Three-dimensional coupled-mode model and characteristics of low-frequency sound propagation in ocean waveguide with seamount topography

Large-scale topography, such as a seamount, substantially impacts low-frequency sound propagation in an ocean waveguide, limiting the application of low-frequency acoustic detecting techniques. A three-dimensional(3D) coupledmode model is developed to calculate the acoustic field in an ocean waveguide with seamount topography and analyze the3D effect. In this model, a correction is introduced in the bottom boundary, theoretically making the acoustic field satisfy the energy conservation. Furthermore, a large azimuth angle calculation range is obtained by using the operator theory and higher-order Pade approximation. Additionally, the model has advantages related to the coupling mode and parabolic equation theory. The couplings corresponding to the effects of range-dependent environment are fully considered, and the numerical implementation is kept feasible. After verifying the accuracy and reliability of the model, low-frequency sound propagation characteristics in the seamount environment are analyzed. The results indicate lateral variability in bathymetry can lead to out-of-plane effects such as the horizontal refraction phenomenon, while the coupling effect tends to restore the abnormal sound field and produces acoustic field diffraction behind the seamount. This model effectively considers the effects of the horizontal refraction and coupling, which are proportional to the scale of the seamount.

Three-dimensional acoustic propagation model for shallow waters based on an indirect boundary element method

This work has a two-fold purpose.On the one hand,the theoretical formulation of a three-dimensional(3D)acoustic propagation model for shallow waters with a constant sound speed is presented,based on the boundary element method(BEM),which uses a half-space Green function instead of the more conventional free-space Green function.On the other hand,a numerical implementation is illustrated to explore the formulation in simple idealized cases,controlled by a few parameters,which provides necessary tests for the accuracy and performance of the model.The half-space Green's function,which has been previously used in scattering and diffraction,adds terms to the usual expressions of the integral operators without altering their continuity properties.Verifications against the wavenumber integration solution of the Pekeris waveguide suggest that the model allows an adequate prediction for the acoustic field.Likewise,numerical experiments in relation to the necessary mesh size for the description of the water-marine sediment interface lead to the conclusion that a transmission loss prediction with acceptable accuracy can be obtained with the use of a limited mesh around the desired evaluation region.

Numerical simulation of three-dimensional fracturing fracture propagation in radial wells

A fracture propagation model of radial well fracturing is established based on the finite element-meshless method.The model considers the coupling effect of fracturing fluid flow and rock matrix deformation.The fracture geometries of radial well fracturing are simulated,the induction effect of radial well on the fracture is quantitatively characterized,and the influences of azimuth,horizontal principle stress difference,and reservoir matrix permeability on the fracture geometries are revealed.The radial wells can induce the fractures to extend parallel to their axes when two radial wells in the same layer are fractured.When the radial wells are symmetrically distributed along the direction of the minimum horizontal principle stress with the azimuth greater than 15,the extrusion effect reduces the fracture length of radial wells.When the radial wells are symmetrically distributed along the direction of the maximum horizontal principal stress,the extrusion increases the fracture length of the radial wells.The fracture geometries are controlled by the rectification of radial borehole,the extrusion between radial wells in the same layer,and the deflection of the maximum horizontal principal stress.When the radial wells are distributed along the minimum horizontal principal stress symmetrically,the fracture length induced by the radial well decreases with the increase of azimuth;in contrast,when the radial wells are distributed along the maximum horizontal principal stress symmetrically,the fracture length induced by the radial well first decreases and then increases with the increase of azimuth.The fracture length induced by the radial well decreases with the increase of horizontal principal stress difference.The increase of rock matrix permeability and pore pressure of the matrix around radial wells makes the inducing effect of the radial well on fractures increase.

Three-dimensional parabolic equation model for seismo-acoustic propagation: Theoretical development and preliminary numerical implementation

A three-dimensional（3D） parabolic equation（PE） model for sound propagation in a seismo-acoustic waveguide is developed in Cartesian coordinates, with x, y, and z representing the marching direction, the longitudinal direction, and the depth direction, respectively. Two sets of 3D PEs for horizontally homogenous media are derived by rewriting the 3D elastic motion equations and simultaneously choosing proper dependent variables. The numerical scheme is for now restricted to the y-independent bathymetry. Accuracy of the numerical scheme is validated, and its azimuthal limitation is analyzed. In addition, effects of horizontal refraction in a wedge-shaped waveguide and another waveguide with a polyline bottom are illustrated. Great efforts should be made in future to provide this model with the ability to handle arbitrarily irregular fluid-elastic interfaces.

Analysis of Three-dimensional Crack Propagation by Using Displacement Discontinuity Method

A technique for modelling of three-dimensional(3D)quasi-statically propagating cracks in elastic bodies by the displacement discontinuity method(DDM)was described.When the crack is closed,the Mohr-coulomb rule on the two contacted surfaces of the crack must be satisfied.A simple iterative method was adopted in order to consider three different states of cracks.Under the assumption that the advance of the point on the crack front would occur only in the normal plane which is through this edge point,the maximum energy release rate criterion is modified to be used as the criterion for the crack growth.With discretization,the process of crack propagation can be seen as the advance of the vertices of the crack front.The program MCP3D was developed based on these theories to simulate the 3D quasi-static crack propagation.A numerical example of a penny-shaped crack subject to tension and compression in an infinite elastic media was analyzed with MCP3D,and the results in comparison with others' show that the present method for 3D crack propagation is effective.

A modified maximum tangential tensile stress criterion for three-dimensional crack propagation

The three-dimensional （3D） crack propagation is a hot issue in rock mechanics. To properly simulate 3D crack propagation, a modified maximum tangential tensile stress criterion is proposed. In this modified criterion, it is supposed that cracks propagate only at crack front in the principal normal plane. The tangential tensile stress at crack front in the principal normal plane in local coordinates is employed to determine crack propagation, which is calculated through coordinate transformation from global to local coordinates. New cracks will propagate when the maximum tangential tensile stress at crack front in the principal normal plane reaches the tensile strength of rock-like materials. Compared with the previous crack propagation criteria, the modified crack propagation criterion is helpful in calculating 3D crack stress intensity factor, and can overcome the limitations of propagation step determined by individual experiences in previous studies. Finally, the 3D crack propagation process is traced by element-free Galerkin method. The numerical results agree well with the experimental ones for a frozen resin sample with prefabricated 3D cracks.

Influence of warm eddies on sound propagation in the Gulf of Mexico

An automatic detection method is employed to identify and track eddies in the Gulf of Mexico. The physical parameters of the eddies, such as lifespan, radius, and distribution position are first examined and used to determine the spatio–temporal evolution of a strong warm eddy separated from the Mexico current. Then, the influence of this strong warm eddy on sound propagation during its lifespan are comprehensively analyzed with the parabolic equation and explained by using the normal mode and ray theories. Additionally, the influence of mesoscale eddies on the redistribution of total depth-integrated energy among the normal modes in the deep water is also discussed. The variation of arrival angle is investigated to explain the spreading acoustic energy caused by eddies. Overall, the results show that warm eddies can change the propagation paths and cause the convergence zone to broaden and approach the sound source. Moreover,the warm eddy can disperse sound energy and cause the total depth-integrated energy to incline to a lower normal mode.Throughout the whole of these three periods(eddy generating, eddy maturing, and eddy terminating), the fluctuation in the transmission loss is up to 30 dB(depending on the relative location of eddy center to the source).

Three-dimensional forward modeling for magnetotelluric sounding by finite element method

A finite element algorithm combined with divergence condition was presented for computing three-dimensional(3D) magnetotelluric forward modeling. The finite element equation of three-dimensional magnetotelluric forward modeling was derived from Maxwell's equations using general variation principle. The divergence condition was added forcedly to the electric field boundary value problem, which made the solution correct. The system of equation of the finite element algorithm was a large sparse, banded, symmetric, ill-conditioned, non-Hermitian complex matrix equation, which can be solved using the Bi-CGSTAB method. In order to prove correctness of the three-dimensional magnetotelluric forward algorithm, the computed results and analytic results of one-dimensional geo-electrical model were compared. In addition, the three-dimensional magnetotelluric forward algorithm is given a further evaluation by computing COMMEMI model. The forward modeling results show that the algorithm is very efficient, and it has a lot of advantages, such as the high precision, the canonical process of solving problem, meeting the internal boundary condition automatically and adapting to all kinds of distribution of multi-substances.

The Effects of Seamounts on Sound Propagation in Deep Water

A propagation experiment was conducted in the South China Sea in 2014 with a flat bottom and seamounts respectively by using explosive sources. The effects of seamounts on sound propagation are analyzed by using the broadband signals. It is observed that the transmission loss （TL） decreases up to 7 dB for the signals in the first shadow zone due to the seamount reflection. Moreover, the TL might increase more than 30 dB in the converge zone due to the shadowing by seamounts. Abnormal TLs and pulse arrival structures at different ranges are explained by using the ray and wave theory. The experimental TLs and arrival pulses are compared with the numerical results and found to be in good agreement.

The Effect of Wood Condition on Sound Wave Propagation

This experiment aims to study the effects and modifications that occurred on acoustic signal harmonics when travelling through wood. The experiment measured the output amplitudes and frequencies of the travelling signals and compared them with the original input signal. The factors under investigation in this experiment included: wood type, wood moisture content (MC), input signal frequencies, signal travelling distance and wood condition (wood with/without cracks). The experiment findings demonstrated that higher input signal frequencies results in higher attenuation of acoustic emissions (AE) travelling through the wood. The results also indicate that: wood type, MC, the signal’s travelling distance, and the orientation of the travelling signal, compared to the wood’s grain direction, affected the signal propagation.

The study of sound wave propagation in rarefied gases using unified gas-kinetic scheme

Sound wave propagation in rarefied monatomic gases is simulated using a newly developed unified gaskinetic scheme （UGKS）. The numerical calculations are carfled out for a wide range of wave oscillating frequencies. The corresponding rarefaction parameter is defined as the ratio of sound wave frequency to the intermolecular particle collision frequency. The simulation covers the flow regime from the continuum to free molecule one. The treatment of the os- cillating wall boundary condition and the methods for eval- uating the absorption coefficient and sound wave speed are presented in detail. The simulation results from the UGKS are compared to the Navier-Stokes solutions, the direct sim- ulation Monte Carlo （DSMC） simulation, and experimental measurements. Good agreement with the experimental data has been obtained in the whole flow regimes for the corresponding Knudsen number from 0.08 to 32. The cur- rent study clearly demonstrates the capability of the UGKS method in capturing the sound wave propagation and its usefulness for the rarefied flow study.

Sound Quality Prediction of Vehicle Interior Noise under Multiple Working Conditions Using Back-Propagation Neural Network Model

This paper presents a back-propagation neural network model for sound quality prediction (BPNN-SQP) of multiple working conditions’ vehicle interior noise. According to the standards and regulations, four kinds of vehicle interior noises under operating conditions, including idle, constant speed, accelerating and braking, are acquired. The objective psychoacoustic parameters and subjective annoyance results are respectively used as the input and output of the BPNN-SQP model. With correlation analysis and significance test, some psychoacoustic parameters, such as loudness, A-weighted sound pressure level, roughness, articulation index and sharpness, are selected for modeling. The annoyance values of unknown noise samples estimated by the BPNN-SQP model are highly correlated with the subjective annoyances. Conclusion can be drawn that the proposed BPNN-SQP model has good generalization ability and can be applied in sound quality prediction of vehicle interior noise under multiple working conditions.

Numerical Study on Nonlinear Sound Propagation for Parametric Array

This paper presents the numerical study on the nonlinear sound propagation for the parametric array using the compressible form of Navier-Stokes equations combined with the mass and energy conservation equations and the state equation. These governing equations are solved by finite difference time domain (FDTD) based method. The numerical result is shown for the parametric sound propagation in the near field of the sound source in cylindrical coordinate. The result indicates the generation of low-frequency unsteady beat by the interaction of two frequency sound waves in the near field, which grows to a difference frequency sound in the far field.

Effect of Seabed Topography Change on Sound Ray Propagation—A Simulation Study

Variation of ocean environmental parameters is important to sound ray propagation. This article studies the problem of sound ray propagation in seawater by BELLHOP ray model. The sensitivities of sound ray propagation to the variations of seabed topography and depth of sound source by simulation. The results show that the depth variation of sound source is the main cause for emerging and disappearing of surface sound channel, accumulation area and deep sound channel. The deviation of sound ray propagation is in accordance with seabed topography change.

Aircraft noise and its nearfield propagation computations

Noise generated by civil transport aircraft during take-off and approach-to-land phases of operation is an environmental problem. The aircraft noise problem is firstly reviewed in this article. The review is followed by a description and assessment of a number of sound propagation methods suitable for applications with a background mean flow field pertinent to aircraft noise. Of the three main areas of the noise problem, i.e. generation, propagation, and ra- diation, propagation provides a vital link between near-field noise generation and far-field radiation. Its accurate assessment ensures the overall validity of a prediction model. Of the various classes of propagation equations, linearised Euler equations are often casted in either time domain or frequency domain. The equations are often solved numerically by computational aeroacoustics techniques, bur are subject to the onset of Kelvin-Helmholtz （K-H） instability modes which may ruin the solutions. Other forms of linearised equations, e.g. acoustic perturbation equations have been proposed, with differing degrees of success.

Damage Initiation and Propagation in Composites Subjected to Low-Velocity Impact:Experimental Results,3D Dynamic Damage Model,and FEM Simulations

A three-dimensional dynamic damage model that fits both small and large damage sizes is developed to predict impact damage initiation and propagation for each lamina of T300-carbon/epoxy laminations.First,13 specimens of the same lamination sequence are subjected to three different impact energies(10 J,15 J,and 20 J).After the impact,the laminates are inspected by the naked eye to observe the damage in the outer layers,and subsequently X-rayed to detect the inner damage.Next,the stress analysis of laminates subjected to impact loading is presented,based on the Hertz contact law and virtual displacement principle.Based on the analysis results,a three-dimensional dynamic damage model is proposed,including the Hou failure criteria and Camanho stiffness degradation model,to predict the impact damage shape and area.The numerical predictions of the damage shape and area show a relatively reasonable agreement with the experiments.Finally,the impact damage initiation and propagation for each lamina are investigated using this damage model,and the results improve the understanding of the impact process.

Electrical Structure of Wulingshan and Middle Jiangnan Orogen by Three-Dimensional Magnetotelluric Data Inversion

Funded by The National Key Research and Development Program of China,China Deep Exploration(Sinoprobe)and The China Geological Suvery Project on 2009–2019,a large scale magnetotelluric sounding(MT)survey grid(Fig.1)has covered whole south China.

MATCH-MODE METHOD AND ITS NUMERICAL SIMULATION FOR ROTOR-STATOR INTERACTION SOURCE MODES AND PROPAGATION MODES IN AN ANNULAR DUCT WITH MULTI-TREATMENTS

The suppressing design of the engine nacelle in an aircraft can benefit from the development of the prediction system for the sound fields in engine ducts which includes the prediction of the source generation and that of sound propagation in ducts. First, the acoustic match mode principle between the source modes of rotor stator interaction noise and the propagation modes is presented in this paper. Second, by utilizing this principle, the theoretical prediction method for rotor stator interaction noise generation and its propagation and attenuation in an annular duct with multi treatments is developed. That means that the prediction of sound propagation and attenuation in the segmented ducts might no longer completely depend on the in duct mode measurements, and the investigation on the sound propagation and attenuation in ducts can be accomplished not only by acoustic mode measurement, but also by making use of the source prediction to determine the source modes excited by rotor stator interaction. The effects of fan speed, blade/vane numbers, axial spacing between rotor and stator on the in duct sound attenuation and generated sound power level before and after ducts (also including the sound power level of blade passing frequency and its harmonics at the inlet of ducts) have been numerically calculated by using this prediction method. The reliability of this prediction method is verified by reasonable agreement between the predicted results with measured results in references. By analyzing the results of calculating cases, some reference criteria are provided for the engineering design of the suppressing engine nacelle.

3-D FRACTURE PROPAGATION SIMULATION AND PRODUCTION PREDICTION IN COALBED

In accordance with the fracturing and producing mechanism in coalbed methane well, and combining the knowledge of fluid mechanics, linear elastic fracture mechanics, thermal transfer, computing mathematics and software engineering, the three-dimensional hydraulic fracture propagating and dynamical production predicting models for coalbed methane well is put forward. The fracture propagation model takes the variation of rock mechanical properties and in-situ stress distribution into consideration. The dynamic performance prediction model takes the gas production mechanism into consideration. With these models, a three-dimensional hydraulic fracturing optimum design software for coalbed methane well is developed, and its practicality and reliability have been proved by ex-ample computation.

Comparative Study of the Propagation of Jet Noise in Static and Flow Environments

In order to analyze the effect of the background flow on the sound prediction of fine-scale turbulence noise,the sound spectra from static and flow environments are compared.It turns out that,the two methods can obtain similar predictions not only at 90 deg to the jet axis but also at mid-and high frequencies in other directions.The discrepancies of predictions from the two environments show that the effect of the jet flow on the sound propagation is related to low frequencies in the downstream and upstream directions.It is noted that there is an obvious advantage of computational efficiency for calculating in static environment,compared with that in flow environment.A good agreement is also observed to some extent between the predictions in static environment and measurements of subsonic to supersonic.It is believed that the predictions in static environment could be an effective method to study the propagation of the sound in jet flow and to predict the fine scale turbulence noise accurately in a way as well.