CN107885934A - Elastic construction acoustic radiation forecasting procedure under ocean channel based on coupling FEM PE - Google Patents
Elastic construction acoustic radiation forecasting procedure under ocean channel based on coupling FEM PE Download PDFInfo
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Abstract
The present invention is to provide elastic construction acoustic radiation forecasting procedure under a kind of ocean channel based on coupling FEM PE.Initially set up structure acoustic radiation multiple physical field coupled wave theory model under the channel circumstance of ocean, radiated sound field on the one-dimensional transversal of depth direction is obtained using FInite Element FEM, using segmentation, Ai Er meter Te interpolation methods are carried out after FEM sound field informations and the perfect matching of parabolic equation method PE lattice points spatially be FEM PE coupling conditions three times, the primary condition that the radiated sound field information is calculated as PE finite difference calculus, then set PE method relevant parameters after carry out ocean channel under elastic construction any site sound field Fast Prediction.The present invention is strong to elastic construction and ocean channel adaptation ability, and the accurate efficiency high of result of calculation, using simple easy to spread.Efficiently solve at present that elastic construction acoustic radiation is given the correct time more than the computationally intensive, physical field run into and many bottleneck sex chromosome mosaicisms such as channel circumstance complexity in advance in the case where studying ocean channel.
Description
Technical field
The present invention relates to elastic construction radiated sound field forecast under a kind of ocean channel and Acoustic Object detection and letter
The research method of efficiently and accurately under the fields such as road ocean environment parameter inverting.
Background technology
The research of acoustic radiation forecasting procedure of the elastic construction under the channel of ocean, it is real-time to carrying out structural vibration radiated noise
Forecast and effectively control have important theoretical research value, and the real-time monitoring and prediction to radiated noise in the channel of ocean, which has, lifts
The effect of sufficient weight, it is one of focus and difficulties that later China's underwater acoustic technology field is paid close attention to for a long time.
However, at present elastic construction under the channel of ocean vibration and acoustic radiation research fluid domain be thought of as mostly it is unbounded
Or half space fluid domain, the research that Acoustic Radiation Problems are coupled to elastic construction multiple physical field under Yu Haiyang channel are still rare.Cause
It is related to fluid structurecoupling for structure sound field problem under channel, sound shell coupling even sound is coupled etc. with the sound border of complicated submarine frontier and answered
Miscellaneous multiple physical field couples environment, and mathematical theory derives and is difficult to solve under these coupling conditions, and numerical model can not be established, structure
Surface vibration information is difficult to obtain.Conventional numeric method (boundary element method BEM, FInite Element FEM, statistical Energy Analysis Approach SEA etc.) will be by
The serious limitation of the factor such as big grid amount of calculation and the coupling of complicated marine environment and multiple physical field, can not carry out correlative study work
Make；Analytic solution can only sound field problem of the analysis part simple structure under simple channel, to any bullet under complicated ocean channel
Property structure acoustic radiation research it is also helpless, also there are some scholars to propose directly to ignore structure and fluid, structure and environment
Coupling, structure is considered as point sound source, but so directly have ignored the Near-Field Acoustic Radiation characteristic of structure.For ocean channel ring
The research in border, generally use ocean theory of sound propagation (parabolic equation method, normal mode method, Wavenumber integration method etc.) carry out channel ring
Border is analyzed, and parabolic equation method (PE) is because accurate carrying out remote sound field result of calculation, and calculating speed is fast and strong adaptability
The features such as, the favor of various countries researcher is received, but research object is usually point-source model under the channel of ocean, under the channel of ocean
Elastic construction acoustic radiation research is seldom related to.Result in jointly above can not effectively carry out letter from Theory Solution and numerical method angle
Elastic construction acoustic radiation is studied under road, but it has particularly important meaning to structure acoustic radiation, forecast and identification under the reclaimed water of ocean,
It is badly in need of exploring a kind of new research method to solve the problems, such as structure acoustic radiation in the channel of ocean.
The content of the invention
It is an object of the invention to provide a kind of strong to elastic construction and ocean channel adaptation ability, as a result accurate efficiency
Height, use elastic construction acoustic radiation forecasting procedure under the simple ocean channel easy to spread based on coupling FEM-PE.
The object of the present invention is achieved like this：
Step 1, elastic construction acoustic radiation local multiple physical field numerical model under the channel of ocean is established, using finite element number
Value method carries out acoustical definition to fluid structurecoupling, the coupling of sound border and infinite point Smerfield radiation conditions respectively, calculates local
Sound field information under the channel fluid domain of ocean；
Step 2, carry out two-dimensional acoustic field under three dimensional channel space and handle, by far field site and structure centre in vertical side
To formation two-dimensional section, and one-dimensional transversal is chosen on the depth direction at a certain distance from distance structure center, extract the transversal
On multiple sound pressure information as sound field extrapolation parabolic equation method initial fields information；
Step 3, sound field information progress and of sound field extrapolation parabolic equation method initial fields to FEM calculation extraction
Match somebody with somebody, result of finite element is intactly matched each lattice point of parabolic equation method space initial fields；
Step 4, setting and finite element identical channel circumstance parameter and site position, to any site acoustic pressure under channel
The quick calculating of sound field extrapolation parabolic equation method is carried out, structure acoustic radiation characteristic under the channel of ocean is obtained, for carrying out channel
Lower elastic construction radiated sound field Fast Prediction.
The present invention can also include：
1st, chosen on the depth direction at a certain distance from distance structure center in one-dimensional transversal, one-dimensional transversal is horizontal
Distance away from structure centre is l ≈ λ for wavelength corresponding to calculating frequency.
2nd, using segmentation, Ai Er meter Te interpolation techniques are carried out to the multiple acoustic pressure of FInite Element and parabolic equation method sound field three times
The matching of space lattice, FInite Element and parabolic equation method coupling condition are established, as parabolic equation method finite difference calculus
The initial fields value of calculating.
The theoretical model of the present invention：
As shown in figure 1, main theory part of the present invention is made up of two large divisions：Multiple physical field FEM numerical computations and PE sound
Field computation, the coupling condition i.e. PE sound fields that FEM and PE is used as by multiple acoustic pressure linear interpolation calculate primary condition.It will be described below
The calculating physical theory of two large divisions.
Multiple physical field local FEM numerical computations
Elastic construction Acoustic Radiation Problems are related to the acoustics such as fluid structurecoupling, the coupling of sound border and infinite boundary under the channel of ocean
Coupling boundary processing, it is as follows to establish acoustic control equation and the border condition of continuity under multiple physical field using finite element：
Fluid structurecoupling equation
On the coupling surface of body structure surface and external fluid contact, the boundary condition of satisfaction is the vibration of body structure surface normal direction
Speed is identical with the vibration velocity of external fluid medium, and the coupled wave equation that structure and fluid can be written is
Wherein, stiffness matrix KijWith damping matrix Cij, mass matrix MijIt is n × n rank matrixes.Subscript a, s and c are sound
Learn sytem matrix, mechanical structure matrix and coupling matrix；Define coupling matrix Kc、McFor AndnseThe structured grid quantity contacted for structure with fluid,
{neBe structured grid normal vector；The π f of ω=2 are angular frequency, and f is frequency (Hz), ρ0For density of sea water；ui、piFor displacement
And sound pressure amplitude, Fst、FatRespectively structure, the coupling excitation load of fluid media (medium) sound.
The Sea surface boundary of ocean channel is usually Dirichlet borders, and the boundary condition of satisfaction is that interface acoustic pressure is zero
pa(x,y,z)|Z=0=0 (2)
Wherein, in order to distinguish seawater and seabed, subscript a and b indicate seawater fluid layer and subsea level respectively.
For liquid seabed, for acoustic pressure p (x, y, z) continuously, normal direction vibration velocity v (x, y, z) is continuous for the boundary condition of satisfaction
pa(x, y, z)=pb(x,y,z) (3)
van(x, y, z)=vbn(x,y,z) (4)
For isotropic elasticity seabed, meet to meet that displacement is continuous and stress is continuous in normal direction, tangential stress is zero
Wherein, u be horizontal displacement in elastomer, w be vertical displacement in elastomer, ρ is Media density, and σ is stress,
λ, μ are rummy constant, define Δ and are
Ocean channel surrounding border is infinite boundary, and finite element numerical method uses PML (Perfectly Matched
Layer, abbreviation PML) technology simulated, the controlling party that PML is converted to absorbed layer by increasing governing equation absorption coefficient
Journey, in order to which reduced equation describes, it is x to make x-axis1Axle, y-axis x2Axle, the PML equations under frequency domain can be written using variables separation
Wherein, σiFor absorption coefficient, vi, piFor the speed and sound pressure amplitude in matching layer domain.
After handling border using PML, make to meet that condition is extinguished in Smerfield far fields on border
p(x,y,z)|R=∞=0 (9)
Acoustic pressure is set to be zero by sound absorption on border, reaching border does not have infinity of the reflected sound with analog channel surrounding
Space.
Structure acoustic radiation numerical value under the channel of ocean is established by fluid structurecoupling equation, sound border coupled wave equation and PML technologies
Model, calculate and obtain Structural radiation sound information, can extract from sea transversal acoustic pressure data on earth, in order that FEM is calculated
As a result condition is set with PE in space lattice perfect matching, it is necessary to by be segmented three times Ai Er meter Te interpolation methods to comprising amplitude and
Phase information sound field data are handled, and are then the initial strip quickly calculated as PE method sound fields as FEM-PE coupling conditions
Part.
PE methods sound field extrapolation theory under the channel of ocean
The starting point for deriving parabolic equation is axisymmetric coordinate (r, z), and harmonic point source changes in sound channel in level
Sound field is by wave equation
Wherein, p is fluid media (medium) acoustic pressure, and ρ (r, z) is fluid density, and c (r, z) is fluid sound speed, zsIt is sound source in z-axis
The position in direction.
Under axisymmetric coordinate, when fluid media (medium) density is constant, time relationship e(-jωt)(ω is angular frequency)
The Helmholtz equation of harmonic point source is
Wherein, k=ω/c are wave number
The parabolic type wave equation of export standard there is several methods that, in strict accordance with Tappert method in the present invention, it is assumed that
The solution form of equation (11) is
P (r, z)=ψ (r, z) v (r) (12)
(12) formula is substituted into (11) formula, variables separation can obtain：
Wherein, k0With reference to wave number, c0With reference to the velocity of sound, and k (r, z)=k0N (r, z), n (r, z)=c0/c(r,z)。
Meeting (k0R) under ＞ ＞ 1 precondition, the solution of formula (13) can be represented with following asymptotic expression form
Then do far field condition and assume ((k0R) ＞ ＞ 1), simplified oval wave equation can be obtained
In order to solve above equation, following two operators are defined first
According to the two of definition operators, ellipse wave equation can be written as form
Factorization is carried out to formula (18), is two components of incoming wave and output wave by equation decomposition, i.e.,
(P+ik0-ik0Q)(P+ik0+ik0Q)ψ-ik0(PQ-QP) ψ=0 (19)
When medium can be exchanged with each other position with apart from unrelated i.e. n ≡ n (z), operator P and Q, thus formula (19) last
It is zero, only considers output wave component, just obtain
In order to subsequently solve conveniently, make here
So as to which the square root operator that formula (17) provides can be written as
With deepening continuously for research, different approximate processings is taken to radical (22), different accuracy requirement can be obtained
With the Parabolic Equation of different propagation angles, conventional processing mode is a kind of very polarizers of big angle scope based on pa moral series expansion
Broad sense PE, the propagation angle that the approximate evaluation method of this radical enables parabolic equation method to handle have nearly reached 90 °, right
Operator Q carries out pa moral series expansion, can obtain
Wherein,M is the item number in expansion.
Bring formula (23) into equation (20), the wide-angle based on the pa moral series expansion of horizontal operator can be obtained
Parabolic equation
The wide-angle PE that the present invention is drawn using Claerbout, need to use finite difference calculus (Finite Difference
Method, abbreviation FDM) solved, need convection body domain to carry out discrete, discrete each side under the channel of ocean during numerical solution
It is to the step pitch of satisfactionΔ r=(2-5) Δ z, the radiated sound field of any site under shallow sea channel can be solved
In formula：
Understand, parabola finite difference calculus is the process that a stepping solves, and can be solved by previous field information next
The information of individual field, it can be solved in initial distance r using the form0Sound field of the place along depth profile.In sound field solution procedure
Need to make specified in more detail to the primary condition and boundary condition of marine environment, generally, sea Free Surface uses sound field soft-sided
Boundary is handled, thus meets ψ (r, 0)=0 on surface, and seabed continues seabed using semo-infinite homogeneous liquid/elastic space processing
The radiation condition that part meets limits by using the artificial absorbed layer that thickness is several wavelength.On establishing the initial field datas of PE
The problem of, it can be designed to that experiment measures or what numerical computations obtained has caused by certain directional sound source along depth direction
Sound field (including amplitude and phase), the present invention obtain labyrinth body sound under multiple physical field local environment by finite element numerical method
Source is in the sound field of depth direction, the initial field condition as PE calculating.
Sound field result P is extracted in depth direction according to FEM calculation, depth coordinate z can be establishedfWith acoustic pressure PfRelation,
Level is away from structure centre r on PE computational fields depth directionso(ro=λ) each depth lattice point (r in place0, z) and sound field can be by following
Ai Er meter Te interpolation methods obtain three times for segmentation
Wherein, zpFor smallest interval [zk,zk+1] on a bit, P'f,kResult function is extracted in node z for finite elementkPlace is led
Numerical value, k=0,1,2,3n, n are that FEM extracts result discrete number.
Sound field values of the PE in each lattice point of depth direction can be obtained by formula (27)Then it is used as PE method sound
The primary condition that field quickly calculatesThat is FEM-PE coupling conditions, using the formula of the finite difference solving method based on padé approximation
(25) sound field stepping calculating is carried out.
The outstanding advantage that the present invention has is：
(a) invention is adaptable to Elastic Structural Shape and ocean channel circumstance type, elasticity knot under the channel of ocean
Structure multiple physical field Local Model using FInite Element establish, therefore can be to arbitrarily complicated structure under different ocean channels radiation
Sound field carries out finite element numerical calculating, has very strong adaptability to structure type.Then the sound field information calculated under local
As the sound source input condition of PE methods, carry out far field sound field under the channel of ocean and calculate.Can be had by deriving standardization PE methods
There is structure acoustic radiation under the ocean channel of liquid seabed (containing sound absorption) to forecast, if ocean seabed is the harder elastic layer of quality,
Theoretical foundation is then carried out to seabed sound field using elastic PE, solves the elastic construction spoke under the ocean channel in flexible layer seabed
Sound field is penetrated, and is similarly used for structure acoustic radiation forecasting problem under shallow sea wedge shape seabed or deep-sea channel, institute is in this way
Fast Prediction can be carried out to any elastic construction radiated sound field under different ocean channels.
(b) invention has the characteristics of calculating few used time, efficiency high when being calculated, by parabolic under the channel of ocean
Square root operator carries out Pade approximate processings in line equation, accelerates convergence and the calculating speed of the calculating of PE methods sound field.Identical
Under the conditions of computing hardware, can quickly calculate conventional numeric method (FInite Element, boundary element method, statistical Energy Analysis Approach etc.) can not mould
Intend or because of computationally intensive and imponderable complicated Acoustic Radiation Problems, and result of calculation precise and high efficiency.
(c) the invention operating process is simply easy to use, and implementation amount is small, is easy in theoretical research and Practical Project
Promote.Its crucial step is that the vertical linear array that test method(s) need to be only extracted or passed through by numerical value normal sections obtains constructional depth side
To acoustic pressure distributed intelligence of reaching the standard grade, after carrying out PE method initial fields perfect matchings, the outfield of elastic construction under the channel of ocean can be carried out
Radiated sound field Fast Prediction.
Compared with conventional forecasting procedure, the invention is strong to elastic construction and ocean channel adaptation ability, and result of calculation is accurate
True efficiency high, using simple easy to spread.Efficiently solve at present that elastic construction acoustic radiation is given the correct time in advance in the case where studying ocean channel
The computationally intensive, physical field run into is more and many bottleneck sex chromosome mosaicisms such as channel circumstance complexity.
Brief description of the drawings
Fig. 1 a are elastic construction radiated sound field forecasting model under the ocean channel that the present invention uses.
Fig. 1 b are the principle schematic that the present invention carries out structure-borne sound field prediction under shallow sea channel.
Fig. 2 is that model is verified in point source acoustic propagation under shallow sea channel.
Fig. 3 a are 20Hz finite elements on depth direction under shallow sea channel and Wavenumber integration method result of calculation comparison diagram.
Fig. 4 a are the inventive method result of calculation and result of finite element comparison diagram under 20z.
Fig. 4 b are the inventive method result of calculation and result of finite element comparison diagram under 30Hz.
Fig. 4 c the inventive method result of calculation and result of finite element comparison diagram under 40Hz.
Fig. 4 d the inventive method result of calculation and result of finite element comparison diagram at 50 hz.
Fig. 5 a are to carry out elastic cylindrical shell acoustic radiation forecast principle figure under the shallow sea channel of ocean using the present invention
Fig. 5 b are that FEM establishes elastic cylindrical shell acoustic radiation local numerical model under the shallow sea channel of ocean.
Fig. 6 a are that FEM in frequency is 100Hz lower section radiated sound field spatial distributions.
Fig. 6 b are that FEM in frequency is 200Hz lower section radiated sound field spatial distributions.
Fig. 6 c are that FEM in frequency is 400Hz lower section radiated sound field spatial distributions.
Fig. 6 d are that FEM in frequency is 800Hz lower section radiated sound field spatial distributions.
Fig. 7 a be the present invention calculate in the case where frequency is 100Hz sound radiation pressure level with distance change curve.
Fig. 7 b be the present invention calculate in the case where frequency is 200Hz sound radiation pressure level with distance change curve.
Fig. 7 c be the present invention calculate in the case where frequency is 400Hz sound radiation pressure level with distance change curve.
Fig. 7 d be the present invention calculate in the case where frequency is 800Hz sound radiation pressure level with distance change curve.
Fig. 8 a are that the present invention calculates the radiated sound field pcolor in the case where frequency is 100Hz.
Fig. 8 b are that the present invention calculates the radiated sound field pcolor in the case where frequency is 200Hz.
Fig. 8 c are that the present invention calculates the radiated sound field pcolor in the case where frequency is 400Hz.
Fig. 8 d are that the present invention calculates the radiated sound field pcolor in the case where frequency is 800Hz.
Fig. 9 table 1 is Pekeris shallow sea channels environment and elastic construction parameter.
Calculating time test of Figure 10 table 2 for the present invention to different calculating frequencies.
Figure 11 table 3 is calculating time test of the present invention to different computer capacities.
Embodiment
Illustrate below and the present invention is described in more detail.
1. initial fields obtain under multiple physical field local environment
Elastic construction Acoustic Radiation Problems are related to the acoustics such as fluid structurecoupling, the coupling of sound border and infinite boundary under the channel of ocean
Coupling boundary processing, it is as follows to establish acoustic control equation and the border condition of continuity under multiple physical field using finite element：
Fluid structurecoupling equation
On the coupling surface of body structure surface and external fluid contact, the boundary condition of satisfaction is the vibration of body structure surface normal direction
Speed is identical with the vibration velocity of external fluid medium, and the coupled wave equation that structure and fluid can be written is
Wherein, stiffness matrix KijWith damping matrix Cij, mass matrix MijIt is n × n rank matrixes.Subscript a, s and c are sound
Learn sytem matrix, mechanical structure matrix and coupling matrix；Define coupling matrix Kc、McFor AndnseThe structured grid quantity contacted for structure with fluid,
{neBe structured grid normal vector；The π f of ω=2 are angular frequency, and f is frequency (Hz), ρ0For density of sea water；ui、piFor displacement
And sound pressure amplitude, Fst、FatRespectively structure, the coupling excitation load of fluid media (medium) sound, are respectively defined as
The Sea surface boundary of ocean channel is usually Dirichlet borders, and the boundary condition of satisfaction is that interface acoustic pressure is zero
pa(x,y,z)|Z=0=0 (2)
Wherein, in order to distinguish seawater and seabed, subscript a and b indicate seawater fluid layer and subsea level respectively.
For liquid seabed, for acoustic pressure p (x, y, z) continuously, normal direction vibration velocity v (x, y, z) is continuous for the boundary condition of satisfaction
pa(x, y, z)=pb(x,y,z) (3)
van(x, y, z)=vbn(x,y,z) (4)
For isotropic elasticity seabed, meet to meet that displacement is continuous and stress is continuous in normal direction, tangential stress is zero
Wherein, u be horizontal displacement in elastomer, w be vertical displacement in elastomer, ρ is Media density, and σ is stress,
λ, μ are rummy constant, define Δ and are
Ocean channel surrounding border is infinite boundary, and finite element numerical method uses PML (Perfectly Matched
Layer, abbreviation PML) technology simulated, the controlling party that PML is converted to absorbed layer by increasing governing equation absorption coefficient
Journey, in order to which reduced equation describes, it is x to make x-axis1Axle, y-axis x2Axle, the PML equations under frequency domain can be written using variables separation
Wherein, σiFor absorption coefficient, vi, piFor the speed and sound pressure amplitude in matching layer domain.
After handling border using PML, make to meet that condition is extinguished in Smerfield far fields on border
p(x,y,z)|R=∞=0 (9)
Acoustic pressure is set to be zero by sound absorption on border, reaching border does not have infinity of the reflected sound with analog channel surrounding
Space.
Structure acoustic radiation number under the channel of ocean is established by fluid-solid coupling equation, sound-border coupled wave equation and PML technologies
It is worth model, calculates and obtain Structural radiation sound information.Set condition perfect in space lattice with PE in order that obtaining FEM result of calculations
Matching is, it is necessary to which by segmentation, Ai Er meter Te interpolation methods comprising amplitude and phase information sound field data to handling three times, then
It is the primary condition quickly calculated as PE method sound fields as FEM-PE coupling conditions.
2. PE methods sound field extrapolation theory under the channel of ocean
The starting point for deriving parabolic equation is axisymmetric coordinate (r, z), and harmonic point source changes in sound channel in level
Sound field is by wave equation
Wherein, p is fluid media (medium) acoustic pressure, and ρ (r, z) is density, and c (r, z) is the velocity of sound, zsIt is sound source in the position in z-axis direction
Put.
Under axisymmetric coordinate, when fluid media (medium) density is constant, time relationship e(-jωt)(ω is angular frequency)
The Helmholtz equation of harmonic point source is
Wherein, k=ω/c are wave number.
The parabolic type wave equation of export standard there is several methods that, in strict accordance with Tappert method in the present invention, it is assumed that
The solution form of equation (11) is
P (r, z)=ψ (r, z) v (r) (12)
(12) formula is substituted into (11) formula, variables separation can obtain：
Wherein, k0With reference to wave number, c0With reference to the velocity of sound.And k (r, z)=k0N (r, z), n (r, z)=c0/c(r,z)。
Meeting (k0R) under ＞ ＞ 1 precondition, the solution of formula (13) can be represented with following asymptotic expression form
Then do far field condition and assume ((k0R) ＞ ＞ 1), simplified oval wave equation can be obtained
In order to solve above equation, following two operators are defined first
According to the two of definition operators, ellipse wave equation can be written as form
Factorization is carried out to formula (18), is two components of incoming wave and output wave by equation decomposition, i.e.,
(P+ik0-ik0Q)(P+ik0+ik0Q)ψ-ik0(PQ-QP) ψ=0 (19)
When medium can be exchanged with each other position with apart from unrelated i.e. n ≡ n (z), operator P and Q, thus formula (19) last
It is zero, only considers output wave component, just obtain
In order to subsequently solve conveniently, make here
So as to which the square root operator that formula (17) provides can be written as
With deepening continuously for research, different approximate processings is taken to radical (22), different accuracy requirement can be obtained
With the Parabolic Equation of different propagation angles, conventional processing mode is a kind of very polarizers of big angle scope based on pa moral series expansion
Broad sense PE, the propagation angle that the approximate evaluation method of this radical enables parabolic equation method to handle have nearly reached 90 °, right
Operator Q carries out pa moral series expansion, can obtain
Wherein,M is the item number in expansion.
Bring formula (23) into equation (20), the wide-angle based on the pa moral series expansion of horizontal operator can be obtained
Parabolic equation
The wide-angle PE that the present invention is drawn using Claerbout, need to use finite difference calculus (Finite Difference
Method, abbreviation FDM) solved, need convection body domain to carry out discrete, discrete each side under the channel of ocean during numerical solution
It is to the step pitch of satisfactionΔ r=(2-5) Δ z, the radiated sound field of any site under shallow sea channel can be solved
In formula：
Understand, parabola finite difference calculus is the process that a stepping solves, and can be solved by previous field information next
The information of individual field, it can be solved in initial distance r using the form0Sound field of the place along depth profile.In sound field solution procedure
Need to make specified in more detail to the primary condition and boundary condition of marine environment, generally, sea Free Surface uses sound field soft-sided
Boundary is handled, thus meets ψ (r, 0)=0 on surface, and seabed continues seabed using semo-infinite homogeneous liquid/elastic space processing
The radiation condition that part meets limits by using the artificial absorbed layer that thickness is several wavelength.On establishing the initial field datas of PE
The problem of, it can be designed to that experiment measures or what numerical computations obtained has caused by certain directional sound source along depth direction
Sound field (including amplitude and phase), the present invention obtain labyrinth body sound under multiple physical field local environment by finite element numerical method
Source is in the sound field of depth direction, the initial field condition as PE calculating.
Sound field result P is extracted in depth direction according to FEM calculation, depth coordinate z can be establishedfWith acoustic pressure PfRelation,
Level is away from structure centre r on PE computational fields depth directionso(ro=λ) each depth lattice point (r in place0, z) and sound field can be by following
Ai Er meter Te interpolation methods obtain three times for segmentation
Wherein, zpFor smallest interval [zk,zk+1] on a bit, P'f,kResult function is extracted in node z for finite elementkPlace is led
Numerical value, k=0,1,2,3n, n are that FEM extracts result discrete number.
Sound field values of the PE in each lattice point of depth direction can be obtained by formula (27)Then it is used as PE method sound
The primary condition that field quickly calculatesThat is FEM-PE coupling conditions, using the formula of the finite difference solving method based on padé approximation
(25) sound field stepping calculating is carried out.
Method Accuracy Verification
Example 1：Point source acoustic propagation calculates under Pekeris shallow sea channels
Establish under axial-symmetric condition as shown in Figure 2 point source propagation model under Pekeris channels, channel depth H=
200m, interface is Dirichlet borders on channel, and lower interface is the velocity of sound layer liquids such as unlimited half space, seawater parameter：Seawater is close
Spend for ρa=1024kg/m3, sound velocity in seawater ca=1500m/s；Seafloor density ρb=1800kg/m3, Bottom sound speed cb=2500m/
s.Sound source is monopole point source, and monopole amplitude is 1, and point Depth is z0=100m.Point is calculated using multiple physical field finite element numerical
Underwater Acoustic Propagation of the source under channel circumstance, it is r=2000m to calculate distance, and is extracted apart from one af at wavelength lambda finite element of point source
(FEM) sound pressure information on whole coastal depth direction (amplitude and phase), as FEM-PE coupling conditions, i.e. PE sound fields meter
The primary condition of calculation, after setting PE to calculate shallow sea channel ambient parameter, the sound field of any site under shallow sea channel can be calculated
Information.
As shown in Figure 3 a, it is being depth at λ=75m apart from point source to couple FEM numerical methods to calculate acquisition by multiple physical field
Frequency is 20Hz multiple sound pressure level on direction, and draws acoustic pressure modulus value distribution curve in the depth direction, and and same channel
Under the conditions of Wavenumber integration method calculation procedure FFP result of calculations contrasted.Then FEM in the accurate result of calculation of depth direction
After being segmented Ai Er meter Te interpolation processings three times, acoustic propagation curve (each site depth of the frequency corresponding to 20Hz is calculated
For 50m), and contrasted with FEM result of calculations under the same terms, as shown in fig. 4 a.Equally, calculate 30Hz, 40Hz and
The sound radiation pressure level of Structural radiation sound is with propagation distance curve map under the conditions of 50Hz, and has been carried out pair with result of finite element
Than as shown in Fig. 4 b, 4c and 4d.It can be seen that under 20Hz, 30Hz, 40Hz and 50Hz frequency the inventive method result of calculation with
The identical property of FEM result of calculations is fine, demonstrates the accuracy that sound field of the present invention calculates.
Method practicality and high efficiency explanation
Example 2：Elastic construction acoustic radiation calculates under Pekeris shallow sea channels
As shown in Figure 5 a, establish elastic cylindrical shell radiated sound field FEM-PE under Pekeris shallow sea channels and calculate theoretical model,
The calculating theory model is broadly divided into numerical value FEM computational fields and PE computational fields, and extraction numerical value FEM computational fields are in the depth direction
Answer sound pressure information and be used as FEM-PE coupling conditions after doing interpolation.Wherein S is elastic construction sound source, zsStructure centre is in z-axis
Position, ρa,caThe respectively density of sea water velocity of sound, ρb,cbRespectively infinitely great layer liquid density and the velocity of sound, PlCoupled for FEM-PE
, λ PlOne, distance structure center wavelength distance, rpIt is any site under PE computational fields apart from the distance of initial fields.
As shown in Figure 5 b, elastic cylindrical shell acoustically radiating under Pekeris shallow sea channels is established using multiple physical field Coupled Numerical method
Model is penetrated, channel circumstance and elastic construction parameter are shown in Fig. 9 table 1, utilize structure acoustic radiation under Finite element arithmetic local fluid
Information, as shown in Fig. 6 a- Fig. 6 d, elastic cylindrical shell is in z-o-y planes under numerical computations Pekeris shallow sea channel local fluids
Corresponding sound-filed simulation under interior 100Hz, 200Hz, 400Hz and 800Hz frequency.And it is extracted apart from one, cylindrical shell center ripple
Sound radiation pressure (amplitude and phase) information on strong point transversal, in order to the discrete lattice points of PE (Δ r, Δ z) carry out space perfect matching,
It is PE sound as FEM and PE coupling conditions after needing the multiple acoustic pressure for calculating FEM extraction to be segmented Ai Er meter Te interpolation three times
Field computation primary condition, elastic construction radiated sound field information under far field condition is then calculated using sound field PE extrapolations, such as Fig. 7 a
To Fig. 7 d, elastic cylindrical shell sound radiation pressure level is calculated under 100Hz, 200Hz, 400Hz and 800Hz frequency respectively with the change of distance
Change curve, each site depth is 3m；Such as Fig. 8 a to Fig. 8 d, bullet under 100Hz, 200Hz, 400Hz and 800Hz frequency is calculated respectively
Property cylindrical shell is in far-field radiation sound-filed simulation pcolor.It can be seen that, elastic construction is basic in far-field radiation sound field under shallow sea channel
Meet cylindrical wave propagation law, its sound field fluctuation details increases with the rising of frequency.
In order to illustrate huge advantage of the present invention in terms of elastic construction acoustic radiation calculating speed under carrying out ocean channel, point
It is other that the sound field calculating time under different distance and different frequency is tested, as shown in Figure 10 table 2 and Figure 11 table 3, test
Fluid environment and elastic construction it is same as described above, test hardware condition parameter Lenovo ThinkStation E30 (Intel
Eight core 3.2GHz CPU, 32GB internal memories).
The table 3 of table 2 and Figure 11 from Figure 10 can be seen that influence of the different distance to the calculating time is than different frequency to calculating
The influence of time is notable, when it is 0-10km to calculate distance, calculates frequency and in change procedure, calculates the time from 100Hz to 800Hz
Smaller increase, because the step pitch that discrete all directions meet under the channel of ocean isΔ r=(2-5) Δ z, when frequency rises
When, vertically and horizontally discrete step increases away from reduction, the increase of discrete unit number, calculating time, but when frequency reaches
During 800Hz upper frequencies, it is only 1min or so to calculate the used time, is entirely capable of elastic construction under competent ocean channel at each frequency
Acoustic radiation quickly calculates.For different computer capacities, even if solving (discrete grid block unit number when distance range reaches 0-100km
Reach million magnitudes), its calculate used time be only 10.2030 minutes, and using conventional finite element calculate the problem when, due to shallow sea
The physic field coupling that structure acoustic radiation is related under channel is more, distance is calculated far, using FEM calculation when distance range reaches 0-
During 1km, computer can not calculate, but be only 0.0179 minute using the calculating time of the invention in the distance range, display
The huge advantage of invention elastic construction acoustic radiation distant calculation in the case where carrying out shallow sea channel, can be quickly to any long distance
Method sound field is solved from the range of.
Claims (3)
1. elastic construction acoustic radiation forecasting procedure under a kind of ocean channel based on coupling FEM-PE, it is characterized in that：
Step 1, elastic construction acoustic radiation local multiple physical field numerical model under the channel of ocean is established, using finite element numerical method
Acoustical definition is carried out to fluid structurecoupling, the coupling of sound border and infinite point Smerfield radiation conditions respectively, calculates local ocean
Sound field information under channel fluid domain；
Step 2, carry out two-dimensional acoustic field under three dimensional channel space and handle, by far field site and structure centre in vertical direction shape
Into two-dimensional section, and one-dimensional transversal is chosen on the depth direction at a certain distance from distance structure center, extracted on the transversal
Initial fields information of the multiple sound pressure information as sound field extrapolation parabolic equation method；
Step 3, sound field information progress and the matching of sound field extrapolation parabolic equation method initial fields to FEM calculation extraction,
Result of finite element is set intactly to match each lattice point of parabolic equation method space initial fields；
Step 4, setting and finite element identical channel circumstance parameter and site position, any site acoustic pressure under channel is carried out
The quick calculating of sound field extrapolation parabolic equation method, obtains structure acoustic radiation characteristic under the channel of ocean, for carrying out bullet under channel
Property Structural radiation sound Fast Prediction.
2. elastic construction acoustic radiation forecasting procedure under the ocean channel according to claim 1 based on coupling FEM-PE, its
It is characterized in：Chosen on the depth direction at a certain distance from distance structure center in one-dimensional transversal, one-dimensional transversal level away from
The distance of structure centre is l ≈ λ for wavelength corresponding to calculating frequency.
3. elastic construction acoustic radiation forecasting procedure under the ocean channel according to claim 1 or 2 based on coupling FEM-PE,
It is characterized in that：Using segmentation, Ai Er meter Te interpolation techniques carry out sky to the multiple acoustic pressure of FInite Element with parabolic equation method sound field three times
Between lattice point matching, FInite Element and parabolic equation method coupling condition are established, as parabolic equation method finite difference calculus meter
The initial fields value of calculation.
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