Vicinity Of Resonance Frequency Research Articles

Static topological mechanics with local resonance

The locally resonant band gaps that lie in the vicinity of resonant frequency have been extensively employed in metamaterials for ultralow-frequency wave control, such as vibration isolation, negative refraction, superlensing, and cloaking. The combination of local resonance and band topology allows for the broadband tunable topological boundary modes, ranging from audible to ultrasonic frequencies. Recently, nontrivial topological boundary modes have been reported in static mechanical systems beyond frequency-based wave dynamics, in which the band gap is typically Bragg-like. In this paper, the concept of local resonance is extended from dynamic to static systems where the inertial effects are absent, and is leveraged to customize the topological modes. We impart a pseudo-mass to the static systems and retrieve the locally resonant band gap. The eigenvalues and associated bulk deformation fields of the topological mode can be tailored by shifting the pseudo-resonant frequency. Moreover, an effective non-reciprocity is achieved by passively breaking the lattice symmetry, and its cooperation with local resonances enables the static metamaterial to shield eccentric deformations and selectively filter boundary loads. All of these models are experimentally validated in an assembled truss-like lattice. This study is expected to provide a platform for exploring locally resonant topological phases without relying on wave motion.

Closed-Form Demonstration and Shake Table Verification of Damping Effect on the Seismic Energy

This paper discusses closed-form demonstrations of the damping effect for a basic mass, spring, and damper (MSD) and a single degree of freedom (SDOF) system that are exposed to harmonic loading. Initially, the energy balance equations of the systems were solved in closed form by considering the damping ratio and loading frequency. Verification of the solutions obtained for SDOF systems is achieved by shake table tests. Based on the analytical and experimental results, it was found that the damping effect is highly related to the ratio of loading frequency to the natural vibrational frequency of the system. For the lower and higher values of the ratio, damping is found to be almost ineffective. However, the effect becomes substantial when the ratio reaches unity i.e. at the resonant frequency. Damping has a reverse relation with seismic energy at the dominant frequency. In contrast, the relation is proportional in the vicinity of resonance frequencies. Hence, considering the damping as a parameter for the energy-based design of structures is suggested.

Simultaneous identification of mechanical properties of functionally graded plates under the Kirchhoff and Tymoshenko models

The paper presents models of deformation of functional-gradient round plates in the framework of the hypotheses of Kirchhoff and Timoshenko. Based on the equations of oscillations and boundary conditions obtained earlier using the Hamilton - Ostrogradsky variational principle, the formulations of problems in a cylindrical coordinate system are written, taking into account the variability of the functions of cylindrical stiffness and density along the radial coordinate. The plates was considered rigidly clamped along the edge. The case of steady-state vibrations caused by a load applied to the surface was considered. A scheme for solving direct problems calculating vibrations of plates based on the Galerkin method is constructed. An analysis of the influence of the functions of cylindrical stiffness and density on the amplitude-frequency characteristics (AFC, acoustic response) was carried out, which revealed that both functions significantly affect the AFC, and the greatest influence is observed in the vicinity of resonant frequencies. The results of the analysis made it possible to formulate new inverse problems of simultaneous identification of the functions of cylindrical stiffness and density of an inhomogeneous circular plate using additional information about the acoustic response for both hypotheses. To solve them, a special projection technique was built, based on the expansion of unknown functions of mechanical characteristics, as well as dynamic quantities (functions of deflection and angle of rotation of the normal) in terms of some systems of linearly independent functions that satisfy the boundary conditions. The coefficients of these expansions are determined from the solution of special systems of linear and nonlinear equations obtained from the formulated weak statements of both problems. As a result, it is possible to identify the desired characteristics in the given classes of functions. The identification results are illustrated with a set of computational experiments for various functions.

Frequency shift of an optical cavity mode due to a single-atom motion

ABSTRACTUsing quantum coherence effects, we have developed a new technique of detection of motion of single atoms or ions in an optical cavity. We have theoretically demonstrated that the presence of a single atom or ion inside cavity leads to a shift in cavity frequency and phase of transmitted probe beams. It has been shown by the use of EIT technique, the change of the phase is extremely sensitive to probe detuning in the vicinity of resonance frequency and can be in the order of .

Dispersion behavior of electromagnetic wave near the resonance in 1D magnetized ferrite photonic crystals

In the present article, we have analyzed the dispersion of electromagnetic wave in the one dimensional magnetized ferrite photonic crystals near the resonance in the permeability of the constituent materials for transverse magnetization in the transverse electric mode. The dispersion relation is obtained by transfer matrix method. It is observed that in the vicinity of resonant frequency, large numbers of oscillations occur in the normalized Bloch wave number. These oscillations in the Bloch wave number are strongly dependent on external magnetic fields, filling factor, and damping constant. The frequency regime of these oscillations is found to be shifted in higher frequency range with increase in the magnitude of the magnetic fields. With increase in the filling factor keeping length of periods fixed, number of oscillations is found to be increased. Near the resonance, effect of incident angle is negligible. It is demonstrated that these nearly equidistant oscillations occurring in the vicinity of resonance may be used for making filter in micro wave frequency range.

Numerical and Experimental Investigation of Interactions Between Free-Surface Waves and A Floating Breakwater with Cylindrical-Dual/Rectangular-Single Pontoon

This paper investigates the hydrodynamic performance of a cylindrical-dual or rectangular-single pontoon floating breakwater using the numerical method and experimental study. The numerical simulation work is based on the multi-physics computational fluid dynamics (CFD) code and an innovative full-structured dynamic grid method applied to update the three-degree-of-freedom (3-DOF) rigid structure motions. As a time-marching scheme, the trapezoid analogue integral method is used to update the time integration combined with remeshing at each time step. The application of full-structured mesh elements can prevent grids distortion or deformation caused by large-scale movement and improve the stability of calculation. In movable regions, each moving zone is specified with particular motion modes (sway, heave and roll). A series of experimental studies are carried out to validate the performance of the floating body and verify the accuracy of the proposed numerical model. The results are systematically assessed in terms of wave coefficients, mooring line forces, velocity streamlines and the 3-DOF motions of the floating breakwater. When compared with the wave coefficient solutions, excellent agreements are achieved between the computed and experimental data, except in the vicinity of resonant frequency. The velocity streamlines and wave profile movement in the fluid field can also be reproduced using this numerical model.

On vibration transmission between interactive oscillators with nonlinear coupling interface

This paper investigates the dynamic characteristics and vibration transmission behaviour of interactive oscillators with nonlinearities at their coupling interface. Three different types of stiffness nonlinearities, i.e., hardening stiffness, softening stiffness and double-well potential type stiffness and cubic damping nonlinearity are considered. Both analytical approximations based on the method of averaging and also numerical integrations are employed to obtain the steady-state response and to determine the vibration transmission level. The time-averaged vibration power variables and kinetic energies of the system and the force transmissibility are formulated and obtained analytically and numerically. Time-averaged transmitted power is used as an index to quantify vibration transmission associated with both periodic responses and non-periodic responses such as chaos. It is found that hardening stiffness nonlinearity at the interface can lead to higher vibration power transmission at high excitation frequencies. In comparison, softening stiffness nonlinearity at the coupling interface can result in higher vibration transmission at lower excitation frequencies. It is shown that the interface with double-well potential stiffness nonlinearity may yield chaotic responses that can significantly affect vibration transmission as indicated by time-averaged transmitted power. It is also found that cubic damping nonlinearity may cause lower time-averaged transmitted and dissipated powers at the interface in the vicinity of resonant frequency. These findings provide better understanding of the effects of nonlinearity at the interface on vibration transmission, and facilitate better designs of coupling interface for control of vibration transmission.

Entanglement characteristics of output optical fields in double-cavity optomechanics

Radiation pressure in an optomechanical system can be used to generate various quantum entanglements between the subsystems. Recently, one paid more attention to the study of quantum entanglement in an optomechanical system. Here in this work, we study the properties of output entanglement between two filtered output optical fields by the logarithmic negativity method in a double-cavity optomechanical system. Our calculations show that the decay rate of the mechanical resonator, the bandwidth of filter function, and non-equal-coupling will evidently affect the value of the output entanglement. In particular, under the parameters of equal-coupling and zero filter bandwidth, the output entanglement in the vicinity of resonant frequency (=0 in the rotating frame) will decease with mechanical decay rate increasing. But under the parameters of equal-coupling and non-zero filter bandwidth, the output entanglement will be suppressed if the center frequency of output field is in the vicinity of the resonant frequency. However, the output entanglement can be enhanced if we adopt a non-equal-coupling to counteract the suppression effect of the filter bandwidth. Furthermore, we find that there are three peaks in the whole center frequency domain of the output field if we adopt strong non-equal-coupling. This is because the normal mode of Hamiltonian Hint will split into three normal modes in this case. Our results can also be used in other parametrically coupled three-mode bosonic systems and may be applied to realizing the state transfer process and quantum teleportation in an optomechanical system.

Investigation of electromagnetic properties of a high absorptive, weakly reflective metamaterial—substrate system with compensated chirality

In the present paper, a theoretical and experimental study of a highly absorptive, weakly reflective coating designed and fabricated on the basis of 3D THz resonant elements is reported. Transmission and reflection of electromagnetic waves from the metamaterial-substrate structure involving a highly absorptive, weakly reflective array of artificial bi-anisotropic elements were analyzed. The samples contained paired right-handed and left-handed helices, due to the fact that the chirality was compensated. The parameters of helices were optimized to achieve roughly identical values of dielectric permittivity and magnetic permeability. As a result, the metamaterial exhibited weak reflectivity in the vicinity of resonance frequency. On the other hand, effective resonance properties of the helices were tuned to ensure substantial absorption of THz radiation. Analytical expressions for the coefficients of radiation reflection and transmission in the samples were derived by solving a boundary-value problem for the propagation of electromagnetic waves in the metamaterial-substrate system. Simulated properties of fabricated structures were compared with experimental data.

Compact e-shape metasurface with dual-band circular polarization conversion

Double-band circular polarization conversion based on novel e-shape resonators is proposed and studied both numerically and experimentally. Both the simulated results and experimental results are in good agreement. At two resonant frequencies, i.e., 11.65GHz and 13.02GHz, the incident y-direction linearly polarized wave can be transformed into right- and left-handed circularly polarized waves, respectively. The proposed structure can transmit a nearly pure circularly polarized wave, with a polarization extinction ratio of greater than 30dB. Moreover, the metasurface is compact with simple geometry, which is not only extremely thin in the propagating direction but also very small in the transverse direction. The retrieval results reveal that the effective refractive index of the e-shape structure is nearly negative in the vicinity of resonant frequencies. The surface current distributions are investigated to illustrate the polarization transformation mechanism. We also analyze the influence of several main geometric parameters for regulating the polarization properties. The proposed e-shape structure is promising for use in the design of polarization control devices.

Research on an pump-probe rubidium magnetometer

In order to measure a weak alternating magnetic field, an optically-pumped Rb magnetometer based on pump-probe structure is investigated and demonstrated. The pumping light and probing light propagate along the z axis and x axis, respectively. A constant polarization magnetic field along the pumping light is applied, which not only stabilizes the polarization of Rb atoms but also tunes resonance frequency of Rb atoms. When a weak alternating magnetic field is applied perpendicularly to the constant magnetic field, the magnetic moment will tip off the z axis and rotate around the z axis. And then the polarization plane of probing light is modulated correspondingly. The x component of the magnetic moment can be obtained with a balanced detector. As a result, a signal proportional to weak alternating magnetic field can be obtained.In order to obtain the magnetic response of the magnetometer, we analyze the signal amplitude as a function of polarization magnetic field strength B0 and transverse relaxation time 2 with numerical simulation. The amplitude-frequency response of the magnetometer is determined mainly by two parameters, namely cutoff frequency c=1/2 and resonance frequency 0= B0, where is the gyromagnetic ratio of Rb atom. At low frequency, that is a0 and a 0c2, the magnetometer has a flat response, here a is the frequency of the weak alternating magnetic field. If 0c, the signal amplitude will be large for large 0 or small c. For a given c, the peak response appears at 0=c. In the vicinity of resonance frequency, if c0, a peak will appear and if c 0, no peak occurs. At high frequency, the amplitude will decrease with the increase of a.We verify the above analyses in experiment. A vapor cell with a short transverse relaxation time is used to obtain large frequency response bandwidth. Through optimizing the powers and frequencies of pumping laser and probing laser, high polarization and detection sensitivity of atomic spin can be obtained. Moreover, through choosing an appropriate polarization magnetic field, the magnetometer can be maximally sensitive to the magnetic field to be measured. The experimental results show that the magnetometer has a sensitivity of about m 0.2; pT/HzHz and bandwidth of about 3.5 kHz. It can be used to detect low field magnetic resonance and high frequency abnormal physical phenomena.

The transmission of an acoustic wave through a rectangular plate between barriers

Abstract The problem of the forced vibrations of a rectangular elastic plate hinged to the sides of an opening in an absolutely stiff partition upon the transmission of a monoharmonic acoustic wave through it is considered. It is assumed that the partition is located between two absolutely stiff barriers, one of which forms an acoustic wave that is incident to the plate due to harmonic vibrations with an assigned displacement amplitude, while the other barrier is fixed and has a deformable energy-absorbing coating made from a material with high damping properties. The behaviour of acoustic media in spaces between a deformable plate and barriers is described by classical wave equations based on the model of an ideal compressible fluid, and the mechanics of the deformation of the plate are described by the equations of motion from the classical linear plate theory with consideration of the internal friction of the plate material according to the Thompson–Kelvin–Voigt hysteretic model. To describe the process of the dynamic deformation of an energy-absorbing coating on a fixed barrier, two-dimensional equations of motion based on the use of a model of a transversely soft layer, a linear approximation of the displacement fields in the direction of the thickness of the coating and consideration of the damping properties of its material also according to the hysteretic model are derived. Analytical solutions of the problem are found with and without consideration of the compliance of the supporting elements of the plate. The influence of the physicomechanical parameters of the mechanical system under consideration on the sound reduction parameters of the plate and the sound pressure in the spaces between the plate and the barriers, as well as of the stress-strain state under forced vibrations of the plate as a function of the frequency of the acoustic wave incident to it, is investigated. It is shown that the mechanical behaviour of the plate in the vicinity of resonance frequencies depends practically completely on the aerodynamic damping and that for stiff building materials, which have, as a rule, small values of the logarithmic decrement of the vibrations, taking into account the internal damping has an insignificant influence on the parameters investigated of the system.

Experimental investigation into amplitude-dependent modal properties of an eleven-span motorway bridge

This paper examines experimentally the effect of forcing and response amplitude on the variability of modal parameters of a bridge. An eleven-span prestressed concrete motorway off-ramp bridge was subjected to multiple dynamic tests with varying excitation levels by using eccentric mass shakers exerting forces in the vertical and lateral direction. The frequency sweeping technique with small increment steps in the vicinity of resonant frequencies was employed to construct frequency response functions at different shaking levels from which the natural frequencies, damping ratios and mode shapes were identified for several vertical, mixed vertical–torsional and lateral modes. Softening dynamic force–displacement relationships were observed for all the modes, and the natural frequencies showed clear and consistent decreasing trends with increasing response amplitude. Modal damping ratios initially increased with increasing response amplitude, but later, for the modes where experimental data were available, stabilised at elevated levels. A finite element (FE) model of the bridge was also created and the experimental modal properties compared to the numerical ones. A good agreement was generally noticed for the lower modes but the higher modes had more error. The FE model was used to assess the likely levels of structural damage that would have a similar effect on the natural frequencies as the amplitude dependence. One numerical damage scenario indicated that a reduction of 20% of stiffness in the middle of the main span would cause larger frequency shifts of some modes but amplitude dependent effects will dominate in other modes. Another numerical damage scenario was a reduction by 50% of stiffness at the bottom of the highest pier, and it was shown this type of damage would result in only one third of the frequency drop caused by the amplitude effects in a single, most affected mode.

Enhanced Microwave Absorption of Flake-Oriented Sendust Sheets by Tape Casting

Electromagnetic absorbers, consisting of the magnetic particles suspended in a nonmagnetic matrix, have been widely used in the telecommunication industry to suppress electromagnetic interference (EMI) [1]. The magnetic material absorbers are required to have high permeability in the vicinity of resonance frequency due to the increasing working frequency of next generation telecommunication devices. Among a variety of potential magnetic absorbers, metallic magnetic particles have been widely studied due to their large saturation magnetization, high permeability and high Snoek's limit [2]. Of particular interest is the shape anisotropy of magnetic particles that may give rise to higher products of permeability and resonance frequency, beyond that of the Snoek's limit. However, because of the brittleness of flaky particles, it is difficult to retain flaky particles completely aligned along the plane of the sample by using rolling process. In this work, we aim to prepare oriented Sendust flakes in sheet form by tape-casting. The oriented Sendust sheets have potential to demonstrate superior microwave absorption performance at high frequencies (1∼4GHz).

Thermal Stressed State of a Magnetic Layer Under Ferromagnetic Resonance

We propose representations for the magnetic field strength and establish expressions for the magnetization, magnetic-field induction, and energy and force factors of the action of magnetic fields under the conditions of ferromagnetic resonance. We determine and analyze the distributions of temperature, displacements, and stresses (the components of both symmetric and asymmetric tensors) over the thickness coordinate and, in particular, in the vicinity of resonance frequencies.

Resonance oscillations of an aerosol in a tube with a diaphragm in the shock free-wave mode

The results of experimental investigations of nonlinear oscillations of a finely dispersed aerosol in a tube with a diaphragm in the shock free-wave mode in the vicinity of resonance frequencies are presented. The frequency dependences of the peak-to-peak amplitude of aerosol pressure oscillations upon different internal diameters of the diaphragm are found. The time dependences of the numerical concentration of the oscillating aerosol droplets are presented. The effect of the frequency and amplitude of piston displacement and the influence of the diaphragm internal diameter on the aerosol clearing time are studied. It is shown that the clearing process of an oscillating aerosol is 5–10 times more efficient than natural deposition of aerosol.

Tunable characteristics of bending resonance frequency in magnetoelectric laminated composites

As the magnetoelectric (ME) effect in piezoelectric/magnetostrictive laminated composites is mediated by mechanical deformation, the ME effect is significantly enhanced in the vicinity of resonance frequency. The bending resonance frequency (fr) of bilayered Terfenol-D/PZT (MP) laminated composites is studied, and our analysis predicts that (i) the bending resonance frequency of an MP laminated composite can be tuned by an applied dc magnetic bias (Hdc) due to the ΔE effect; (ii) the bending resonance frequency of the MP laminated composite can be controlled by incorporating FeCuNbSiB layers with different thicknesses. The experimental results show that with Hdc increasing from 0 Oe (1 Oe=79.5775 A/m) to 700 Oe, the bending resonance frequency can be shifted in a range of 32.68 kHz ≤ fr ≤ 33.96 kHz. In addition, with the thickness of the FeCuNbSiB layer increasing from 0 μm to 90 μm, the bending resonance frequency of the MP laminated composite gradually increases from 33.66 kHz to 39.18 kHz. This study offers a method of adjusting the strength of dc magnetic bias or the thicknesses of the FeCuNbSiB layer to tune the bending resonance frequency for ME composite, which plays a guiding role in the ME composite design for real applications.

Double H-shaped metamaterial resonator for low phase noise voltage controlled oscillator

In this article, we propose a voltage controlled oscillator (VCO) using a double H-shaped metamaterial resonator (DHMR) based on a high Q value.The proposed DHMR exhibits a metamaterial characteristic which has a zero phase coefficient at the vicinity of resonance frequency. The proposed DHMR is designed to be a high Q by a strong coupling of the E-field at the resonance frequency. These characteristics made phase noise performance in the synthesizer using the proposed VCO excellent. The proposed VCO with DHMR is designed to apply to an X-Band frequency synthesizer of radar systems. The output power, the phase noise and the tuning range are 7.33 dBm, −121.3 dBc/Hz at 100 kHz offset carrier frequency and over 120 MHz, respectively. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 54:1059–1063, 2012; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.26694

Resonant phenomena in irregular acoustic waveguides of the coastal wedge type

Analysis of acoustic power radiated by a source in the Pekeris waveguide and calculated within the framework of a non-self-adjoint model statement of the corresponding boundary problem is made. A significant increase in power, in comparison to the classical solution, is noted. This result has been achieved owing to correct description of energy loss from the waveguide into the half-space in the vicinity of resonant frequencies and owing to excitation of a boundary-type near-bottom wave. The results of experimental study of the sound field in the coastal wedge are an example of the resonant character of sound field excitation in the waveguide-half-space system with consequent sound energy capture by the waveguide.

Terahertz spectra and soft optical phonons of PbB4O7 crystal

The terahertz(1012Hz)spectra, Raman spectra and infrared-visible-UV spectra are analyzed for PbB4O7 crystal sample. A resonance peak appears in the curve of the dielectric function ε(ν) in the frequency range of 0.25—2.5 THz. The analysis supports that soft optical phonons exist in PbB4O7 crystal from four aspects: 1) the change curve ε(ν) of the dielectric function satisfies the Lyddane-Sachs-Teller relation; 2) a strong Raman scattering peak appears in the vicinity of resonance frequency (3.10 THz); 3) absorption coefficient curve α(ν) meets the characteristics of polaritons; 4) the dispersion relation curve ν(k) of the photon transmitting from the crystal reveals a frequency gap. The soft optical phonon exists in PbB4O7 crystal, which means that the frequency curve of the photon transmitting from the crystal will suffer splitting when the condition of producing polariton is satisfied. And the dispersion curve splits a higher branch and a lower one. This may help us find a new method of changing the frequency of the photon.