Method of reverberation ray matrix for static analysis of planar framed structures composed of anisotropic Timoshenko beam members

Based on the method of reverberation ray matrix（MRRM）, a reverberation matrix for planar framed structures composed of anisotropic Timoshenko（T） beam members containing completely hinged joints is developed for static analysis of such structures.In the MRRM for dynamic analysis, amplitudes of arriving and departing waves for joints are chosen as unknown quantities. However, for the present case of static analysis, displacements and rotational angles at the ends of each beam member are directly considered as unknown quantities. The expressions for stiffness matrices for anisotropic beam members are developed. A corresponding reverberation matrix is derived analytically for exact and unified determination on the displacements and internal forces at both ends of each member and arbitrary cross sectional locations in the structure. Numerical examples are given and compared with the finite element method（FEM） results to validate the present model. The characteristic parameter analysis is performed to demonstrate accuracy of the present model with the T beam theory in contrast with errors in the usual model based on the Euler-Bernoulli（EB） beam theory. The resulting reverberation matrix can be used for exact calculation of anisotropic framed structures as well as for parameter analysis of geometrical and material properties of the framed structures.

A procedure of the method of reverberation ray matrix for the buckling analysis of a thin multi-span plate

A procedure of the method of reverberation ray matrix(MRRM)is developed to perform the buckling analysis of thin multi-span rectangular plates having internal line supports or stiffeners.A computation algorithm for the reverberation ray matrix in the MRRM is derived to determine the buckling loading.Specifically,the analytical solutions are presented for the buckling of the structure having two opposite simply-supported or clamped-supported edges with spans,while the constraint condition of two remaining edges may be in any combination of free,simply-supported,and clamped boundary conditions.Furthermore,based on the analysis of matrices relating to the unknown coefficients in the solution form for the deflection in terms of buckling modal functions,some recursive equations(REs)for the MRRM are introduced to generate a reduced reverberation ray matrix with unchanged dimension when the number of spans increases,which promotes the computation efficiency.Several numerical examples are given,and the present results are compared with the known solutions to illustrate the validity and accurateness of the MRRM for the buckling analysis.

Performance Evaluation and Effectiveness of the Reverberation Room

This research presents a thorough evaluation of the reverberation room at Acoustics Laboratory in National Institute of Standards(NIS)according to the related international standards.The evaluation aims at examining the room performance and exploring its effectiveness in the frequency range from 125 Hz to 10000 Hz according to the international standard requirements.The room,which was designed and built several years ago,is an irregular rectangular shape free from diffusers.Its volume is about 158.84 m^(3),which meets the requirement of the ISO 354 standard Lmax<1.9V^(1/3).Cut-off frequencies of one and one-third octave are 63 Hz and 100 Hz respectively;however Schroder frequency is 400 Hz.Calculations of cut-off frequency and modal density showed adequate modes that give acceptable uniformity starting comfortably from frequency of 125 Hz.The room has a reverberation time that is suitable for its size over the frequency range of interest.The room sound absorption surface area and its sound absorption coefficient satisfy the criteria given in ISO 3741 and ISO 354.There is an accepted diffuse sound field inside the room due to the standard deviation of measured sound level,which is less than 1.5 dB over all the frequency range.The only exception was 125 Hz which may be due to a lack of diffusivity of the sound field at this frequency.The evaluation proves that the NIS reverberation room is in full agreement with the international standards,which in turns qualifies the room to host measurements inside without concerns.

Frequency-selective attenuation of sound propagation and reverberation in shallow water

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Improving sound diffusion in a reverberation tank using a randomly fluctuating surface

Underwater reverberation environments that satisfy the conditions of uniformity and isotropy of the diffuse field can be used to measure the acoustic characteristics of underwater targets.This study combines two practical indicators—the standard deviation of the absolute sound pressure field(to indicate uniformity)and the analysis of the wavenumber spectrum in the spherical harmonics domain(to indicate isotropy)—for an accurate evaluation of the diffusion of the sound field in a reverberation tank.A method is proposed that can improve the narrow-band diffusion of the sound field by employing a randomly fluctuating surface.An acoustic experiment was performed in a reverberation water tank(1.2 m×1 m×0.8 m),where a randomly fluctuating surface was generated by making waves.The experimental results show that as the wave motion contributes effectively to the random reflection of sound rays in all directions,the uniformity and isotropy are improved significantly when the surface is fluctuating randomly.This work helps to ensure accurate measurements of the characteristics of underwater targets in reverberation tanks.

Novel Way to Suppress Reverberation Based on Fractional Fourier Transform

A novel method of anti-reverberation based on the fractional Fourier transformation is presented. By virtue of the fact that it has a good focus property in the fractional Fourier domain, the linearly frequency modulation (LFM) signal can be seperated from the reverberation through a swept-frequency filter. With the actual reverberation data and the LFM pulse for seperation, the good results are obtained: the reverbareation is largely removed, and relatively the better performance is shown under the lower signal reverberation ratio (SRR). Based on the theorical analyses and simulation results, two schemes for detecting targets are provided: one is the detection of the LFM echo from the target with a threshold by means of this method directly; the other is to detect the target by means of other methods, with this method performing pre-process to increase SRR, which need enough large SRR.

The Effect of Television Decors on the Change of Reverberation Time of the Studio

Reverberation time within studio’s decor is changed because of addition of its surface to the overall surfaces of the studio and also the additional absorption of its materials. It seems reverberation time changes due to studio’s decor is little because surface of the decor is small in comparison with the overall surfaces of the studio and surface has an important role in room constant and therefore in reverberation time. But these changes do not only depend on added surfaces and their absorption. Reverberation time is also dependent on shape of the decor and sometimes. It can decrease the effects of added surfaces which are used to increase the reverberation time. In this paper, a standard television studio is designed and implemented by using ODEON and 12 different decor which their dimensions and materials are similar to the actual ones, are applied inside the studio. Then studio’s decor effects on reverberation time of the studio are computed, compared and analyzed.

A Deep-Water Bottom Reverberation Model Based on Ray Theory

Ocean reverberation is an important issue in underwater acoustics due to the significant influence on working performance of the active sonars. In this paper, a uniform bottom-reverberation model is proposed based on ray theory, which can calculate monostatic and bistatic reverberation intensity and explain the generation process of deep-water reverberation. The mesh meth-od is firstly used in this model by dividing bottom scatterers into a number of grids. Then reverberation is calculated based on the exact time of scattering signal generated on each grid. Due to exact arrival time, the presented model can provide more accurate result than classical models, in which scatterers are usually treated as circular rings or elliptical rings. Numerical results are compared with reverberation data collected from the South China Sea deep-water experiment with different receiving distances and depths. The simulated and experimental results agree well overall.

Nonlinear Acoustic Shadow Method to Reduce Reverberation Artifact

A novel technique for reducing reverberation artifact in acoustic shadow imaging using nonlinear ultrasound interaction, called nonlinear acoustic shadow method, has been developed and experimentally studied. In this technique, the conventional acoustic shadow method is modified by using the secondary wave generated by nonlinear interaction of two primary sound waves emitted from parametric array. Either conventional or nonlinear acoustic shadow imaging is carried out for aluminum square cylinder and the size of the shadow is compared. The result shows that the nonlinear acoustic shadow method reduces reverberation artifact inside the square cylinder and has better accuracy in the size measurement than conventional acoustic shadow method.

Method of coupled mode for long-range bottom reverberation

The theory of coupled mode is used for modeling the long-range bottom reverberation in shallow water caused by bottom roughness. The distant bottom reverberation level and spatial coherence of impulsive source are both derived. The results agree with those from the classical reverberation model, and are compared with the experimental data. The influence of source bandwidth and the distance between sources and receivers on the intensity of bottom reverberation are particularly discussed. The method is shown to be available for both the monoand the bi-static cases.

An oscillation phenomenon of low frequency reverberation in the shallow water and its physical explanation

An oscillation phenomenon of the low frequency reverberation intensity was observed in several shallow water reverberation experiments. This phenomenon cannot be explained by the widely used incoherent reverberation theory. In this paper, to explain the observed oscillation phenomenon, a normal mode based coherent reverberation theory is presented. The theoretical analysis and numerical results show that modal interference can cause the regular oscillation phenomenon of the low frequency reverberation intensity, and the oscillation frequency is determined by the normal mode eigen-values. A new method to estimate the bottom sound speed based on the oscillation frequency of reverberation intensity was presented in this paper. The experimental results at three different sites indicate that the bottom sound speed estimated from the oscillation frequency of reverberation intensity agrees with that inverted from Matched Field Processing (MFP) well.

Interference structure of shallow water reverberation in time-frequency distribution

The striations of the reverberation spectrum in the time-frequency distribution were observed in a shallow water acoustic experiment in 2002. A model following the coherent reverberation model developed in 2002 is presented to explain the observed striations. To examine the consistency between the measured data and numerical predictions, we have used a method based on Radon transform for determining the slope of the striations to the measured reverberation data and numerical predictions. The results indicate that the previously developed coherent reverberation model can predict the interference structure of the reverberation intensity in the time-frequency distribution.

The space-time coupling statistical model of reverberation from moving platforms

The space-time coupling characteristic of reverberation is one of key problems in the range of reverberation suppression with space-time processing methods.Traditional methods are not based on statistical characteristics of reverberation and not suitable to analyze the space-time coupling characteristics of reverberation in dealing with problems of reverberation extensions in the actual sea environment and non-ideal arrays.The space-time coupling relationship of moving platforms is deduced and then its space-time coupling statistical model is presented.The model describes the space-time coupling law of reverberation under the conditions as complex acoustic reverberation environments and an arbitrarily specified array.The mathematical expressions of space-time coupling relationship are described when the arrays have ideal narrow beams.The space-time distribution laws of reverberation from moving platforms are shown clearly by the analytical results and computer simulations,which validates the statistical model above.The space-time distribution law of reverberation from an uniform linear array(ULA),which is a non-ideal array,is also calculated by numerical methods.It is shown that the space-time distribution law of reverberation from any actual array can be acquired with the statistical model,and to support theoretically for reverberation suppression algorithms and systems design based on space-time processing.

Diagnostics for the structure of AGNs'broad line regions with reverberation mapping data:confirmation of the two-component broad line region model

We re-examine the ten Reverberation Mapping(RM) sources with public data based on the two-component model of the Broad Line Region(BLR).In fitting their broad Hβ Mlines,six of them only need one Gaussian component,one of them has a double-peak profile,one has an irregular profile,and only two of them need two components,i.e.,a Very Broad Gaussian Component(VBGC) and an Inter-Mediate Gaussian Component(IMGC).The Gaussian components are assumed to come from two distinct regions in the two-component model;they are the Very Broad Line Region(VBLR) and the Inter-Mediate Line region(IMLR).The two sources with a two-component profile are Mrk 509 and NGC 4051.The time lags of the two components of both sources satisfy tIMLR/tVBLR=V 2VBLR/V 2IMLR,where tIMLR and tVBLR are the lags of the two components while VIMLR and VVBLR represent the mean gas velocities of the two regions,supporting the two-component model of the BLR of Active Galactic Nuclei(AGNs).The fact that most of these ten sources only have the VBGC confirms the assumption that RM mainly measures the radius of the VBLR;consequently,the radius obtained from the R-L relationship mainly represents the radius of VBLR.Moreover,NGC 4051,with a lag of about 5 days in the one component model,is an outlier on the R-L relationship as shown in Kaspi et al.(2005);however this problem disappears in our two-component model with lags of about 2 and 6 days for the VBGC and IMGC,respectively.

Research on strong reverberation suppression for high resolution active sonar

Resolution enhancement of active sonar can suppress the reverberation.While it also makes the envelope data distribution diverge from Rayleigh distribution to K-distribution.The stronger scattering speckles,the heavier of the K-distribution tails.The envelope amplitudes of these strong scattering speckles are usually very big.As the interfering target,the strong reverberation decreases the performances of the background power level estimation and the target detection.The fuzzy statistical normalization processing(FSNP) is introduced to suppress the strong reverberation firstly in this paper.Then how the strong reverberation and the FSNP affect the distribution of K-distributed sonar data is studied.The influence on the constant false alarm rate(CFAR) detection performance caused by the strong reverberation and the FSNP is also simulated and analyzed.Performance comparisons between the CFAR detector based on FSNP and the conventional CFAR detectors are carried out.The simulation results show that the strong reverberation can make the shape parameter of the interfering K-distributed data become smaller than that of the original K-distributed data.While the FSNP can suppress the strong reverberation,increase the shape parameter value,and improve the performance of the shape parameter estimator and the CFAR detector.

A study on effect of sonochemistry in a reverberation field

In this paper, an ultrasound with frequency of 815 kHz was used to research the sonochemical yield in a small-size reverberation field by the method of fluorescent spectrum analysis. There are two characteristics on the effect of sonochemistry in the reverberation field: First, the cavitation threshold was about 0.3 W / cm2 (it was 0.7 W / cm2 in travelling field); Second, when the sound intensity was larger than the threshold, the sonochemical yield increased as the intensity increased and increased rapidly after the intensity was at 1.69-2.13 W / cm2, so that there was a upturned point in the curve of the result (which would tend to saturation in the travelling field). The theoretical analysis shows that the reason of the threshold decrease is that the sound energy density becomes high in the reverberation field, and the upturned point results from the disturbance of the radiation pressure on the liquid surface. Therefore, by experiment and theory this paper shows that a reverberation field has to be built for the higher sonochemical yield.

The numerical simulation of the average reverberation intensities in shallow water

A reverberation model for estimating the average reverberation intensity in layered shallow water is presented.The reverberation intensity is calculated in terms of ray theory for short range and normal mode theory for long range. The calculation accuracy has been improved by taking into account the effect of complex eigenvalues on the incident normal mode field. From the comparison between different scattering models it has been shown that the separable bistatic-backscattering model is acceptable. This makes it possible to calculate reverberation by using only the monostatic-backscattering coefficient and to save greatly the computing time.

An analysis of reverberation fluctuation by mean square derivation

A method for evaluating the fluctuation of the reverberation envelope is proposed and examined through simulation and real data in this paper.This method is different from the coefficient of variation which is only a function of the first and second order moment of the reverberation statistical model.By using the standard variance of the mean square derivate(MSD) of the reverberation envelope,the paper shows that the reverberation fluctuation is a function of the bandwidth of the emitted signal,and that a large value of the square variance means little fluctuation of the reverberation envelope.Theoretical studies show that the standard variance is proportional to the bandwidth of the emitted signal,so we conclude that less time width or larger bandwidth of the transmitted signal produces less fluctuation.Simulation and real active sonar data processing are used to verify this conclusion.

GENERALIZED REVERBERATION MATRIX FORMULATION FOR WAVE PROPAGATION IN MULTILAYERED MEDIUM

Generalized reverberation matrix （GRM） formulation is presented to investigate elastic wave propagation in a complex multilayered solid by the combination of reverberation-ray matrix （RRM） method and stiffness matrix （SM） method. RRM method formulates a reverberation matrix, which reflects the reflection or refraction of the elastic waves in the multilayered solid. However, the dimension of RRM increases as the sublayer number increases, which may result in lower calculation efficiency of the generalized rays. SM formulation yields a system matrix of the constant dimension to promise higher calculation efficiency, but it is difficult to identify the generalized rays. In order to calculate the generalized rays in the complex multi-layered solid efficiently, the RRM formulation is applied to the interested sublayer for the evaluation of the generalized rays and SM formulation to the other sublayers, to construct a generalized reverberation matrix of the constant dimension, which is independent of the sublayer number. Numerical examples show that GRM formulation has higher calculation efficiency for the generalized rays in the complex multilayered-solid configuration compared with RRM formulation.

Time reversal imaging of suspended target in strong reverberation

The weighted wideband time-reversal imaging approach of full signal subspaces was proposed.The extended target is modeled as an infinite number of independent point-like scatterers,and the imaging is constructed by accumulating all time-reversal images over all signal subspaces and the entire bandwidth in the region of suspected targets.On the bottom of a laboratory water waveguide,a cylindrical shell was used to produce reverberation.Two experiments were carried out.The first experiment is that an extended target was suspended near the cylindrical shell,whose echo and the reverberation reflected by the cylindrical shell were in different time windows.The second experiment is that a point-like target was suspended above the cylindrical shell,thus the echo and the reverberation were in the same time window.The experimental results show that the imaging quality of the proposed method is better than that of the conventional time reversal imaging methods for weak suspended targets in a strong reverberation background.