibrational Hamiltonian of a semi-rigid polyatomic molecule when resonances are present can be reduced to a quasi-diagonal form using second-order vibrational perturbation theory. Obtaining exact vibrational energy levels requires subsequent numerical diagonalization of the Hamiltonian matrix including the first- and second-order resonance coupling coefficients. While the first-order Fermi resonance constants can be easily calculated, the evaluation of the second-order Darling-Dennison constants requires more complicated algebra for seven individual cases with different numbers of creation-annihilation vibrational quanta. The difficulty in precise evaluation of the Darling-Dennison coefficients is associated with the previously unrecognized interference with simultaneously present Fermi resonances that affect the form of the canonically transformed Hamiltonian. For the first time, we have presented the correct form of the general expression for the evaluation of the Darling-Dennison constants that accounts for the underlying effect of Fermi resonances. The physically meaningful criteria for selecting both Fermi and Darling-Dennison resonances are discussed and illustrated using numerical examples.

Rocking filter induced mechanically in a highly birefringent microstructured polymer fiber.

We present the possibility of mechanical inducement of a rocking filter in a birefringent microstructured polymer fiber, which resonantly couples polarization modes. A birefringence in the fiber used for rocking filter fabrication is induced by two large holes adjacent to the core. Because of the small pitch distance of the microstructured cladding, the phase and the group modal birefringence in this fiber are relatively high and equal, respectively, 1.2×10-4 and -2×10-4 at λ=800 nm, while the fiber loss is 5 dB/m at λ=850 nm. We demonstrate transmission characteristics of rocking filters mechanically induced in this fiber. A 22dB deep first-order resonance located in the visible spectral range was observed, accompanied by a second-order resonance in the near-infrared. We also show that by changing the filter period and load applied to the fiber, one can tune the resonance position and depth.

Modal characteristics and phase response of vibrator under excitation of sweep frequency

To analyze the dynamic responses of vibrator, a vibrator-ground coupling vibration model considering sweep frequency is proposed based on half-space theory, and modal characteristics and phase response of the structure are investigated. Results show that the sweep frequency has a significant effect on the dynamic responses of the vibrator. The natural frequency of the vibrator changes with sweep frequency, and the resonance may occur at 2.071 Hz and 53.12 Hz. The vibrator has two mode shapes. The first-order mode shape is that the reaction mass and the baseplate move in the same direction and the structure is dominated by the reaction mass. At the second-order resonance, the reaction mass and the baseplate move in opposite directions and the baseplate dominates the system. The phase of the vibrator also changes with the frequency and varies greatly. The phases of reaction mass acceleration, baseplate acceleration and ground force suffer abrupt changes at about 2 Hz and 50 Hz. Especially, the phase of the baseplate acceleration experiences a 180° jumping at about 50 Hz. The abrupt change/jumping frequencies of the phase are basically the same as the natural frequencies, indicating that the resonance has significant effect on the vibrator output.

Effects of underdamped step-varying second-order stochastic resonance for weak signal detection

Stochastic resonance (SR) has been proved to be an effective approach for weak signal detection. In this paper, an underdamped step-varying second-order SR (USSSR) method is proposed to further improve the output signal-to-noise ratio (SNR). In the method, by selecting a proper underdamped damping factor and a proper calculation step, the weak periodic signal, the noise and the potential can be matched with each other in the regime of second-order SR to generate an optimal dynamical system. The proposed method has three distinct merits as: 1) secondary filtering effect produces a low-noise output waveform; 2) good band-pass filtering effect attenuates the multiscale noise that locates in high- and (or) low-frequency domains; and 3) good anti-noise capability in detecting weak signal being submerged in heavy background noise. Numerical analysis and application verification are performed to confirm the effectiveness and efficiency of the proposed method in comparison with a traditional SR method.

Height-related magnetoelectric performance of PZT/Ni layered composites

The effect of height on performance of the PZT/Ni cylindrical bilayered magnetoelectric (ME) composites was studied in situ in this paper. Multiple resonant peaks appear between 1 and 300 kHz frequency for cylinders of different heights. The first resonance frequency does not change with the cylinder height decreasing, but the second and the third resonant frequencies increase. The first three resonant modes are attributed to the cylinder radial, first-order height resonance, and second-order height resonance, respectively. The appropriate size and resonance frequency were chosen to obtain the highest ME voltage coefficient when designing cylindrical bilayered magnetoelectric devices. This article provides reference to design cylindrical magnetoelectric devices.

Influence of Inelastic Resistance on Vibrodiagnostic Parameters of the Presence of a Closing Crack in an Elastic Body Under Superharmonic Resonance

The authors discuss the methods for approximate determination of vibrodiagnostic parameters of the presence of a closing mode I fatigue crack in an elastic body taking into account various types of inelastic resistance under second-order superharmonic resonance.

Second-order resonance among an array of two rows of vertical circular cylinders

Experimental and theoretical works are conducted on the first-order and second-order wave interactions among an array of two rows of vertical circular cylinders.We show that both the first-order and the second-order resonance of dynamic free-surface displacement could in some cases be quite relevant among an array of two rows of vertical cylinders not only in theory but also in real phenomena. In some cases, on the other hand, we show that large free-surface displacement predicted theoretically is quite attenuated in reality probably due to viscous dissipation.