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 invention relates to a high-efficiency and accurate research method in the fields of elastic structure radiation sound field prediction under an ocean channel, underwater sound target detection, channel ocean environment parameter inversion and the like.
Background
The research of the acoustic radiation forecasting method of the elastic structure under the ocean channel has important theoretical research value for developing the real-time forecasting and effective control of the vibration radiation noise of the structure, plays a significant role in the real-time monitoring and forecasting of the radiation noise in the ocean channel, and is one of the hot spots and difficult problems which are long-term concerned in the technical field of underwater sound in China.
However, at present, the fluid domain of the elastic structure under the ocean channel for vibration and sound radiation research is mostly considered as an unbounded or half-space fluid domain, and the research on the problem of coupling the elastic structure under the ocean channel with multiple physical fields and sound radiation is not common. Because the structure sound field problem under the channel relates to complex multi-physical field coupling environments such as fluid-solid coupling, sound shell coupling, even sound and sound boundary coupling of complex seabed boundaries, and the like, the mathematical theory derivation is difficult to solve under the coupling conditions, a numerical model cannot be established, and the structure surface vibration information is difficult to obtain. The traditional numerical method (boundary element method BEM, finite element method FEM, statistical energy method SEA and the like) is severely limited by factors such as large grid calculated amount, complex marine environment, multi-physical field coupling and the like, and related research work cannot be carried out; the analytic solution can only analyze the problem of the sound field of a partial simple structure under a simple channel, can not be used for researching the sound radiation of any elastic structure under a complex ocean channel, and partial scholars propose to directly neglect the coupling effect of the structure and fluid and the structure and environment and consider the structure as a point sound source, but directly neglect the near-field sound radiation characteristic of the structure. For the research of the ocean channel environment, the channel environment analysis is usually performed by adopting an ocean sound propagation theory (a parabolic equation method, a normal wave method, a wave number integration method and the like), and the parabolic equation method (PE) is favored by researchers in various countries because of the characteristics of accurate calculation result, high calculation speed, strong adaptability and the like of a remote sound field, but a research object is usually a point source model under an ocean channel, and the research on the sound radiation of an elastic structure under the ocean channel is rarely involved. The above results in that the research on the acoustic radiation of the elastic structure under the channel cannot be effectively carried out from the angles of theoretical solution and numerical method, but the method has very important significance on the acoustic radiation, prediction and identification of the underwater structure in the ocean, and a new research method for solving the problem of the acoustic radiation of the structure in the ocean channel is urgently needed to be explored.
Disclosure of Invention
The invention aims to provide a coupling FEM-PE-based acoustic radiation forecasting method for an elastic structure under an ocean channel, which has strong adaptability to the elastic structure and the ocean channel, accurate result, high efficiency, simple use and easy popularization.
The purpose of the invention is realized as follows:
establishing an acoustic radiation local multi-physical field numerical model of an elastic structure under an ocean channel, respectively performing acoustic definition on fluid-solid coupling, acoustic boundary coupling and a Smirfield radiation condition at infinity by adopting a finite element numerical method, and calculating sound field information under a fluid domain of the local ocean channel;
step two, performing two-dimensional sound field processing in a three-dimensional channel space, forming a two-dimensional section in the vertical direction through a far-field point and a structure center, selecting a one-dimensional section line in the depth direction at a certain distance from the structure center, and extracting complex sound pressure information on the section line as initial field information of a sound field extrapolation parabolic equation method;
matching the sound field information extracted by finite element calculation with the sound field extrapolation parabolic equation method initial field to enable the finite element calculation result to be completely matched with each lattice point of the parabolic equation method space initial field;
and fourthly, setting channel environment parameters and field point positions which are the same as those of the finite elements, and rapidly calculating sound field extrapolation parabolic equation method for sound field sound pressure of any field point under the channel to obtain sound radiation characteristics of the structure under the ocean channel for rapidly forecasting the radiation sound field of the elastic structure under the channel.
The present invention may further comprise:
1. and selecting one-dimensional section lines in the depth direction at a certain distance from the center of the structure, wherein the distance between the horizontal distance of the one-dimensional section lines and the center of the structure is equal to the wavelength corresponding to the calculated frequency, namely l ≈ lambda.
2. And matching space lattice points of complex sound pressure of a finite element method and a sound field of a parabolic equation method by adopting a segmented cubic ensemble interpolation technology, and establishing a coupling condition of the finite element method and the parabolic equation method as an initial field value calculated by the finite difference method of the parabolic equation method.
The theoretical model of the invention is as follows:
as shown in fig. 1, the main theoretical part of the present invention is composed of two major parts: and performing multi-physical-field FEM numerical calculation and PE sound field calculation, and taking the linear interpolation of complex sound pressure as a coupling condition of FEM and PE, namely an initial condition of PE sound field calculation. The two major parts of the computational physics theory will be explained below.
Multi-physics field local FEM numerical calculation
The acoustic radiation problem of the elastic structure under the ocean channel relates to acoustic coupling boundary processing such as fluid-solid coupling, acoustic boundary coupling, infinite boundary and the like, and an acoustic control equation and boundary continuous conditions under a multi-physical field are established by adopting finite elements as follows:
fluid-solid coupled equation
On the coupling surface of the structure surface contacting with the external fluid, the boundary condition is satisfied that the vibration speed of the structure surface normal direction is the same as the vibration speed of the external fluid medium, and the coupling equation of the structure and the fluid can be written as
Wherein the stiffness matrix KijAnd a damping matrix CijQuality matrix MijAre all n × n order momentsAnd (5) arraying. Subscripts a, s and c are an acoustic system matrix, a mechanical structure matrix and a coupling matrix; defining a coupling matrix Kc、McIs composed of And isnseNumber of structural grids for structure to contact fluid, { n }eIs the normal vector of the structural grid; ω 2 π f is the angular frequency, f is the frequency (Hz), ρ0Is the density of seawater; u. ofi、piFor displacement and sound pressure amplitude, Fst、FatRespectively, the structure and the fluid medium are acoustically coupled with the excitation load.
The sea surface boundary of the ocean channel is usually Dirichlet boundary, and the boundary condition is met by the condition that the interface sound pressure is zero
pa(x,y,z)|z＝0＝0 (2)
Wherein, in order to distinguish between sea water and sea floor, subscripts a and b denote the sea water fluid layer and the sea floor layer, respectively.
For liquid seabed, the boundary conditions are satisfied that the sound pressure p (x, y, z) is continuous, and the normal vibration velocity v (x, y, z) is continuous
pa(x,y,z)＝pb(x,y,z) (3)
van(x,y,z)＝vbn(x,y,z) (4)
For isotropic elastic seabed, the requirements of displacement continuity and stress continuity in the normal direction and zero tangential stress are met
Wherein u is the horizontal displacement in the elastomer, w is the vertical displacement in the elastomer, ρ is the density of the medium, σ is the stress, λ, μ are the Ramami constants, and Δ is defined as
The peripheral boundary of the ocean channel is an infinite boundary, a finite element numerical method is simulated by adopting a PML (Perfectly MatchedLayer, PML for short) technology, the PML is converted into a control equation of an absorption layer by adding an absorption coefficient to the control equation, and in order to simplify the equation description, the x axis is taken as x1The axis and the y axis are x2Axis, the PML equation in the frequency domain can be written using the separation variables
Wherein σiTo the absorption coefficient, vi，piTo match the velocity and sound pressure amplitude of the layer domain.
After the PML is adopted to process the boundary, the Smerfield far-field extinction condition is met on the boundary
p(x,y,z)|r＝∞＝0 (9)
The sound pressure is made zero at the boundary by sound absorption to the point where no sound is reflected at the boundary to simulate an infinite space around the channel.
A structural acoustic radiation numerical model under an ocean channel is established through a fluid-solid coupling equation, an acoustic boundary coupling equation and a PML technology, structural radiation sound field information is calculated and obtained, acoustic pressure data from the sea surface to a sectional line can be extracted, in order to enable an FEM calculation result to be perfectly matched with a PE setting condition at a space lattice point, the sound field data containing amplitude and phase information needs to be processed through a segmented cubic Elmit interpolation method, and then the processed sound field data is used as an FEM-PE coupling condition, namely, the initial condition for rapidly calculating a PE method sound field.
PE method sound field extrapolation theory under ocean channel
The starting point of the derivation of the parabolic equation is an axisymmetric coordinate system (r, z), and the sound field of a simple harmonic point source in a horizontally-changed sound channel is formed by a wave equation
Wherein p is fluid medium sound pressure, rho (r, z) is fluid density, c (r, z) is fluid sound velocity, zsIs the position of the sound source in the z-axis direction.
Under the axisymmetric coordinate system, when the density of the fluid medium is constant, the time relation is e(-jωt)The Helmholtz equation for a simple harmonic point source of (omega is the angular frequency) is
Wherein k is the wave number
There are several ways to derive the standard parabolic wave equation, and in the present invention, the solution form of equation (11) is assumed to be strictly in accordance with the method of Tappert
p(r,z)＝ψ(r,z)v(r) (12)
Substituting equation (12) into equation (11) to separate the variables:
wherein k is0Reference wave number, c0Reference sound velocity, and k (r, z) ═ k0n(r,z)，n(r,z)＝c0/c(r,z)。
At the point of satisfying (k)0Under the precondition of r) > 1, the solution of formula (13) can be represented by the following asymptotic formula
Then, make far-field condition hypothesis0r) > 1) to obtain a simplified elliptic wave equation
To solve the above equation, the following two operators are first defined
From the two defined operators, the elliptic wave equation can be written in the form
Factoring equation (18) into two components, an input wave and an output wave, i.e.
(P+ik0-ik0Q)(P+ik0+ik0Q)ψ-ik0(PQ-QP)ψ＝0 (19)
When the medium is independent of distance, i.e. n ≡ n (z), the operators P and Q may exchange positions with each other, so that the last term of equation (19) is zero, and only the output wave component is considered, resulting in
For the convenience of subsequent solution, the order is
Thus the square root operator given by equation (17) can be written as
With the continuous and deep research, the root equation (22) is processed by different approximation treatments to obtain parabolic equations with different precision requirements and different propagation angles, the common treatment mode is a wide PE (polyethylene) with a very large angle range based on Pascal series expansion, the root approximation treatment method enables the propagation angles which can be processed by the parabolic equation method to almost reach 90 degrees, and the operator Q is subjected to Pascal series expansion to obtain the propagation angles
Wherein,m is the number of terms in the expansion.
By substituting equation (23) into equation (20), a large-angle parabolic equation based on a Padd series expansion of the horizontal operator can be obtained
The invention adopts the large-angle PE obtained by Claerbout, a Finite difference method (FDM for short) is needed for solving, the fluid domain needs to be dispersed in the numerical solving process, and the step pitch satisfied by each dispersed direction under the ocean channel isThe radiation sound field of any field point under the shallow sea channel can be solved by changing delta r to (2-5) delta z
In the formula:
it can be known that the parabolic finite difference method is a step-by-step solving process, and the information of the next field can be solved from the information of the previous field, and the initial distance r can be solved by adopting the form0To a sound field distributed along the depth. In the sound field solving process, the initial conditions and boundary conditions of the marine environment need to be specified in detail, generally, the free surface of the sea surface adopts sound field soft boundary processing, so that psi (r,0) is satisfied at the surface, the seabed adopts semi-infinite uniform liquid/elastic space processing, and the radiation conditions satisfied by the seabed continuation part are limited by using an artificial absorption layer with the thickness of several wavelengths. Regarding the problem of establishing the initial field data of the PE, the sound field (including amplitude and phase) along the depth direction generated by a sound source with certain directivity obtained by experimental measurement or numerical calculation can be specified, and the sound field of a sound source with a complex structure body in the depth direction under a multi-physical-field local environment is obtained by a finite element numerical method and serves as the initial field condition for the calculation of the PE.
Extracting sound field result P in depth direction according to finite element calculation to establish depth coordinate zfAnd the sound pressure PfIn the PE computation domain depth sideUpward horizontal distance from the center r of the structureo(roλ) at each depth lattice point (r)0Z) the sound field can be obtained by the following segmented cubic ensemble interpolation method
Wherein z ispIs a minimum interval [ zk,zk+1]Point of above, P'f,kExtracting a result function at node z for the finite elementkThe derivative value, k is 0,1,2, 3. cndot. n, n is the discrete number of FEM extraction results.
The sound field value of each lattice point of PE in the depth direction can be obtained by the formula (27)Then used as the initial condition for rapidly calculating the sound field by the PE methodThat is, the FEM-PE coupling condition, the sound field step calculation is performed using equation (25) based on the finite difference solution of the pade approximation.
The invention has the outstanding advantages that:
(a) the invention has strong adaptability to the shape of the elastic structure and the type of the ocean channel environment, and the multi-physical field local model of the elastic structure under the ocean channel is established by adopting a finite element method, so that finite element numerical calculation can be carried out on the radiation sound field of any complex structure under different ocean channels, and the invention has strong adaptability to the structure type. And then, the sound field information calculated under the local area is used as a sound source input condition of a PE method, and far-field sound field calculation under an ocean channel is carried out. The method can forecast the sound radiation of the structure under the ocean channel with the liquid seabed (including sound absorption) by deducing a standardized PE method, if the ocean seabed is a hard elastic layer, the elastic PE is adopted to theoretically establish an ocean sound field, the sound field of the structure under the ocean channel with the elastic layer seabed is solved, and the method is also used for forecasting the sound radiation of the structure under the shallow-sea wedge-shaped seabed or the deep-sea channel, so that the method can quickly forecast the sound field of any elastic structure under different ocean channels.
(b) The method has the characteristics of less calculation time and high efficiency in calculation, and the convergence and calculation speed of the PE method sound field calculation are accelerated by carrying out the Pade approximation processing on the square root operator in the parabolic equation under the ocean channel. Under the same calculation hardware condition, the problem of complex acoustic radiation which cannot be simulated by a traditional numerical method (a finite element method, a boundary element method, a statistical energy method and the like) or cannot be calculated due to large calculation amount can be quickly calculated, and the calculation result is accurate and efficient.
(c) The method has the advantages of simple operation process, convenient use, small implementation workload and easy popularization in theoretical research and actual engineering. The method has the key step that the external field radiation sound field of the elastic structure under the ocean channel can be rapidly forecasted only by acquiring the linear sound pressure distribution information in the depth direction of the structure through numerical method transversal extraction or through a vertical line array of a test method and perfectly matching the initial field of a PE method.
Compared with the traditional forecasting method, the method has strong adaptability to the elastic structure and the ocean channel, accurate and efficient calculation result, simple use and easy popularization. The method effectively solves the bottleneck problems of large calculation amount, multiple physical fields, complex channel environment and the like in the process of researching acoustic radiation prediction of the elastic structure under the ocean channel at present.
Drawings
Fig. 1a is a forecasting model of the elastic structure radiation sound field under the ocean channel adopted by the invention.
FIG. 1b is a schematic diagram of the present invention for performing sound field prediction of a structure under shallow sea channels.
Fig. 2 is a verification model of point source acoustic propagation under shallow sea channels.
FIG. 3a is a comparison graph of the 20Hz finite element and the wave number integration method calculation results in the depth direction under the shallow sea channel.
FIG. 4a is a graph comparing the results of the method of the present invention at 20z with those of finite element calculations.
FIG. 4b is a graph comparing the results of the method of the present invention at 30Hz with those of finite element calculations.
FIG. 4c is a graph comparing the results of the method of the present invention at 40Hz with those of finite element calculations.
FIG. 4d is a comparison of the results of the inventive method at 50Hz and finite element calculations.
FIG. 5a is a schematic diagram of the acoustic radiation prediction of the elastic cylindrical shell under the channel of the ocean shallow sea by using the present invention
FIG. 5b is a diagram for FEM to establish an acoustic radiation local numerical model of the elastic cylindrical shell under the ocean shallow sea channel.
FIG. 6a shows spatial distribution of a cross-sectional radiation sound field of FEM at a frequency of 100 Hz.
FIG. 6b shows spatial distribution of cross-sectional radiation sound field of FEM at 200 Hz.
FIG. 6c shows spatial distribution of cross-sectional radiation sound field of FEM at 400 Hz.
FIG. 6d shows spatial distribution of cross-sectional radiation sound field of FEM at 800 Hz.
FIG. 7a is a graph of the radiation sound pressure level as a function of distance calculated by the present invention at a frequency of 100 Hz.
FIG. 7b is a graph of the radiation sound pressure level as a function of distance calculated by the present invention at a frequency of 200 Hz.
FIG. 7c is a graph of the radiation sound pressure level as a function of distance calculated by the present invention at a frequency of 400 Hz.
FIG. 7d is a graph of the radiation sound pressure level as a function of distance calculated by the present invention at a frequency of 800 Hz.
FIG. 8a is a pseudo-color graph of the radiation sound field calculated at a frequency of 100Hz in accordance with the present invention.
FIG. 8b is a pseudo-color graph of the radiation sound field calculated at a frequency of 200Hz in accordance with the present invention.
FIG. 8c is a pseudo-color graph of the radiation sound field calculated by the present invention at a frequency of 400 Hz.
FIG. 8d is a pseudo-color graph of the radiation sound field calculated by the present invention at a frequency of 800 Hz.
Table 1 of fig. 9 shows Pekeris shallow sea channel environment and elastic structure parameters.
Table 2 of fig. 10 is a calculation time test for different calculation frequencies according to the present invention.
Table 3 of FIG. 11 is a test of the calculation time for different calculation ranges according to the present invention.
Detailed Description
The invention is described in more detail below by way of example.
1. Initial field acquisition in a multi-physics local environment
The acoustic radiation problem of the elastic structure under the ocean channel relates to acoustic coupling boundary processing such as fluid-solid coupling, acoustic boundary coupling, infinite boundary and the like, and an acoustic control equation and boundary continuous conditions under a multi-physical field are established by adopting finite elements as follows:
fluid-solid coupled equation
On the coupling surface of the structure surface contacting with the external fluid, the boundary condition is satisfied that the vibration speed of the structure surface normal direction is the same as the vibration speed of the external fluid medium, and the coupling equation of the structure and the fluid can be written as
Wherein the stiffness matrix KijAnd a damping matrix CijQuality matrix MijAre all n × n order matrices. Subscripts a, s and c are an acoustic system matrix, a mechanical structure matrix and a coupling matrix; defining a coupling matrix Kc、McIs composed of And isnseNumber of structural grids for structure to contact fluid, { n }eIs the normal vector of the structural grid; ω 2 π f is the angular frequency, f is the frequency (Hz), ρ0Is the density of seawater; u. ofi、piFor displacement and sound pressure amplitude, Fst、FatThe coupled excitation loads of the structure and the fluid medium are respectively defined as
The sea surface boundary of the ocean channel is usually Dirichlet boundary, and the boundary condition is met by the condition that the interface sound pressure is zero
pa(x,y,z)|z＝0＝0 (2)
Wherein, in order to distinguish between sea water and sea floor, subscripts a and b denote the sea water fluid layer and the sea floor layer, respectively.
For liquid seabed, the boundary conditions are satisfied that the sound pressure p (x, y, z) is continuous, and the normal vibration velocity v (x, y, z) is continuous
pa(x,y,z)＝pb(x,y,z) (3)
van(x,y,z)＝vbn(x,y,z) (4)
For isotropic elastic seabed, the requirements of displacement continuity and stress continuity in the normal direction and zero tangential stress are met
Wherein u is the horizontal displacement in the elastomer, w is the vertical displacement in the elastomer, ρ is the density of the medium, σ is the stress, λ, μ are the Ramami constants, and Δ is defined as
The peripheral boundary of the ocean channel is an infinite boundary, a finite element numerical method is simulated by adopting a PML (Perfectly MatchedLayer, PML for short) technology, the PML is converted into a control equation of an absorption layer by adding an absorption coefficient to the control equation, and in order to simplify the equation description, the x axis is taken as x1The axis and the y axis are x2Axis, the PML equation in the frequency domain can be written using the separation variables
Wherein σiTo the absorption coefficient, vi，piTo match the velocity and sound pressure amplitude of the layer domain.
After the PML is adopted to process the boundary, the Smerfield far-field extinction condition is met on the boundary
p(x,y,z)|r＝∞＝0 (9)
The sound pressure is made zero at the boundary by sound absorption to the point where no sound is reflected at the boundary to simulate an infinite space around the channel.
And establishing a structural acoustic radiation numerical model under the ocean channel through a flow-solid coupling equation, an acoustic-boundary coupling equation and a PML technology, and calculating to obtain structural radiation sound field information. In order to enable the FEM calculation result to be perfectly matched with the PE setting condition at the space lattice point, the sound field data containing amplitude and phase information needs to be processed through a three-time segmentation Elmith interpolation method, and then the processed sound field data is used as an FEM-PE coupling condition, namely an initial condition for rapidly calculating a PE method sound field.
2. PE method sound field extrapolation theory under ocean channel
The starting point of the derivation of the parabolic equation is an axisymmetric coordinate system (r, z), and the sound field of a simple harmonic point source in a horizontally-changed sound channel is formed by a wave equation
Wherein p is fluid medium sound pressure, rho (r, z) is density, c (r, z) is sound velocity, z issIs the position of the sound source in the z-axis direction.
Under the axisymmetric coordinate system, when the density of the fluid medium is constant, the time relation is e(-jωt)The Helmholtz equation for a simple harmonic point source of (omega is the angular frequency) is
Wherein k ═ ω/c is the wave number.
There are several ways to derive the standard parabolic wave equation, and in the present invention, the solution form of equation (11) is assumed to be strictly in accordance with the method of Tappert
p(r,z)＝ψ(r,z)v(r) (12)
Substituting equation (12) into equation (11) to separate the variables:
wherein k is0Reference wave number, c0Reference is made to the speed of sound. And k (r, z) ═ k0n(r,z)，n(r,z)＝c0/c(r,z)。
At the point of satisfying (k)0Under the precondition of r) > 1, the solution of formula (13) can be represented by the following asymptotic formula
Then, make far-field condition hypothesis0r) > 1) to obtain a simplified elliptic wave equation
To solve the above equation, the following two operators are first defined
From the two defined operators, the elliptic wave equation can be written in the form
Factoring equation (18) into two components, an input wave and an output wave, i.e.
(P+ik0-ik0Q)(P+ik0+ik0Q)ψ-ik0(PQ-QP)ψ＝0 (19)
When the medium is independent of distance, i.e. n ≡ n (z), the operators P and Q may exchange positions with each other, so that the last term of equation (19) is zero, and only the output wave component is considered, resulting in
For the convenience of subsequent solution, the order is
Thus the square root operator given by equation (17) can be written as
With the continuous and deep research, the root equation (22) is processed by different approximation treatments to obtain parabolic equations with different precision requirements and different propagation angles, the common treatment mode is a wide PE (polyethylene) with a very large angle range based on Pascal series expansion, the root approximation treatment method enables the propagation angles which can be processed by the parabolic equation method to almost reach 90 degrees, and the operator Q is subjected to Pascal series expansion to obtain the propagation angles
Wherein,m is the number of terms in the expansion.
By substituting equation (23) into equation (20), a large-angle parabolic equation based on a Padd series expansion of the horizontal operator can be obtained
The invention adopts the large-angle PE obtained by Claerbout, a Finite difference method (FDM for short) is needed for solving, the fluid domain needs to be dispersed in the numerical solving process, and the step pitch satisfied by each dispersed direction under the ocean channel isThe radiation sound field of any field point under the shallow sea channel can be solved by changing delta r to (2-5) delta z
In the formula:
it can be known that the parabolic finite difference method is a step-by-step solving process, and the information of the next field can be solved from the information of the previous field, and the initial distance r can be solved by adopting the form0To a sound field distributed along the depth. In the sound field solving process, the initial conditions and boundary conditions of the marine environment need to be specified in detail, generally, the free surface of the sea surface adopts sound field soft boundary processing, so that psi (r,0) is satisfied at the surface, the seabed adopts semi-infinite uniform liquid/elastic space processing, and the radiation conditions satisfied by the seabed continuation part are limited by using an artificial absorption layer with the thickness of several wavelengths. Regarding the problem of establishing the initial field data of the PE, the sound field (including amplitude and phase) along the depth direction generated by a sound source with certain directivity obtained by experimental measurement or numerical calculation can be specified, and the sound field of a sound source with a complex structure body in the depth direction under a multi-physical-field local environment is obtained by a finite element numerical method and serves as the initial field condition for the calculation of the PE.
Extracting sound field result P in depth direction according to finite element calculation to establish depth coordinate zfAnd the sound pressure PfIn the depth direction of the PE calculation domain, from the center r of the structure in the horizontal directiono(roλ) at each depth lattice point (r)0Z) the sound field can be obtained by the following segmented cubic ensemble interpolation method
Wherein z ispIs a minimum interval [ zk,zk+1]Point of above, P'f,kExtracting a result function at node z for the finite elementkThe derivative value, k is 0,1,2, 3. cndot. n, n is the discrete number of FEM extraction results.
The sound field value of each lattice point of PE in the depth direction can be obtained by the formula (27)Then used as the initial condition for rapidly calculating the sound field by the PE methodThat is, the FEM-PE coupling condition, the sound field step calculation is performed using equation (25) based on the finite difference solution of the pade approximation.
Method accuracy verification
Example 1: pekeris shallow sea channel point source acoustic propagation calculation
Establishing a point source sound propagation model under a Pekeris channel under an axisymmetric condition as shown in FIG. 2, wherein the channel depth H is 200m, the upper interface of the channel is a Dirichlet boundary, the lower interface is an infinite half-space equal-sound-velocity liquid layer, and the seawater parameters are as follows: density of sea water is rhoa＝1024kg/m3Speed of sound c of sea watera1500 m/s; density of the sea bottom ρb＝1800kg/m3Sea bottom speed of sound cb2500 m/s. The sound source is a monopole point source, the amplitude of the monopole is 1, and the depth of the point source is z0100 m. The method comprises the steps of adopting a finite element numerical value of multiple physical fields to calculate sound field transmission of a point source under a channel environment, wherein the calculation distance is r equal to 2000m, extracting sound pressure information (amplitude and phase) of a Finite Element (FEM) at a wavelength lambda away from the point source in the whole shallow sea depth direction, using the sound pressure information as an FEM-PE coupling condition, namely an initial condition of PE sound field calculation, setting PE to calculate shallow sea channel environment parameters, and calculating sound field information of any field point under a shallow sea channel.
As shown in fig. 3a, complex sound pressure values with a frequency of 20Hz in the depth direction at a distance λ of 75m from the point source are obtained by means of multi-physical field coupling FEM numerical calculation, and a distribution curve of sound pressure mode values in the depth direction is drawn and compared with the calculation results of the wave number integration calculation program FFP under the same channel conditions. Then, after performing piecewise cubic ensemble interpolation processing on the accurate calculation result of the FEM in the depth direction, an acoustic propagation curve (depth of each field point is 50m) corresponding to a frequency of 20Hz is calculated, and compared with the calculation result of the FEM under the same condition, as shown in fig. 4 a. Similarly, radiation sound pressure levels of the structure radiation sound field at 30Hz, 40Hz and 50Hz were calculated as propagation distance curves and compared with the finite element calculation results, as shown in FIGS. 4b, 4c and 4 d. It can be seen that the calculated results of the method of the invention are well consistent with the calculated results of FEM under the frequencies of 20Hz, 30Hz, 40Hz and 50Hz, and the accuracy of the sound field calculation of the invention is verified.
Description of the practical and efficient methods
Example 2: computation of acoustic radiation of elastic structure under Pekeris shallow sea channel
As shown in fig. 5a, a FEM-PE calculation theoretical model of the elastic cylindrical shell radiation sound field under the Pekeris shallow sea channel is established, the calculation theoretical model is mainly divided into a numerical FEM calculation domain and a PE calculation domain, and complex sound pressure information of the numerical FEM calculation domain in the depth direction is extracted and interpolated to serve as a FEM-PE coupling condition. Wherein S is an elastic structure sound source, zsPosition of the centre of the structure on the z-axis, pa,caRespectively sea water density sound velocity, rhob,cbRespectively an infinite liquid layerDensity and speed of sound, PlFor FEM-PE coupling field, λ is PlOne wavelength distance, r, from the center of the structurepThe distance of any field point under the field from the initial field is calculated for the PE.
As shown in fig. 5b, an acoustic radiation model of the elastic cylindrical shell under the Pekeris shallow sea channel is established by using a multi-physical-field coupling numerical method, parameters of a channel environment and an elastic structure are shown in table 1 of fig. 9, structural acoustic radiation information under local fluid is calculated by using a finite element method, and as shown in fig. 6a to 6d, corresponding acoustic field distributions of the elastic cylindrical shell under the Pekeris shallow sea channel local fluid at frequencies of 100Hz, 200Hz, 400Hz, and 800Hz in a z-o-y plane are calculated numerically. In order to perform space perfect matching with PE discrete grid points (delta r, delta z), segmented three-time Elmer interpolation is required to be performed on complex sound pressure extracted by FEM calculation, the complex sound pressure is used as an FEM and PE coupling condition, namely a PE sound field calculation initial condition, then the sound field PE extrapolation is adopted to calculate the elastic structure radiation sound field information under a far field condition, as shown in figures 7a to 7d, variation curves of the elastic cylindrical shell radiation sound pressure level with the distance under 100Hz, 200Hz, 400Hz and 800Hz frequencies are calculated respectively, and the depth of each field point is 3 m; as shown in fig. 8a to 8d, pseudo-color distribution patterns of the elastic cylindrical shell in the far-field radiation sound field at frequencies of 100Hz, 200Hz, 400Hz and 800Hz were calculated, respectively. It can be seen that the elastic structure under the shallow sea channel basically meets the cylindrical wave propagation rule in the far field radiation sound field, and the fluctuation details of the sound field increase along with the increase of the frequency.
To illustrate the great advantage of the present invention in terms of the calculation speed of acoustic radiation of elastic structures under ocean channels, the acoustic field calculation time at different distances and different frequencies was tested, as shown in table 2 of fig. 10 and table 3 of fig. 11, the tested fluid environment and elastic structure were the same as described above, and the hardware condition parameters were tested for Lenovo ThinkStation E30 (intel octal 3.2GHz CPU, 32GB memory).
As can be seen from Table 2 of FIG. 10 and Table 3 of FIG. 11, the influence of different distances on the calculation time is more significant than the influence of different frequencies on the calculation time when the calculation distance is 0 to 10In km, the calculation time is slightly increased in the process of changing the calculation frequency from 100Hz to 800Hz, because the step distance satisfied by each discrete direction under the ocean channel isWhen the frequency rises, the discrete steps in the vertical direction and the horizontal direction are reduced, the number of discrete units is increased, and the calculation time is increased, but when the frequency reaches the higher frequency of 800Hz, the calculation time is only about 1min, and the method is completely suitable for the rapid calculation of the sound radiation of the elastic structure under the ocean channel under each frequency. For different calculation ranges, even if the solving distance range reaches 0-100km (the number of discrete grid units reaches the million magnitude), the calculation time is only 10.2030 minutes, while when the problem is calculated by adopting the traditional finite element, because the physical field coupling related to the sound radiation of the structure under the shallow sea channel is more, the calculation distance is long, when the distance range reaches 0-1km, the computer cannot calculate by adopting the finite element calculation, but the calculation time in the distance range is only 0.0179 minutes by adopting the method disclosed by the invention, so that the huge advantage of the method for performing the sound radiation remote calculation of the elastic structure under the shallow sea channel is shown, and the method sound field in any remote range can be quickly solved.
Claims (3)
1. A coupled FEM-PE-based acoustic radiation forecasting method for an elastic structure under an ocean channel is characterized by comprising the following steps:
establishing an acoustic radiation local multi-physical field numerical model of an elastic structure under an ocean channel, respectively performing acoustic definition on fluid-solid coupling, acoustic boundary coupling and a Smirfield radiation condition at infinity by adopting a finite element numerical method, and calculating sound field information under a fluid domain of the local ocean channel;
step two, performing two-dimensional sound field processing in a three-dimensional channel space, forming a two-dimensional section in the vertical direction through a far-field point and a structure center, selecting a one-dimensional section line in the depth direction at a certain distance from the structure center, and extracting complex sound pressure information on the section line as initial field information of a sound field extrapolation parabolic equation method;
matching the sound field information extracted by finite element calculation with the sound field extrapolation parabolic equation method initial field to enable the finite element calculation result to be completely matched with each lattice point of the parabolic equation method space initial field;
and fourthly, setting channel environment parameters and field point positions which are the same as those of the finite elements, and rapidly calculating sound field extrapolation parabolic equation method for sound field sound pressure of any field point under the channel to obtain sound radiation characteristics of the structure under the ocean channel for rapidly forecasting the radiation sound field of the elastic structure under the channel.
2. The coupled FEM-PE based method for forecasting acoustic radiation of elastic structures under ocean channel according to claim 1, wherein the coupled FEM-PE based method comprises the following steps: and selecting one-dimensional section lines in the depth direction at a certain distance from the center of the structure, wherein the distance between the horizontal distance of the one-dimensional section lines and the center of the structure is equal to the wavelength corresponding to the calculated frequency, namely l ≈ lambda.
3. The method for forecasting acoustic radiation of elastic structures under ocean channels based on coupled FEM-PE as claimed in claim 1 or 2, wherein: and matching space lattice points of complex sound pressure of a finite element method and a sound field of a parabolic equation method by adopting a segmented cubic ensemble interpolation technology, and establishing a coupling condition of the finite element method and the parabolic equation method as an initial field value calculated by the finite difference method of the parabolic equation method.
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