Low-frequency bandgap and vibration suppression mechanism of a novel square hierarchical honeycomb metamaterial

The suppression of low-frequency vibration and noise has always been an important issue in a wide range of engineering applications.To address this concern,a novel square hierarchical honeycomb metamaterial capable of reducing low-frequency noise has been developed.By combining Bloch’s theorem with the finite element method,the band structure is calculated.Numerical results indicate that this metamaterial can produce multiple low-frequency bandgaps within 500 Hz,with a bandgap ratio exceeding 50%.The first bandgap spans from 169.57 Hz to 216.42 Hz.To reveal the formation mechanism of the bandgap,a vibrational mode analysis is performed.Numerical analysis demonstrates that the bandgap is attributed to the suppression of elastic wave propagation by the vibrations of the structure’s two protruding corners and overall expansion vibrations.Additionally,detailed parametric analyses are conducted to investigate the effect ofθ,i.e.,the angle between the protruding corner of the structure and the horizontal direction,on the band structures and the total effective bandgap width.It is found that reducingθis conducive to obtaining lower frequency bandgaps.The propagation characteristics of elastic waves in the structure are explored by the group velocity,phase velocity,and wave propagation direction.Finally,the transmission characteristics of a finite periodic structure are investigated experimentally.The results indicate significant acceleration amplitude attenuation within the bandgap range,confirming the structure’s excellent low-frequency vibration suppression capability.

Experiment on low-frequency electromagnetic waves propagating in shock-tube-generated magnetized cylindrical enveloping plasma

We propose a method of applying a static magnetic field to reduce the attenuation of the magnetic field component(SH) of low-frequency electromagnetic(LF EM) waves in dense plasma. The principle of this method is to apply a static magnetic field to limit electron movement, thereby increasing the equivalent resistance and thus reducing the induced current and SH. We consider the static magnetic field acting on the plasma of the entire induced current loop rather than on the local plasma, where the induced current is excited by the magnetic field component of LF EM waves. Analytical expressions of SH suitable for magnetized cylindrical enveloping plasma are derived by adopting an equivalent circuit approach, by which SHis calculated with respect to various plasma parameter settings. The results show that SH can be reduced under a static magnetic field and the maximum magnetic field strength that mitigates blackout is less than 0.1 T. Experiments in which LF EM waves propagate in a shock-tubegenerated magnetized cylindrical enveloping plasma are also conducted. SH measured under the magnetic field(the magnetic field strength B0 acting on the magnetic field probe was about0.06 T) reduces at f=10 MHz and f=30 MHz when ne≈1.9×1013 cm-3, which is consistent with theoretical results. The verification of the theory thus suggests that applying a static magnetic field with a weak magnetic field has the potential to improve the transmission capacity of LF EM waves in dense plasma.

Analysis of Second-Harmonic Generation of Low-Frequency Dilatational Lamb Waves in a Two-Layered Composite Plate

We analyze the effect of second-harmonic generation（SHG） of primary Lamb wave propagation in a two-layered composite plate, and then investigate the influence of interfacial properties on the said effect at low frequency. It is found that changes in the interfacial properties essentially affect the dispersion relation and then the maximum cumulative distance of the double-frequency Lamb wave generated. This will remarkably influence the efficiency of SHG. To overcome the complications arising from the inherent dispersion and multimode natures in analyzing the SHG effect of Lamb waves, the present work focuses on the analysis of the SHG effect of low-frequency dilatational Lamb wave propagation. Both the numerical analysis and finite element simulation indicate that the SHG effect of low-frequency dilatational Lamb wave propagation is found to be much more sensitive to changes in the interfacial properties than primary Lamb waves. The potential of using the SHG effect of low-frequency dilatational Lamb waves to characterize a minor change in the interfacial properties is analyzed.

Defects detection in typical positions of bend pipes using low-frequency ultrasonic guided wave

In order to analyze the possibility of detecting defects in bend pipe using low-frequency ultrasonic guided wave, the propagation of T(0,1) mode and L(0,2) mode through straight-curved-straight pipe sections was studied. FE(finite element) models of bend pipe without defects and those with defects were introduced to analyze energy distribution, mode transition and defect detection of ultrasonic guided wave. FE simulation results were validated by experiments of four different bend pipes with circumferential defects in different positions. It is shown that most energy of T(0,1) mode or L(0,2) mode focuses on extrados of bend but little passes through intrados of bend, and T(0,1) mode or L(0,2) mode is converted to other possible non-axisymmetric modes when propagating through the bend and the defect after bend respectively. Furthermore, L(0,2) mode is more sensitive to circumferential notch than T(0,1) mode. The results of this work are beneficial for practical testing of pipes.

Seasonal Variation of Stationary and Low-Frequency Rossby Wave Rays

The wave rays and their seasonal variation of stationary and low-frequency Rossby waves are studied by using the Runge-Kutta scheme. The results show that for stationary waves the rays can reach lower latitudes in winter, and are limited in higher latitudes in summer. The main differences between the stationary and low-frequency wave rays are that low-frequency waves can propagate across the equator and the easterlies will not be an obstacle on their propagation. It explained to some extent the interaction of disturbances between the Northern and Southern Hemispheres. The lower wave frequencies and the stronger easterly flow are, the more difficult low-frequency waves will be to propagate across the equator. The waves with 20-day period are easier to propagate across the equator than that with 50-day period. The winter is the most favorable season for low-frequency waves to propagate into another hemisphere.

Dispersion Equation of Low-Frequency Waves Driven by Temperature Anisotropy

The plasma temperature （or the kinetic pressure） anisotropy is an intrinsic characteristic of a collisionless magnetized plasma. In this paper, based on the two-fluid model, a dispersion equation of low-frequency （ω〈〈ωci, ωci the ion gyrofrequency） waves, including the plasma temperature anisotropy effect, is presented. We investigate the properties of low-frequency waves when the parallel temperature exceeds the perpendicular temperature, and especially their dependence on the propagation angle, pressure anisotropy, and energy closures. The results show that both the instable Alfven and slow modes are purely growing. The growth rate of the Alfven wave is not affected by the propagation angle or energy closures, while that of the slow wave depends sensitively on the propagation angle and energy closures as well as pressure anisotropy. The fast wave is always stable. We also show how to elaborate the symbolic calculation of the dispersion equation performed using Mathematica Notebook.

Low-Frequency Waves Forced by Large-scale Topography in the Barotropic Model

A barotropic model containing large-scale topography and zonal mean flow is established to discuss the effects of large-scale topography on the low-frequency waves. The results show that what affects low-frequency waves mostly is maximal height of topography and topographic slope. The former makes frequency of topographic Rossby waves decrease, the latter makes Rossby waves instable. Moreover, when topographic slope is appropriate, it can also make Rossby waves turn into low-frequency waves.

RADIATIVE COOLING AND BROADBAND PHENOMENON IN LOW-FREQUENCY WAVES

In this paper, we analyze the effects of radiative cooling on the pure baroclinic low-frequency waves under the approximation of equatorial β-plane and semi-geostrophic condition. The results show that radiative cooling does not, exclusively, provide the damping effects on the development of low-frequency waves.Under the delicate radiative-convective equilibrium, radiative effects will alter the phase speed and wave period,and bring about the broadband of phase velocity and wave period by adjusting the vertical profiles of diabaticheating. When the intensity of diabatic heating is moderate and appropriate, it is conductive to the de-velopment and sustaining of the low-frequency waves and their broadband phenomena, not the larger, the better. The radiative cooling cannot be neglected in order to reach the moderate and appropriate intensity of diabatic heating.

Impacts of SST and SST Anomalies on Low-Frequency Oscillation in the Tropical Atmosphere

Considering the multiscale character of LFO effects of SST on LFO in the tropical atmosphere （low-frequency oscillation） in the tropical atmosphere, the are discussed by using an absolute ageostrophic, baroclinic model. Here, SST effects include sea surface heating and forcing of SST anomalies （SSTAs）. Studies of the influences of sea surface heating on LFO frequency and stability show that sea surface heating can slow the speed of waves and lower their frequency when SST is comparatively low; while higher SST leads to unstable waves and less periods of LFO. Since the impact of a SSTA on ultra-long waves is more evident than that on kilometer-scale waves, long-wave approximation is used when we continue to study the effect of SSTAs. Results indicate that SSTAs can lead to a longer period of LFO, and make waves unstable. In other words, positive （negative） SSTAs can make waves decay （grow）.

NUMERICAL EXPERIMENTS OF EFFECT OF SSTA OVER THE INDIAN OCEAN ON ATMOSPHERIC LOW-FREQUENCY OSCILLATION IN THE EXTRATROPICAL LATITUDE

Numerical experiments on forcing dissipation and heating response of dipole (unipole) are carried out using global spectral models with quasi-geostrophic barotropic vorticity equations. For each experiment model integration is run for 90 days on the condition of three-wave quasi-resonance. The results are given as follows: Under the effects of dipole (unipole) forcing source and basic flow intensity, there exist strong interactions among the three planetary waves and quasi-biweekly and intraseasonal oscillation of the three planetary waves. In the meantime, the changes in the intensity of dipole or unipole forcing source and basic flow have different frequency modulation effects on LFO in the middle and higher latitudes. The results of the stream function field of three quasi-resonant waves evolving with time confirm that the low-frequency oscillation exists in extratropical latitude.

The Propagation of Disturbances Excited by Low-Frequency Oscillations in the Tropics

The propagation of disturbances excited by low-frequency oscillations in the tropics is investigated by applying the theory of wave packet dynamics. For simplicity, a linearized barotropic model is adopted and the zonal circulation is taken as basic current. Suppose that the disturbances or waves are superimposed on jet-like westerly basic cur-rent and excited by the forcing in the tropics. We have (1) only the eastward propagating (m>0, n>0 and σ>0) low-frequency disturbances and the stationary (σ = 0) waves can propagate into the middle and high latitudes in the Northern Hemisphere; the others, such as the westward propagating low-frequency wave (m>0, n<0, σ<0) and the high-frequency waves, are restricted only in the vicinity of source region; (2) a stationary wave (σ = 0) reaches a given latitude even more quickly than some low-frequency ones (σ>0) due to the fact that the group velocity of stationary wave is larger; (3) there is a whole wave train excited by the forcing in the tropics and extended into the middle and high latitudes, if the amplitude of the source is independent on time, especially, the low-frequency wave (σ > 0) is of travelling type propagating along the ray; (4) if the source lasts only for an interval of time, namely, its amplitude also has the character of low-frequency oscillation, the excited wave train is not always a whole one, but is restricted in the vicinity of source region in the beginning, extended from the source region to the middle and high latitudes in its saturated stage, after that it gradually becomes weaker and weaker and is detectable only in some area at high latitude, and eventually disappears. Undoubtedly, case (4) is closer to the reality, even though case (3) gives a more impressive wavy pattern.

Algorithm of sky-ground-wave signal separation in CDMA system

To solve the problem of the sky-wave interference in radio positioning system operating in CDMA mode, an algorithm of sky-ground-wave separation is provided. Based on the MLE （maximum likelihood estimate）, and by estimating the amplitude and the phase of the sky-wave signal, the provided algorithm for separating skyground-wave is implemented. The mathematics model used for signal processing is established, and the possible solutions are provided. The structure and signal processing flow implementing the presented algorithm in the receiver are presented. A multi-channels signal searching idea is adopted, some of which process the sky-wave signal, and some of which process the ground-wave signal. Numerical analysis and simulation show that the proposed algorithm has higher accuracy, more rapid processing speed, and simpler implementation for the estimation of the sky-wave signal parameter, and can separate the sky-wave signal and ground-wave signal from the arrival combination signal effectively.

THE EFFECTS OF THE PLATEAU'S TOPOGRAPHIC GRADIENT ON ROSSBY WAVES AND ITS NUMERICAL SIMULATION

By using barotropic model equations, this article analyzed the characteristics of Rossby waves, the propaga- tion features of wave energy and the influence of dynamic and thermal effects of the Tibetan Plateau on Rossby waves, and the focus is on discussing the plateau＇s topographic gradient effects on atmospheric Rossby waves. Then based on the WRF3.2 and the NCEP/NCAR FNL reanalysis data, we devised comparative tests of changing the plateau＇s topo- graphic gradient and simulated a process of persistent heavy rain that happened in May 2010 in South China. The re- sults are shown as follows. The Tibetan Platean＇s topography is conducive to the formation of atmospheric Rossby waves, while the platean＇s terrain, its friction and heating effects can all make the atmospheric Rossby waves develop into the planetary waves; The effects of platean＇s north and south slopes on the Rossby wave＇ phase velocity is opposite, and when the slope reached a certain value can the quasi-steady normal fluctuations be generated; Simultaneously, due to the plateau＇s topographic gradient, descending motion appears at the west side of the plateau while ascending motion appears at the east side, and the vertical movement increased with the amplification of topographic gradients. The plateau＇s topographic gradient also obviously amplified the precipitation in South China, and the rainfall area increased with the amplification of topographic gradients and gradually moved from south to north and from west to east, which is conducive to the occurrence and development of convective activities in the downstream areas of the Tibetan Plateau; Moreover, for the plateau＇s dynamic and thermal effects, the Rossby wave＇ propagation shows upstream effects of ener- gy dispersion, so the plateau can then affect the weather in downstream areas. Moreover, the wave group velocity in- creased with the degree of topographic slope.

Infra-Gravity Wave Generation by the Shoaling Wave Groups over Beaches

A physical parameter, fib, which was used to meet the forcing of primary short waves to be off-resonant before wave breaking, has been considered as an applicable parameter in the infra-gravity wave generation. Since a series of modulating wave groups for different wave conditions are perfonned to proceed with the resonant mechanism of infra- gravity waves prior to wave breaking, the amplitude growth of incident bound long wave is assumed to be simply controlled by the normalized bed slope, fib. The results appear a large dependence of the growth rate, a, of incident bound long wave, separated by the three-array method, on the normalized bed slope, fib. High spatial resolution of wave records enables identification of the cross-correlation between squared short-wave envelopes and infra-gravity waves. The cross- shore structure of infra-gravity waves over beaches presents the mechanics of incident bound- and outgoing free long waves with the formation of free standing long waves in the nearshore region. The wave run-up and amplification of infra-gravity waves in the swash zone appear that the additional long waves generated by the breaking process would modify the cross-shore structure of free standing long waves. Finally, this paper would further discuss the contribution of long wave breaking and bottom friction to the energy dissipation of infra-gravity waves based on different slope conditions.

Theoretical and Experimental Study on the Acoustic Wave Energy After the Nonlinear Interaction of Acoustic Waves in Aqueous Media

Based on the Burgers equation and Manley-Rowe equation, the derivation about nonlinear interaction of the acoustic waves has been done in this paper. After nonlinear interaction among the low-frequency weak waves and the pump wave, the analytical solutions of acoustic waves＇ amplitude in the field are deduced. The relationship between normalized energy of high-frequency and the change of acoustic energy before and after the nonlinear interaction of the acoustic waves is analyzed. The experimental results about the changes of the acoustic energy are presented. The study shows that new frequencies are generated and the energies of the low-frequency are modulated in a long term by the pump waves, which leads the energies of the low-frequency acoustic waves to change in the pulse trend in the process of the nonlinear interaction of the acoustic waves. The increase and decrease of the energies of the low-frequency are observed under certain typical conditions, which lays a foundation for practical engineering applications.

Experimental Research on the Low Frequency Wave That Radiates into the Air before the Failure of Rock

Experiments on sonic transmission show that a slabstone can directly transmit part of the energy of a wave excited by knocking or by a transducer into the air. The other part of the wave energy can generate the normal mode of vibration on the slabstone and excite measurable acoustic signals in the air. The dominant frequency is related to the size of the slabstone. These results indicate that the acoustic emission (AE) in rock also displays similar behavior if the source is shallow. It is demonstrated that with the nucleation and propagation of cracks, the dominant frequency of the radiated wave will be lower. When the frequency becomes very low, the wave can be transmitted through the rock into the air and be received by a microphone. According to the theory of similarity of size, there will be low-frequency waves before strong earthquakes because of nucleation of cracks, which can be received by special low-frequency transducers or infrasonic detectors. Before earthquakes, the mechanism of precursors could be very complicated. They might be produced by plastic creep or attributed to liquids but not brittle fracture in most cases. So the periods of the produced waves will be longer. This perhaps accounts for the lack of foreshocks before many strong earthquakes.

Reverse time migration based on normalized wavefield decomposition imaging condition

With the increasing complexity of prospecting objectives,reverse time migration( RTM) has attracted more and more attention due to its outstanding imaging quality. RTM is based on two-way wave equation,so it can avoid the limits of angle in traditional one-way wave equation migration,image reverse branch,prism waves and multi-reflected wave precisely and obtain accurate dynamic information. However,the huge demands for storage and computation as well as low frequency noises restrict its wide application. The normalized cross-correlation imaging conditions based on wave field decomposition are derived from traditional cross-correlation imaging condition,and it can eliminate the low-frequency noises effectively and improve the imaging resolution. The practical procedure includes separating source and receiver wave field into one-way components respectively,and conducting cross-correlation imaging condition to the post-separated wave field. In this way,the resolution and precision of the imaging result will be promoted greatly.

THE DIABATIC WAVES IN BAROTROPIC MODEL

The equations of barotropic model are used to discuss the effects of diabatic factors such as heat-ing of convective condensation, evaporation-wind feedback and CISK on the Rossby wave and the Kelvin wave. In low latitudes we have obtained the angular frequency and analyzed the period and stability of waves. The result shows the existence of the diabatic factors not only enlarges the period of adiabatic waves but also changes the stability of waves. Thus we think that the so-called intraseasonal oscillation and some other low-frequency oscillations are a kind of diabatic waves which are important factors producing the long-term weather changes and short-term climatic evolution.

Thermal Effects of the Tibetan Plateau on Rossby Waves from the Diabatic Quasi-Geostrophic Equations of Motion

From the diabatic quasi-geostrophic equations of motion, the authors analyze the characteristics of diabatic Rossby waves including the thermal effects of the Tibetan Plateau. When the basic zonal flow is barotropic, it is demonstrated that the cooling of the Tibetan Plateau in winter not only facilitates the meridional propagation of Rossby waves but is an important driving mechanism of the intraseasonal oscillations in middle and high latitudes. When the basic zonal flow is baroclinic, it is found that the cooling of the Tibetan Plateau in winter facilitates the instability of Rossby waves, while in summer there is a threshold for the influence of the heating of the Tibetan Plateau on the stability of Rossby waves.

CISK-related Rossby Waves in the Tropical Atmosphere

In terms of a baroclinic quasi-geostrophic waveufiltering technique in connection with a dimensionless parameter,n(z),of condensation-released latent heat that indicates the CISK mechanism,a model is established for describing tropical atmosphere CISK-Rossby waves alongside its analytical solution. Theoretical study shows that thereexists pronounced difference between Rossby waves, CISK-involving and classic, and the former can be used to interpret some aspects of the low--frequency oscillation in the tropical atmosphere.