A three-dimensional acousto-elastic calculation method based on combined potential

Abstract

The application discloses a three-dimensional acoustic-elasticity calculation method based on a combination potential, relates to the field of three-dimensional acoustic-elasticity calculation of a ship, and comprises the following steps: constructing a velocity potential in an outer flow field of a ship structure in water as a linear combination of a single-layer potential and a double-layer potential, and constructing a boundary integral equation on a wet surface of the ship structure in water; according to a fluid-structure coupling boundary condition on the wet surface of the ship structure in water, solving the boundary integral equation on the wet surface of the ship structure in water by using a boundary element method to obtain a virtual source intensity distribution on the wet surface of the ship structure in water; and calculating acoustic-elasticity response parameters according to the virtual source intensity distribution on the wet surface of the ship structure in water and structural dry modal displacements. By constructing the velocity potential in the outer flow field of the ship structure in water as the linear combination of the single-layer potential and the double-layer potential, irregular frequencies in acoustic-elasticity calculation can be effectively eliminated without increasing the calculation scale and modeling workload, and the efficiency of three-dimensional acoustic-elasticity analysis can be significantly improved.

Description

Technical Field

[0001] This application relates to the field of three-dimensional acoustoelasticity calculation of ships, and in particular to a three-dimensional acoustoelasticity calculation method based on combined potential. Background Technology

[0002] During navigation, the ship's structure in the water is subjected to excitation from the internal mechanical operation, resulting in vibration and sound radiation. Calculating and analyzing the vibration and sound radiation of ship structures in water is crucial for guiding their acoustic design. Currently, three-dimensional acoustoelastic theory and calculation methods for ships are widely used in the computational analysis of coupled vibration and sound radiation problems of ship structures in water. This method uses the acoustic indirect boundary integral method to handle the external water domain during fluid-structure interaction modeling. Because it does not require meshing of the external water domain and can automatically satisfy the radiation boundary conditions at infinity, it effectively avoids errors caused by water truncation, thus achieving high computational efficiency and accuracy. However, when numerically solving the acoustic indirect boundary integral equation of the external water domain using the boundary element method, the problem of irregular frequencies (also known as spurious characteristic frequencies) arises. At and near irregular frequency points, the numerical calculation results are distorted, and the irregular frequency phenomenon usually manifests as obvious peaks (valleys) on the numerical calculation result curve, which can be mixed with the peaks (valleys) of the physically existing structural vibration response curve, severely interfering with subsequent resonant frequency identification and response characteristic analysis.

[0003] To address the irregular frequency problem encountered in the three-dimensional acoustoelasticity calculation and analysis of ships, the article "Method for Eliminating Irregular Frequency in Hydroelasticity of Acoustic Media, Ship Mechanics, 2013, 17(10):1202-1208" first proposed the Real Space Virtual Impedance Closed Surface Method (CVIS method). This method introduces a virtual impedance surface inside the structure to absorb the resonance of the virtual inner flow domain, thereby eliminating the irregular frequency phenomenon. Patent CN 110390071 A further proposes an acoustoelasticity calculation method based on the complex space virtual impedance closed surface, based on the existing real space virtual impedance closed surface method. These methods all introduce virtual impedance closed surfaces, construct boundary integral equations for the outer flow domain and the virtual inner flow domain respectively, and solve them simultaneously to eliminate the irregular frequency problem encountered in acoustoelasticity calculation. However, due to the introduction of virtual impedance surfaces and the need to solve the boundary integral equations simultaneously, this type of method increases the number of grids and unknowns in the calculation model, thereby increasing the computational load and memory usage. Furthermore, when using this method for three-dimensional acoustoelastic modeling, it is necessary to customize parameters such as the size and imaginary factor of the virtual impedance surface according to different calculation models. This will undoubtedly introduce additional uncertainties and seriously affect the accuracy and reliability of the numerical calculation results. Summary of the Invention

[0004] To address the aforementioned problems and technical requirements, this application proposes a three-dimensional acoustoelasticity calculation method based on combined potential. The technical solution of this application is as follows:

[0005] A three-dimensional acoustoelasticity calculation method based on combined potential includes the following steps:

[0006] Based on the potential function theory, the velocity potential in the external flow domain of a ship structure in water is constructed as a linear combination of single-layer and double-layer potentials. The single-layer potential represents the velocity potential generated by a continuously distributed monopole source on the wet surface of the ship structure in water, and the double-layer potential represents the velocity potential generated by a continuously distributed dipole source on the wet surface of the ship structure in water.

[0007] Based on the velocity potential in the form of a linear combination, a boundary integral equation is constructed on the wetted surface of a ship structure in water. The boundary integral equation on the wetted surface of a ship structure in water is an integral equation about the distribution of virtual source strength on the wetted surface of a ship structure in water. The virtual source strength represents the source strength generated by the continuous distribution of monopole and dipole sources on the wetted surface of a ship structure in water.

[0008] Based on the fluid-structure interaction boundary conditions on the wetted surface of the ship structure in water, the boundary element method is used to solve the boundary integral equation on the wetted surface of the ship structure in water, and the virtual source intensity distribution on the wetted surface of the ship structure in water is obtained.

[0009] The acoustoelastic response parameters are calculated based on the virtual source intensity distribution and dry modal displacement of the wet surface of the ship structure in water. The dry modal displacement of the wet surface of the ship structure in water is obtained in advance based on modal analysis. The acoustoelastic response parameters characterize the acoustic field information of the external flow domain of the ship structure in water.

[0010] A further technical solution is to determine the r-th order velocity potential φ at any point r in the external flow domain of the ship structure in the water. r (r) is:

[0011] φ r (r)=φ r ′(r)+νφ r "(r)

[0012] Where, field point r∈E, E is the outer flow domain of the ship structure in water, φ r ′(r) is the r-th order single-layer potential at field point r, φ r ″(r) is the r-th order double-layer potential at field point r, and ν is the combination coefficient and ν = i / k. k is the sound wave number and k = ω / c, ω is the angular frequency of the sound wave, and c is the speed at which the sound wave propagates in the fluid.

[0013] A further technical solution is to determine the r-th order single-layer potential φ at any point r in the external flow domain of the ship structure in the water. r ′(r) is:

[0014]

[0015] The r-th order double-layer potential φ at any point r in the external flow domain of a ship structure in water r "(r) is:

[0016]

[0017] in, Where E is the wetted surface of the ship structure in the water, and n is the wetted surface of the ship structure in the water. The unit outward normal vector, r0, is the wetted surface of the ship structure in water. The source point on the graph, G(r,r0), is the Green's function term. It is the partial derivative term of the Green's function, σ r (r0) is the r-th order virtual source strength of source point r0.

[0018] A further technical solution involves constructing the boundary integral equations on the wetted surface of a ship's structure in water, including:

[0019] Based on the boundary limit properties of potential function theory, the outward normal direction derivative of the velocity potential in the linear combination form is obtained, and when the field point r in the outer flow domain of the underwater ship structure approaches the wet surface of the underwater ship structure, the boundary integral equation on the wet surface of the underwater ship structure is obtained; the boundary limit properties indicate that the normal derivative of the single-layer potential has a step characteristic at the boundary.

[0020] A further technical solution is that the boundary integral equation on the wetted surface of the ship's structure in water is:

[0021]

[0022] Among them, venues It is any field point on the wet surface of the ship structure. The r-th order velocity potential at that point, It is a step term generated by the boundary step property of the normal derivative of a single-layer potential. It is a venue The rth order virtual source strength.

[0023] The further technical solution involves calculating the acoustoelastic response parameters, including:

[0024] The surface velocity potential of the wetted surface of the ship structure in water is calculated based on the virtual source strength distribution. Combined with the structural dry modal displacement of the wetted surface of the ship structure in water, the generalized additional mass coefficient matrix and the generalized additional damping coefficient matrix are calculated. The generalized additional mass coefficient and the generalized additional damping coefficient are used to characterize the fluid-structure interaction effect.

[0025] Substituting the generalized additional mass coefficient matrix and the generalized additional damping coefficient matrix into the acoustic-elastic coupling dynamics equation, the principal coordinate response of the ship structure in water is obtained by solving the equation.

[0026] Based on the principal coordinate response and the velocity potential in the external flow domain of the ship structure in water, the acoustoelastic response parameters are calculated.

[0027] Its further technical solution is to base the solution on any field point on the wet surface of the ship's structure in water. The rth order virtual source strength Calculations were performed on any field point on the wetted surface of the ship's structure in water. The r-th order surface velocity potential at the location for:

[0028]

[0029] A further technical solution involves obtaining the principal coordinate response of the ship's structure in water, including:

[0030] Based on any field point on the wetted surface of a ship's structure in water The j-th order surface velocity potential φ at the location j (ω) and the r-th order structural dry mode displacement vector u of the wetted surface of the ship structure in water. r The generalized additional mass coefficients of the r-th and j-th mode couplings of the generalized additional mass coefficient matrix A(ω) are calculated respectively. And the generalized additional damping coefficients of the r-th and j-th mode coupling of the generalized additional damping coefficient matrix B(ω)

[0031] Substituting the generalized additional mass coefficient matrix A(ω) and the generalized additional damping coefficient matrix B(ω) into the acoustic-elastic coupling dynamic equation, we obtain the principal coordinate response of the ship structure in water; the acoustic-elastic coupling dynamic equation is:

[0032] {-ω 2 [a+A(ω)]+iω[b+B(ω)]+c}q(ω)=G(ω)

[0033] Where a is the generalized mass coefficient matrix, b is the generalized damping coefficient matrix, c is the generalized stiffness coefficient matrix, G(ω) is the generalized force column vector, and q(ω) is the principal coordinate response column vector, and q(ω) = [q1(ω),...,q r (ω),...,q M (ω)] T M is the truncated mode number, [] T Represents the matrix transpose; ρ0 is the fluid medium density; Re{} represents taking the real part of the complex number; Im{} represents taking the imaginary part of the complex number; r and j are both integer parameters and 1≤r≤M, 1≤j≤M.

[0034] The further technical solution is that the acoustoelastic response parameters include radiated sound pressure p(r,ω) and radiated sound power P(ω);

[0035] Based on any r-th order principal coordinate response q r (ω) and the r-th order velocity potential φ at any point r in the external flow domain of the ship structure in the water. r (r), determine the radiated sound pressure at any point r in the external flow domain of the ship structure in the water.

[0036] Based on any r-th order principal coordinate response q r The generalized additional damping coefficient matrix B(ω) and the generalized additional damping coefficient B coupled in any r-th and j-th modes are the generalized additional damping coefficient B. rj (ω), determine the radiated acoustic power in the external water domain of the ship structure in water. (·) * This indicates finding the conjugate of a complex number.

[0037] A further technical solution is to determine the fluid-structure interaction boundary conditions on the wetted surface of the ship structure as follows: The derivative of the velocity potential in the outward normal direction on the wetted surface of the ship structure is equal to the velocity in the outward normal direction of the dry modal displacement of the structure. Among them, u r Wet surfaces of ship structures in water The r-th order structural dry mode displacement vector, where n is the wet surface of the ship structure in water. The unit outward normal vector,

[0038] ω is the angular frequency of the sound wave.

[0039] The beneficial technical effects of this application are:

[0040] This application discloses a three-dimensional acoustoelasticity calculation method based on combined potentials. By constructing the velocity potentials of each order in the external flow domain of a ship as a combined potential in the form of a linear combination of single-layer and double-layer potentials, it effectively solves the problem of irregular frequencies encountered in three-dimensional acoustoelasticity calculations. Moreover, since this method does not introduce additional virtual impedance surfaces, it can reduce the overall number of meshes in the wetted surface element model during modeling, thereby reducing the modeling workload, facilitating modeling, and making it easy to implement, which is of great significance for practical engineering applications. Furthermore, since there is no virtual wetted surface outside the actual wetted surface of the ship structure in water, it is not necessary to construct boundary integral equations for the internal flow domain. Compared with existing methods that use virtual impedance surfaces to eliminate irregular frequencies, the method of this application mathematically avoids solving simultaneous boundary integral equations, effectively reducing the computational load and memory consumption of equation solving, and significantly improving the efficiency of three-dimensional acoustoelasticity analysis.

[0041] Furthermore, the method of eliminating irregular frequencies by introducing a virtual impedance surface into the model is essentially a physical method. The effective frequency band of this method is related to the size of the physically introduced virtual impedance surface, thus limiting its applicability. In contrast, the method in this application modifies the velocity potential of the external flow domain of the underwater ship structure and improves the boundary integral equations on the wetted surface of the underwater ship structure mathematically. It is not limited by physical space and is therefore applicable across the entire frequency band, capable of eliminating irregular frequencies in all bands. Attached Figure Description

[0042] Figure 1 This is a flowchart of a three-dimensional acoustic elasticity calculation method.

[0043] Figure 2 This is a three-dimensional acoustic elastic computational mesh model of an underwater ship structure, as exemplified by one of the embodiments.

[0044] Figure 3 This is the frequency response curve of the n=0 mode with added mass coefficient and added damping coefficient.

[0045] Figure 4 This is the frequency response curve of the n=1 mode with added mass coefficient and added damping coefficient.

[0046] Figure 5 This is the frequency response curve of the n=2 modal with added mass coefficient and added damping coefficient.

[0047] Figure 6 This is the frequency response curve of the n=3 modal with added mass coefficient and added damping coefficient.

[0048] Figure 7 This is the frequency response curve of the n=4 modal with added mass coefficient and added damping coefficient. Detailed Implementation

[0049] The specific embodiments of this application will be further described below with reference to the accompanying drawings.

[0050] This application discloses a three-dimensional acoustoelasticity calculation method based on combined potential. Please refer to [link / reference]. Figure 1 The flowchart shown illustrates the specific steps of this method:

[0051] Step 1: Based on the potential function theory, the velocity potential in the external flow domain of the ship structure in water is constructed as a linear combination of single-layer and double-layer potentials.

[0052] In classical three-dimensional acoustoelasticity theory, the velocity potential of each order in the external flow domain is usually expressed as a single-layer potential based on the simple source method. Although this expression is concise, it is essentially derived by simultaneously solving the Helmholtz equations for the inner and outer flow domains. This is equivalent to implicitly including a virtual inner flow domain when solving the outer flow domain problem. Therefore, it is easy to understand that irregular frequencies will occur when the inner flow domain resonates. To solve this irregular frequency problem, this application improves upon the simple source method by constructing the velocity potential in the outer flow domain of the underwater ship structure as a linear combination of a single-layer potential and a double-layer potential.

[0053] In one embodiment, the r-th order velocity potential φ at any point r in the external flow domain of the ship structure in water r (r) is:

[0054] φ r (r)=φ r ′(r)+νφ r "(r) (1)

[0055] Where, field point r∈E, E is the outer flow domain of the ship structure in water, φ r ′(r) is the r-th order single-layer potential at field point r, φ r ″(r) is the r-th order double-layer potential at field point r, and ν is the combination coefficient and ν = i / k. k is the sound wave number and k = ω / c, ω is the angular frequency of the sound wave, and c is the speed at which the sound wave propagates in the fluid.

[0056] The monolayer potential represents the velocity potential generated by a continuously distributed monopole source on the wetted surface of a ship structure in water. It is a potential function expressed as the surface integral of the source intensity distribution and the Green's function on the wetted surface of the ship structure. Specifically, the r-th order monolayer potential φ at any field point r in the external flow domain of the ship structure in water is... r ′(r) is:

[0057]

[0058] The double-layer potential represents the velocity potential generated by a continuously distributed dipole source on the wetted surface of a ship structure in water. It is a potential function expressed as the surface integral of the source intensity distribution and the normal derivative of the Green's function. Specifically, the r-th order double-layer potential φ at any field point r in the external flow domain of the ship structure in water is... r "(r) is:

[0059]

[0060] in, Where E is the wetted surface of the ship structure in the water, and n is the wetted surface of the ship structure in the water. The unit outward normal vector, r0, is the wetted surface of the ship structure in water. The source point on the graph, G(r,r0), is the Green's function term. It is the partial derivative term of the Green's function, σ r (r0) is the r-th order virtual source strength of source point r0.

[0061] A single-layer potential primarily reflects the source intensity distribution on a wetted surface, but its use alone relies on the closed equations of the inner basin boundary conditions. A double-layer potential, through the Green's function normal derivative term, introduces boundary normal gradient information, allowing it to independently describe the wave characteristics of the outer basin without implicitly assuming a virtual inner basin. By constructing the outer basin velocity potential as a linear combination of single-layer and double-layer potentials, the source distribution characteristics of the single-layer potential and the normal derivative characteristics of the double-layer potential are combined. This mathematically avoids the virtual inner basin resonance problem implicit in traditional single-potential function expressions, thus eliminating irregular frequency interference without introducing an additional virtual impedance surface.

[0062] Step 2: Based on the velocity potential in the form of this linear combination, construct the boundary integral equation on the wetted surface of the ship structure in the water. The boundary integral equation on the wetted surface of the ship structure in the water is an integral equation about the virtual source intensity distribution on the wetted surface of the ship structure in the water. The virtual source intensity represents the source intensity jointly generated by the continuously distributed monopole source and dipole source on the wetted surface of the ship structure in the water.

[0063] In one embodiment, constructing the boundary integral equations on the wetted surface of a ship structure in water includes:

[0064] Based on the boundary limit properties of potential function theory, the outward normal direction derivative of the velocity potential in the linear combination form is obtained, and when the field point r in the outer flow domain of the underwater ship structure approaches the wet surface of the underwater ship structure, the boundary integral equation on the wet surface of the underwater ship structure is obtained; the boundary limit properties indicate that the normal derivative of the single-layer potential has a step characteristic at the boundary.

[0065] According to the boundary limit properties of potential function theory: a single-layer potential has no singularity on the surface, but its derivative has singularity, with unequal inner and outer limits, and discontinuities on the surface; a double-layer potential is discontinuous on the surface, but its derivative is continuous. Based on this, when calculating the derivative of a single-layer potential along the outward normal direction, if the field point *r* in the external flow domain of the underwater ship structure approaches the wetted surface of the underwater ship structure, a step term will be added to the derivative result. The boundary integral equation on the wetted surface of the underwater ship structure is:

[0066]

[0067] Among them, venues It is any field point on the wet surface of the ship structure. The r-th order velocity potential at that point, This is a step term arising from the boundary step characteristic of the single-layer potential normal derivative. Since the derivative in the outward normal direction is equivalent to approaching the surface from the outer flow domain, this step term is subtracted from the derivative result. It is a venue The rth order virtual source strength.

[0068] As can be seen from formula (4), when constructing the boundary integral equation, the equation is directly closed within the external flow domain framework through the coupling effect of the normal derivative term and the source distribution term, avoiding dependence on the virtual internal flow domain. This combination essentially eliminates the mathematical premise of internal flow domain acoustic resonance, making the solution of the boundary integral equation on the wet surface of the ship structure in water correspond only to the real physical field of the external flow domain, thereby suppressing the generation of irregular frequencies from the root, and eliminating the need to introduce an additional virtual impedance surface to absorb internal flow domain resonance.

[0069] Step 3: Based on the fluid-structure interaction boundary conditions on the wetted surface of the ship structure in water, the boundary element method is used to solve the boundary integral equation on the wetted surface of the ship structure in water, and the virtual source strength distribution on the wetted surface of the ship structure in water is obtained.

[0070] Based on the fact that the outward normal derivative of the velocity potential on the wetted surface of a ship structure in water is equal to the outward normal velocity of the dry modal displacement of the structure, the fluid-structure interaction boundary conditions on the wetted surface of the ship structure in water are determined as follows: Among them, u r Wet surfaces of ship structures in water The r-th order structural dry mode displacement vector, where n is the wet surface of the ship structure in water. The unit outward normal vector, ω is the angular frequency of the sound wave.

[0071] Substituting the fluid-structure interaction boundary conditions on the wetted surface of the ship structure into the boundary integral equation (Equation 4) on the wetted surface of the ship structure, we obtain:

[0072]

[0073] Further, by using the boundary element method to solve formula (5), the distribution of virtual source strengths of each order on the wetted surface of the ship structure in water can be obtained. Among them, the structural dry modal displacement of the wetted surface of the ship structure in water represents the displacement amplitude and direction of each node on the wetted surface of the ship structure in water, which essentially corresponds to the vibration characteristics of the structure under vacuum modes. The structural dry modal displacement of the wetted surface of the ship structure in water is obtained in advance based on modal analysis. The Green function term G(r,r0) is the fundamental solution of the Helmholtz equation in three-dimensional infinite domain fluid, and its expression is: |r-r0| is the distance between the field point and the source point. It should be noted that the virtual source strength obtained here has a different physical meaning than the source strength in the classical simple source method. The virtual source strength represents the source strength generated by the combined effects of monopole and dipole sources continuously distributed on the wetted surface of the ship structure in water, while the source strength in the classical simple source method represents the source strength generated by monopole sources. The specific process of solving the boundary element method can be found in existing technologies and will not be elaborated upon here.

[0074] Step 4: Based on the virtual source intensity distribution and structural dry modal displacement of the wet surface of the ship structure in water, the acoustoelastic response parameters are calculated. The structural dry modal displacement of the wet surface of the ship structure in water is obtained in advance based on modal analysis. The acoustoelastic response parameters characterize the acoustic field information of the external flow domain of the ship structure in water.

[0075] In one embodiment, the calculated acoustoelastic response parameters include:

[0076] (1) The surface velocity potential of the wet surface of the ship structure in water is calculated based on the virtual source strength distribution, and the generalized additional mass coefficient matrix and the generalized additional damping coefficient matrix are calculated by combining the structural dry modal displacement of the wet surface of the ship structure in water. The generalized additional mass coefficient and the generalized additional damping coefficient are used to characterize the fluid-structure interaction effect.

[0077] Based on the obtained field points on the wetted surface of the ship structure in water The rth order virtual source strength Calculations were performed on any field point on the wetted surface of the ship's structure in water. The r-th order surface velocity potential at the location for:

[0078]

[0079] (2) Substitute the generalized additional mass coefficient matrix and the generalized additional damping coefficient matrix into the acoustic elastic coupling dynamic equation to solve for the principal coordinate response of the ship structure in water.

[0080] The specific method for obtaining the principal coordinate response of a ship structure in water is as follows: based on any field point on the wetted surface of the ship structure in water... The j-th order surface velocity potential φ at the location j (ω) and the r-th order structural dry mode displacement vector u of the wetted surface of the ship structure in water. r The generalized additional mass coefficients of the r-th and j-th mode couplings of the generalized additional mass coefficient matrix A(ω) are calculated respectively. And the generalized additional damping coefficients of the r-th and j-th mode coupling of the generalized additional damping coefficient matrix B(ω) Formula (6) can be used to calculate the field point on the wetted surface of the ship structure in water. Surface velocity potentials at various orders Here This refers to the surface velocity potential at a certain acoustic wave angular frequency ω. By solving for this potential with respect to each acoustic wave angular frequency, we can obtain the surface velocity potential φ(ω) as a function of ω, thus obtaining the j-th order surface velocity potential φ. j (ω).

[0081] Substituting the generalized additional mass coefficient matrix A(ω) and the generalized additional damping coefficient matrix B(ω) into the acoustic-elastic coupling dynamic equation, we obtain the principal coordinate response of the ship structure in water; the acoustic-elastic coupling dynamic equation is:

[0082] {-ω 2 [a+A(ω)]+iω[b+B(ω)]+c}q(ω)=G(ω) (7)

[0083] Where a is the generalized mass coefficient matrix, b is the generalized damping coefficient matrix, c is the generalized stiffness coefficient matrix, and G(ω) is the generalized force column vector. a, b, and c are generalized matrices obtained by calculating the structure's mass, damping, and stiffness matrices using the finite element method based on the orthogonality of the structural dry modal displacement vectors, followed by modal coordinate transformation. G(ω) is obtained by projecting the external loads from the physical space onto the modal space based on the structural dry modal displacement vectors. The specific calculation process for modal analysis can be found in existing technologies. q(ω) is the principal coordinate response column vector and q(ω) = [q1(ω),...,q...]. r (ω),...,q M (ω)] T M is the truncated mode number, [] T denoted as matrix transpose; ρ0 is the fluid medium density; Re{} denotes taking the real part of the complex number; Im{} denotes taking the imaginary part of the complex number; the rows and columns of the generalized additional mass coefficient matrix and the generalized additional damping coefficient matrix correspond to the number of modes of each order. There is a coupling effect between different modes, so the subscripts r and j are used to represent the mode order. r and j are both integer parameters and 1≤r≤M, 1≤j≤M.

[0084] (3) Based on the principal coordinate response and the velocity potential in the external flow domain of the ship structure in the water, the acoustic elastic response parameters are calculated.

[0085] In one embodiment, the acoustoelastic response parameters include radiated sound pressure p(r,ω) and radiated sound power P(ω); based on any r-th order principal coordinate response q r (ω) and the r-th order velocity potential φ at any point r in the external flow domain of the ship structure in the water. r (r), determine the radiated sound pressure at any point r in the external flow domain of the ship structure in the water.

[0086]

[0087] Based on any r-th order principal coordinate response q r The generalized additional damping coefficient matrix B(ω) and the generalized additional damping coefficient B coupled in any r-th and j-th modes are the generalized additional damping coefficient B. rj (ω), determine the radiated acoustic power in the external water domain of the ship structure in water. (·) * This indicates finding the conjugate of a complex number.

[0088] Typical underwater vessel structures include the main structure of underwater vehicles, which is usually spherical in shape, such as the pressure hull of a submersible, using a spherical structure to withstand high external hydrostatic pressure. To verify the effectiveness of the method in this application, a spherical shell model with a unit force acting on its bottom is used as a case study for three-dimensional acoustoelastic calculation and analysis. The main parameters of the model are shown in Table 1. The constructed dry structure and wet surface element mesh of the model are shown in Table 1. Figure 2 As shown, the average size of each grid cell is approximately 0.36m, with a total of 2400 quadrilateral grid cells. The calculation frequency band is 1Hz to 400Hz, with a frequency interval of 1Hz.

[0089] Table 1. Main parameters of the spherical shell model

[0090] spherical shell radius 5 m Shell thickness 0.05 m Structural material density 7860 <![CDATA[kg·m -3 ]]> Young's modulus of elasticity 210 GPa Poisson's ratio 0.3 -- Modal damping ratio 0.01 -- Fluid medium density 1025 <![CDATA[kg·m -3 ]]> Speed ​​of sound in fluid 1500 <![CDATA[m·s -1 ]]>

[0091] For the above spherical shell structure, the theoretical solution for irregular frequencies is obtained using formula (8).

[0092] j n (2πfa / c)=0 (8)

[0093] Where, j n () is the nth-order spherical Bessel function, a is the radius of the spherical shell, c is the speed of sound in the fluid, and f is the frequency.

[0094] The theoretical solutions for the irregular frequencies of the acoustoelastic calculation model of the spherical shell are shown in Table 2.

[0095] Table 2. Theoretical values ​​of irregular frequencies in the acoustoelastic calculation model of the spherical shell.

[0096]

[0097] Figures 3 to 7 Figures (a and b) show the frequency response curves for the added mass coefficient and added damping coefficient for modes 0 through 4. Figure (a) shows the frequency response curve for the added mass coefficient, and Figure (b) shows the frequency response curve for the added damping coefficient. The red dashed line in the figures represents the result obtained using the conventional simple source method for three-dimensional acoustoelastic calculations, while the blue solid line represents the result obtained using the combined potential-based three-dimensional acoustoelastic calculation method proposed in this application. Figures 3 to 7The irregular frequencies corresponding to each mode from 1Hz to 400Hz extracted from the red dashed line are as follows: the irregular frequency corresponding to n=0 is 150.300Hz, the irregular frequency corresponding to n=1 is 215.369Hz, the irregular frequency corresponding to n=2 is 275Hz, the irregular frequency corresponding to n=3 is 334Hz, and the irregular frequency corresponding to n=4 is 391Hz. The calculation results show that the calculated values ​​of the three-dimensional acoustic elasticity are consistent with the theoretical values ​​in Table 2, proving that irregular frequency phenomena do indeed exist at the peaks (valleys) on the curves at these frequency points. The blue solid line in the figure does not contain any peaks (valleys), indicating that the irregular frequency phenomena corresponding to each mode can be completely eliminated using the method of this application, thus confirming the effectiveness of the method of this application.

[0098] The above descriptions are merely preferred embodiments of this application, and this application is not limited to the above embodiments. It is understood that other improvements and variations that can be directly derived or conceived by those skilled in the art without departing from the spirit and concept of this application should be considered to be included within the protection scope of this application.

Claims

1. A three-dimensional acoustoelasticity calculation method based on combined potential, characterized in that, The three-dimensional acoustoelasticity calculation method includes: Based on the potential function theory, the velocity potential in the external flow domain of a ship structure in water is constructed as a linear combination of a single-layer potential and a double-layer potential; the single-layer potential represents the velocity potential generated by a continuously distributed monopole source on the wet surface of the ship structure in water, and the double-layer potential represents the velocity potential generated by a continuously distributed dipole source on the wet surface of the ship structure in water. Based on the velocity potential in the linear combination form, a boundary integral equation is constructed on the wetted surface of the underwater ship structure. The boundary integral equation on the wetted surface of the underwater ship structure is an integral equation about the virtual source strength distribution on the wetted surface of the underwater ship structure. The virtual source strength represents the source strength jointly generated by the continuously distributed monopole and dipole sources on the wetted surface of the underwater ship structure. Based on the fluid-structure interaction boundary conditions on the wetted surface of the underwater ship structure, the boundary integral equation on the wetted surface of the underwater ship structure is solved using the boundary element method to obtain the virtual source strength distribution on the wetted surface of the underwater ship structure. The acoustoelastic response parameters are calculated based on the virtual source intensity distribution and dry modal displacement of the wet surface of the underwater ship structure. The dry modal displacement of the wet surface of the underwater ship structure is obtained in advance based on modal analysis. The acoustoelastic response parameters characterize the acoustic field information of the outer flow domain of the underwater ship structure. Any point in the outer basin of the underwater ship structure The first r First-order velocity potential for: Among them, venues , E It is the outer basin of the waterway for ship structures in the water. It is a venue The first r Single-layer potential, It is a venue The first r Double-layer potential, It is the combination coefficient and , , k It is the sound wave number and , It is the angular frequency of sound waves. c It is the speed at which sound waves propagate in a fluid; Any point in the outer basin of the underwater ship structure The first r Single-layer potential for: Any point in the outer basin of the underwater ship structure The first r Double-layer potential for: in, It is an external basin E The corresponding wetted surface of the ship structure in water, n is the wetted surface of the ship structure in water. The unit outward normal vector, Wet surfaces of ship structures in water The source point on, It is a Green's function term. These are the partial derivatives of the Green's function. It is the source point The r Virtual source strength; The calculated acoustoelastic response parameters include: The surface velocity potential of the wetted surface of the ship structure in water is calculated based on the virtual source strength distribution. Combined with the structural dry modal displacement of the wetted surface of the ship structure in water, the generalized additional mass coefficient matrix and the generalized additional damping coefficient matrix are calculated. The generalized additional mass coefficient and the generalized additional damping coefficient are used to characterize the fluid-structure interaction effect. Substituting the generalized additional mass coefficient matrix and the generalized additional damping coefficient matrix into the acoustic-elastic coupling dynamics equation and solving it, the principal coordinate response of the underwater ship structure is obtained. Based on the principal coordinate response and the velocity potential in the external flow domain of the underwater ship structure, the acoustoelastic response parameters are calculated. The principal coordinate response of the underwater ship structure is obtained as follows: Based on any field point on the wetted surface of the underwater ship structure The first j Surface velocity potential and the wet surface of the underwater ship structure r 1st-order structural dry modal displacement vector The generalized additional mass coefficient matrix was calculated respectively. The r First-order mode and the second-order mode j Generalized additional mass coefficient of first-order modal coupling and the generalized additional damping coefficient matrix The r First-order mode and the second-order mode j Generalized additional damping coefficient of first-order modal coupling ; The generalized additional mass coefficient matrix and the generalized additional damping coefficient matrix Substituting the equations into the acoustic-elastic coupling dynamics equations and solving them, the principal coordinate response of the underwater ship structure is obtained; the acoustic-elastic coupling dynamics equations are: Where a is the generalized mass coefficient matrix, b is the generalized damping coefficient matrix, and c is the generalized stiffness coefficient matrix. It is a generalized force column vector. It is the principal coordinate response column vector and M is the truncated mode number. Indicates matrix transpose; It represents the density of the fluid medium, Re{} denotes taking the real part of the complex number, and Im{} denotes taking the imaginary part of the complex number. r , j All are integer parameters and , .

2. The three-dimensional acoustoelasticity calculation method according to claim 1, characterized in that, The boundary integral equations for the wetted surface of the underwater ship structure include: Based on the boundary limit properties of potential function theory, the outward normal direction derivative of the velocity potential in the linear combination form is obtained, and the field point in the external flow domain of the ship structure in water is... When approaching the wetted surface of the ship structure in water, the boundary integral equation on the wetted surface of the ship structure in water is obtained; the boundary limit property indicates that the normal derivative of the single-layer potential has a step characteristic at the boundary.

3. The three-dimensional acoustoelasticity calculation method according to claim 2, characterized in that, The boundary integral equation on the wetted surface of the underwater ship structure is: Among them, venues , It is any point on the wetted surface of the ship structure. The first r First-order velocity potential, It is a step term generated by the boundary step property of the normal derivative of a single-layer potential. It is a venue The r Virtual source strength.

4. The three-dimensional acoustoelasticity calculation method according to claim 1, characterized in that, Based on any field point on the wetted surface of the underwater ship structure The r Virtual source strength The field point on the wetted surface of the ship structure in the water was calculated. The first r Surface velocity potential for: 。 5. The three-dimensional acoustoelasticity calculation method according to claim 1, characterized in that, The acoustic elastic response parameters include radiated sound pressure. and radiated sound power ; According to any number r First-order principal coordinate response and any point in the external flow domain of the aforementioned underwater ship structure The first r First-order velocity potential Determine any point in the external flow domain of the underwater ship structure. Radiated sound pressure at the location ; According to any number r First-order principal coordinate response and the generalized additional damping coefficient matrix In any number r First-order mode and the second-order mode j Generalized additional damping coefficient of first-order modal coupling Determine the radiated acoustic power in the outer water domain of the underwater ship structure. , This indicates finding the conjugate of a complex number.

6. The three-dimensional acoustoelasticity calculation method according to claim 1, characterized in that, Based on the fact that the outward normal derivative of the velocity potential on the wetted surface of the underwater ship structure is equal to the outward normal velocity of the dry modal displacement of the structure, the fluid-structure interaction boundary conditions on the wetted surface of the underwater ship structure are determined as follows: ,in, Wet surfaces of ship structures in water The r The dry modal displacement vector of the structure, where n is the wetted surface of the ship structure in water. The unit outward normal vector, , It is the angular frequency of sound waves.

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