CN113111603B - Double-floating-body platform wave excitation force and motion response forecasting method - Google Patents

Double-floating-body platform wave excitation force and motion response forecasting method Download PDF

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CN113111603B
CN113111603B CN202110370295.1A CN202110370295A CN113111603B CN 113111603 B CN113111603 B CN 113111603B CN 202110370295 A CN202110370295 A CN 202110370295A CN 113111603 B CN113111603 B CN 113111603B
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郑雄波
姬铭泽
李晓乐
闫涵
周双红
张晓威
朱智伟
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Abstract

The invention belongs to the technical field of motion response forecasting of multi-floating-body marine structures, and particularly relates to a double-floating-body platform wave excitation force and motion response forecasting method. The invention constructs a new Green function, and the green function introduces a wave adjustment factor, thereby increasing the sensitivity of the function to waves and improving the accuracy of the algorithm. The invention applies a new Green function to the boundary integral equation, forms a new fast multipole boundary element method by discrete processing of the boundary integral equation and combining with the fast multipole technology, thereby improving the application range of the ocean structure in the potential flow problem and improving the calculation efficiency. Compared with the traditional boundary element method, the method is sensitive to waves, high in calculation accuracy and high in speed, can be used for efficiently and accurately calculating the hydrodynamic coefficient of the multi-floating-body offshore structure, and has great advantages in the aspect of hydrodynamic calculation of large-scale offshore structures.

Description

Double-floating-body platform wave excitation force and motion response forecasting method
Technical Field
The invention belongs to the technical field of motion response forecasting of a multi-floating-body ocean structure, and particularly relates to a method for forecasting wave excitation force and motion response of a double-floating-body platform.
Background
In the existing numerical method, the Boundary Element Method (BEM) has obvious advantages compared with other numerical algorithms, and after the Green function is selected, the boundary element method transfers the solution of the whole domain to the boundary, so that the grid division and the unknown quantity setting are only needed to be carried out on the surface of the ocean structure, the calculation storage quantity and the calculation time are reduced, and the preparation in the early stage is relatively less. The conventional boundary element method has many advantages, but after the Boundary Integral Equation (BIE) is discretized, the coefficient matrix of the linear equation system is generated, so that the solution of the equation system needs a large amount of calculation time and calculation amount, and the calculation amount is increased by the square magnitude of the unknown number. When the unknown quantity is small, the calculation efficiency of BEM is high. However, for large ocean structures, the number of boundary elements is very large, the calculation amount and the storage space are multiplied, the capacity requirement on a computer is increased, and the advantages of the boundary element method cannot be fully utilized.
The method is characterized in that a plurality of unknown units are needed when the boundary element method is applied to hydrodynamic calculation of the multi-floating-body marine structure, and in order to overcome the defect that the conventional boundary element method is used for hydrodynamic calculation of a large marine structure, a fast multipole technique is applied to the boundary element method, namely the fast multipole boundary element method, so that the hydrodynamic problem of the multi-floating-body marine structure is solved, and the calculation storage amount is reduced on the basis of improving the efficiency.
When the boundary element method is used for analyzing the hydrodynamic performance of the marine structure, the number of unknown quantities is gradually increased along with the increase of the size of the structure, so that the memory and the calculated quantity required by the method for numerical calculation are greatly increased, and the advantage of the boundary element method for the numerical calculation of the structure is offset. The fast multipole technique can solve the calculation problem of the interaction between a large number of particles, effectively combines the fast multipole technique with a boundary element method to solve the engineering problem of large-scale structures, and fully improves the calculation efficiency.
Through search, the invention patent document with publication number CN109344531A discloses a three-dimensional frequency domain numerical method for forecasting the wave-floating load of a multi-floating-body structure, which is characterized in that: reading a grid file, and calculating the ship hydrostatic force by utilizing grid information; calculating an influence coefficient matrix of the simple Green function; calculating an influence coefficient matrix of a complex frequency domain Green function; solving each unit radiation velocity potential by using a Taylor expansion boundary element method; solving hydrodynamic coefficients of all monomers of the multi-floating-body structure; solving a motion equation of the multiple floating bodies; and solving the whole multi-floating-body structure and the wave force and the wave load of each single body. The invention relates to a numerical calculation method of a multi-floating-body marine structure based on a green function which is improved to meet the boundary condition of a free surface, which is different from a numerical calculation method for forecasting the multi-floating-body structure disclosed in an invention patent document with publication number CN109344531A in the following points:
1. the difference in green functions. The green functions disclosed in the invention patent document with publication number CN109344531A are simple green functions and complex frequency domain green functions, respectively. The Green function adopted by the invention not only meets the boundary condition of the free surface, but also increases the wave adjustment factor. By adopting the Green function, the sensitivity of the algorithm to waves is increased, and the accuracy of the algorithm is improved.
2. The boundary elements are computed differently. The multi-floating-body hydrodynamic coefficient solving method disclosed in the invention patent document with publication number CN109344531A applies the taylor expansion boundary element method to solve. The method adopted by the invention is a rapid multipole boundary element method combining a rapid multipole technology and a boundary element. The fast multipole boundary element method combining the improved free surface Green function improves the calculation efficiency and is convenient for the calculation of large-scale marine structures and multi-floating-body marine structures.
Disclosure of Invention
The invention aims to provide a method for forecasting wave excitation force and motion response of a double-floating-body platform.
The purpose of the invention is realized by the following technical scheme: the method comprises the following steps:
step 1: inputting a double-floating-body platform to be forecasted and a motion state j thereof, and acquiring an integral boundary region S of the double-floating-body platform0Boundary region S of first floating bodybAAnd a boundary region S of the second floating bodybB(ii) a Inputting environmental parameters including wave frequency omega and wave height H; wherein, j ═ {1,2,3,4,5,6} represents respectively the states of motion of rolling, surging, heaving, rolling, pitching, and yawing;
and 2, step: calculating the solution p of the boundary integral equation which satisfies the speed potential when the double-floating-body platform is in the jth motion statej、qj；
The boundary integral equation about the velocity potential is:
Figure BDA0003009010530000021
wherein p isj、qjIs an integral boundary region S of the double-floating-body platform0Two points of (a) point pjHas the coordinates of (x)1j,y1j,z1j) Point q ofjHas the coordinates of (x)2j,y2j,z2j)；α(qj) Represents point qjThe boundary smoothness of (a);
Figure BDA0003009010530000022
representing the Green function G (p)j,qj) About point pjPartial derivative in the vertical direction; phi () is the velocity potential;
Figure BDA0003009010530000023
represents point qjVelocity potential phi (q)j) About point qjPartial derivatives in the vertical direction;
green function G (p)j,qj) The expression of (a) is:
Figure BDA0003009010530000024
wherein f iskIs a wave regulatory factor; h. lambda and mu are constants;
Figure BDA0003009010530000025
Figure BDA0003009010530000026
J0() Is a Bessel function;
the expression for the velocity potential φ () is:
φ(x,y,z)＝Re[φI(x,y,z)e-iωt+φD(x,y,z)e-iωt+φR(x,y,z)e-iωt]
wherein phiI(x, y, z) denotes the incident potential,. phi.,D(x, y, z) represents the diffraction potential,. phiR(x, y, z) represents a radiation potential;
and step 3: calculating a hydrodynamic coefficient of the double-floating-body platform in a j-th motion state;
Figure BDA0003009010530000031
Figure BDA0003009010530000032
Figure BDA0003009010530000033
Figure BDA0003009010530000034
wherein k isAjThe motion direction of the first floating body is the motion direction of the double-floating-body platform in the motion state j; k is a radical of formulaBjThe moving direction of the second floating body when the double-floating-body platform is in a moving state j;
and 4, step 4: calculating the predicted value f of the wave excitation force received by the first floating body of the double-floating-body platformexAThe predicted value f of the wave excitation force on the second floating bodyexB；
Figure BDA0003009010530000035
Figure BDA0003009010530000036
And 5: calculating the predictive value RAO of the first float motion response of a dual float platformAThe predicted value RAO of the motion response of the second floating bodyB；
Figure BDA0003009010530000037
Figure BDA0003009010530000038
ξAAnd xiBSolving according to the motion equation to obtain:
(-ω2(MAj+aAA)-iωbAA+CA)ξA+(-ω2aAB-iωbAB)ξB＝fexA+FLAj
(-ω2aBA-iωbBA)ξA+(-ω2(MBj+aBB)-iωbBB+CB)ξB＝fexB+FLBj
wherein, MAjThe mass of the first floating body is the mass of the double-floating-body platform in the motion state j; mBjThe mass of the second floating body when the double-floating-body platform is in the motion state j; cAIs the hydrostatic restoring force of the first floating body; cBIs the hydrostatic restoring force of the second floating body; when j is {1,2,3}, namely the double-floating-body platform is in a swaying, surging or heaving motion state, FLAjRepresenting the force of the connection means between the first and second float on the first float, FLBjRepresenting the acting force of the connecting device between the first floating body and the second floating body on the second floating body; when j ═ 4,5,6, i.e. the dual buoyant platform is in roll, pitch or yaw motion, FLAjRepresents the moment of action of the connection device between the first float and the second float on the first float, FLBjThe moment of action of a connecting device between the first floating body and the second floating body on the second floating body is represented; fLAjAnd FLBjEqual in size and opposite in direction.
The invention has the beneficial effects that:
the invention constructs a new green function, and the green function introduces a wave adjustment factor, thereby increasing the sensitivity of the function to waves and improving the accuracy of the algorithm. The invention applies a new Green function to the boundary integral equation, forms a new fast multipole boundary element method by discrete processing of the boundary integral equation and combining with the fast multipole technology, thereby improving the application range of the ocean structure in the potential flow problem and improving the calculation efficiency. Compared with the traditional boundary element method, the method is sensitive to waves, high in calculation accuracy and high in speed, can be used for efficiently and accurately calculating the hydrodynamic coefficient of the multi-floating-body offshore structure, and has great advantages in the aspect of hydrodynamic calculation of large-scale offshore structures.
Drawings
Fig. 1 is a diagram showing the variation of the storage capacity of the fast multipole boundary element method and the boundary element method.
Fig. 2 is a diagram of the change of the fast multipole boundary element method and the calculation time of the boundary element method.
Fig. 3 is a graph comparing radiation damping.
Fig. 4 is an additional mass comparison graph.
Fig. 5 is a graph of the effect of geometry on wave excitation force.
FIG. 6 is a graph of the effect of geometry on capture width ratio.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The invention relates to numerical calculation of a multi-floating-body marine structure and a large marine structure, and belongs to the field of calculation method analysis of a potential flow theory.
The invention provides a method for forecasting wave excitation force and motion response of a double-floating-body platform, which solves the numerical problem of calculation of three-dimensional frequency domain hydrodynamic performance with wave sensitivity. The method is sensitive to waves, high in calculation accuracy and high in speed, and has great advantages in the aspect of hydrodynamic calculation of large ocean structures compared with the traditional boundary element method.
A method for forecasting the wave excitation force and motion response of a double-floating-body platform comprises the following steps:
step 1: inputting a double-floating-body platform to be forecasted and a motion state j thereof, and acquiring an integral boundary region S of the double-floating-body platform0Boundary region S of the first floating bodybAAnd a boundary region S of the second floating bodybB(ii) a Inputting environmental parameters including wave frequency omega and wave height H; wherein, j ═ {1,2,3,4,5,6} represents respectively the states of motion of rolling, surging, heaving, rolling, pitching, and yawing;
and 2, step: calculating the solution p of the boundary integral equation which satisfies the velocity potential when the double-floating-body platform is in the j motion statej、qj；
The boundary integral equation about the velocity potential is:
Figure BDA0003009010530000051
wherein p isj、qjIs an integral boundary region S of the double-floating-body platform0Two of (2)Point, point pjHas the coordinates of (x)1j,y1j,z1j) Point q ofjHas the coordinates of (x)2j,y2j,z2j)；α(qj) Represents point qjThe boundary smoothness of (a);
Figure BDA0003009010530000052
representing the Green function G (p)j,qj) About point pjPartial derivatives in the vertical direction; phi () is the velocity potential;
Figure BDA0003009010530000053
representing point qjVelocity potential phi (q)j) About point qjPartial derivatives in the vertical direction;
green function G (p)j,qj) The expression of (a) is:
Figure BDA0003009010530000054
wherein f iskIs a wave regulatory factor; h. lambda and mu are constants;
Figure BDA0003009010530000055
Figure BDA0003009010530000056
J0() Is a Bessel function;
the expression for the velocity potential φ () is:
φ(x,y,z)＝Re[φI(x,y,z)e-iωt+φD(x,y,z)e-iωt+φR(x,y,z)e-iωt]
wherein phi isI(x, y, z) denotes the incident potential,. phi.,D(x, y, z) represents the diffraction potential,. phiR(x, y, z) represents the radiation potential;
and step 3: calculating the hydrodynamic coefficient of the double-floating-body platform in the jth motion state;
Figure BDA0003009010530000061
Figure BDA0003009010530000062
Figure BDA0003009010530000063
Figure BDA0003009010530000064
wherein k isAjThe motion direction of the first floating body is the motion direction of the double-floating-body platform in the motion state j; k is a radical ofBjThe motion direction of the second floating body is the motion direction of the double floating body platform in the motion state j;
and 4, step 4: calculating the predicted value f of the wave excitation force received by the first floating body of the double-floating-body platformexAThe predicted value f of the wave excitation force on the second floating bodyexB；
Figure BDA0003009010530000065
Figure BDA0003009010530000066
And 5: calculating a predicted value RAO of a first float motion response of a dual float platformAThe predicted value RAO of the motion response of the second floating bodyB；
Figure BDA0003009010530000067
Figure BDA0003009010530000068
ξAAnd xiBSolving according to the motion equation to obtain:
(-ω2(MAj+aAA)-iωbAA+CA)ξA+(-ω2aAB-iωbAB)ξB＝fexA+FLAj
(-ω2aBA-iωbBA)ξA+(-ω2(MBj+aBB)-iωbBB+CB)ξB＝fexB+FLBj
wherein M isAjWhen the double-floating-body platform is in a motion state j, the mass of the first floating body is the mass of the object; mBjThe mass of the second floating body when the double-floating-body platform is in the motion state j; cAIs the hydrostatic restoring force of the first floating body; cBIs the hydrostatic restoring force of the second floating body; when j is {1,2,3}, namely the double-floating-body platform is in a swaying, surging or heaving motion state, FLAjRepresenting the force of the connection means between the first and second float on the first float, FLBjRepresenting the acting force of the connecting device between the first floating body and the second floating body on the second floating body; when j is {4,5,6}, namely the double-floater platform is in a rolling, pitching or yawing motion state, FLAjRepresenting the moment of action of the connection means between the first and second float on the first float, FLBjRepresenting the moment of action of the connecting device between the first floating body and the second floating body on the second floating body; fLAjAnd FLBjEqual in size and opposite in direction.
The Green function used by the invention not only meets the boundary condition of the free surface, but also adds the wave regulating factor f taking wave number as variablekThe sensitivity to waves is increased. The expression of a new green's function used in the present invention is:
Figure BDA0003009010530000071
wherein the wave number is a linear function fkThe wave number linear function medium wave can be applied to wave characteristics under different periodsThe wave adjustment factor is adjusted so that it meets different wave characteristics.
The invention specifically comprises the following five steps:
[1] reading the grid file after the multi-floating-body boundary is dispersed, and calculating a boundary integral equation by utilizing a multipole technology;
[2] expanding a Green function containing wave regulating factors with wave numbers as variables in the dispersed boundary integral into a product of a source point and a field point;
[3] performing multipole moment and multipole expansion calculation on the Green function containing the wave number linear function through the expanded harmonic function;
[4] dividing the dispersed source points and the field points into a near field and a far field according to the distribution of the dispersed source points and the field points, directly calculating the near field by adopting a traditional boundary element method, calculating the far field by adopting a new fast multipole technology, and finally adding the near field part and the far field part to obtain a velocity potential;
[5] and obtaining the hydrodynamic coefficient of the multiple floating bodies according to the speed potential calculation result, and analyzing the hydrodynamic performance.
The invention establishes a new Green function, the wave adjustment factor is introduced into the function, the sensitivity of the function to waves is increased, and the accuracy of the algorithm is improved. The invention applies a new Green function to a boundary integral equation, forms a new fast multipole boundary element method by discrete processing of the boundary integral equation and combining with a fast multipole technology. Therefore, the application range of the ocean structure in the potential flow problem is improved, and the calculation efficiency is improved. The method provided by the invention can be used for efficiently and accurately calculating the hydrodynamic coefficient of the multi-floating-body offshore structure, and provides an accurate calculation basis for the design of the device.
Assuming that the fluid is an ideal fluid without viscosity, rotation and compressibility, the fluid velocity potential phi in the flow field satisfies the Laplace equation
Figure BDA0003009010530000072
For two second-order continuous differentiable functions phi and G in an arbitrary space omega, the Green's equation holds
Figure BDA0003009010530000073
The green formula needs to satisfy the following conditions: free noodle
Figure BDA0003009010530000081
Remote conditions
Figure BDA0003009010530000082
Bottom conditions
Figure BDA0003009010530000083
The boundary integral equation with respect to the velocity potential can thus be expressed as
Figure BDA0003009010530000084
Where the velocity potential is Φ (x, y, z) ═ Re (Φ (x, y, z) e-iωt)＝Re[φI(x,y,z)e-iωt+φD(x,y,z)e-iωt+φR(x,y,z)e-iωt]
Wherein phiI(x, y, z) denotes the incident potential,. phi.,D(x, y, z) represents the diffraction potential,. phiRAnd (x, y and z) represent radiation potential, and the diffraction potential and the radiation potential in the velocity potential can be respectively solved according to a control equation and different object plane conditions.
Aiming at a multi-body boundary equation, an interpolation function of eight points is introduced, the coefficient is calculated by applying Gaussian integral, a whole coordinate system is converted into a local coordinate system, and a discrete boundary integral equation is obtained by quadratic discretization
Figure BDA0003009010530000085
Figure BDA0003009010530000086
Figure BDA0003009010530000087
Figure BDA0003009010530000088
…
In the formula ui *、ui *′、ui *″、ui *"'indicates the function of green' in a green,
Figure BDA0003009010530000089
is the normal partial derivative of the green function.
Solving the discrete boundary integral equation by combining a boundary element method and a fast multipole technology, wherein the far field part is calculated by the fast multipole technology, and the near field part is calculated by the boundary element method. Firstly, numbering and hierarchically dividing the dispersed points to form a tree structure; secondly, expanding a Greens function containing wave number as a variable adjusting factor into a product form of a source point and a field point; and finally, calculating local expansion coefficients and multipole moment of momentum of the improved Green function meeting the free surface by three multipole expansion methods of M2M, M2L and L2L.
∫SG(x,y)q(x)dS(x)＝∫S_nearG(x,y)q(x)dS(x)+∫S_farG(x,y)q(x)dS(x)
According to the speed potential calculating method, the hydrodynamic coefficient generated by the multiple floating bodies when the multiple floating bodies move, namely the hydrodynamic coefficient influenced by other floating bodies on the multiple floating bodies can be obtained.
Figure BDA0003009010530000091
Figure BDA0003009010530000092
Figure BDA0003009010530000093
Figure BDA0003009010530000094
aAA、bAA、aBBAnd bBBExpressed as the coefficient of the water power generated by the floating body when moving, aAB、bAB、aBAAnd bBARepresenting the hydrodynamic coefficient of influence under the action of other floats.
The wave excitation force and the motion response are expressed as the following four expressions.
Wave excitation force:
Figure BDA0003009010530000095
Figure BDA0003009010530000096
motion response:
Figure BDA0003009010530000097
ξAthe following can be obtained according to the motion equation:
(-ω2(MAj+aAA)-iωbAA+CA)ξA+(-ω2aAB-iωbAB)ξB＝fexA+FLAj
(-ω2aBA-iωbBA)ξA+(-ω2(MBj+aBB)-iωbBB+CB)ξB＝fexB+FLBj
wherein, MAjWhen the double-floating-body platform is in a motion state j, the mass of the first floating body is the mass of the object; mBjThe mass of the second floating body when the double-floating-body platform is in the motion state j; cAIs the hydrostatic restoring force of the first floating body; cBThe hydrostatic restoring force of the second floating body; when j is {1,2,3}That is, when the double-floating-body platform is in a state of swaying, surging or heaving motion, FLAjRepresenting the force of the connection means between the first and second float on the first float, FLBjRepresenting the acting force of the connecting device between the first floating body and the second floating body on the second floating body; when j is {4,5,6}, namely the double-floater platform is in a rolling, pitching or yawing motion state, FLAjRepresenting the moment of action of the connection means between the first and second float on the first float, FLBjThe moment of action of a connecting device between the first floating body and the second floating body on the second floating body is represented; fLAjAnd FLBjF of equal size, opposite direction, different connection formsLThe expressions differ, for a hinged or a sliding slot connection, if the movement of the object in a certain direction cannot be limited, the term is zero.
As shown in FIG. 1, the numerical calculation method of the present invention is characterized by a smaller calculation amount compared with the calculation memory amount of the boundary element method. The storage capacity of the two methods is in an ascending trend along with the increase of the number of the unknown quantities, the rising speed of the traditional boundary element method is higher, the required storage capacity is larger, and when the number of the unknown quantities is larger and larger, the storage capacity of the numerical value calculation method is smaller than that of the traditional boundary element calculation, so that the advantage of reducing the calculation storage capacity is fully verified. The three-dimensional frequency domain hydrodynamic numerical method for calculating the wave sensitivity reduces the requirement on calculation capacity.
As shown in fig. 2, the computation time for both methods is increasing as the unknown is gradually increased. When the number of the unknown quantity is less than 4000, the calculation time of the boundary element method is shorter, the efficiency is higher, and when the number of the unknown quantity is higher than 4000, the calculation time of the traditional boundary element is far higher than that of FMM-BEM, so that the FMM-BEM is more suitable for a large-scale physical model with multiple floating bodies and multiple unknown quantities.
As shown in fig. 3 and 4, the calculation result of the three-dimensional frequency domain hydrodynamic numerical method with wave sensitivity provided by the present invention is compared with the calculation result of the conventional boundary element method, and the errors of the calculation results of the two methods for calculating the additional mass and the radiation damping are small, thereby fully verifying the accuracy of the numerical calculation method.
As shown in fig. 5 and fig. 6, by analyzing the hydrodynamic performance of the floaters with different geometric configurations by applying the high efficiency and accuracy of the invention patent, the peak value and the width bandwidth of the conical-bottom cylindrical floater calculated by the invention patent are both larger than those of the other two floaters, so that the FMM-BEM provides an effective method for hydrodynamic numerical analysis.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (1)

1. A method for forecasting wave excitation force and motion response of a double-floating-body platform is characterized by comprising the following steps:
step 1: inputting a double-floating-body platform to be predicted and a motion state j thereof, and acquiring an integral boundary region S of the double-floating-body platform0Boundary region S of first floating bodybAAnd a boundary region S of the second floating bodybB(ii) a Inputting environmental parameters including wave frequency omega and wave height H; wherein j ═ {1,2,3,4,5,6} represents the motion state of swaying, surging, heaving, rolling, pitching, and yawing, respectively;
step 2: calculating the solution p of the boundary integral equation which satisfies the velocity potential when the double-floating-body platform is in the j motion statej、qj；
The boundary integral equation about the velocity potential is as follows:
Figure FDA0003009010520000011
wherein p isj、qjIs an integral boundary region S of the double-floating-body platform0Two points of (1), point pjHas the coordinates of (x)1j,y1j,z1j) Point q ofjHas the coordinates of (x)2j,y2j,z2j)；α(qj) Represents point qjThe boundary smoothness of (1);
Figure FDA0003009010520000012
representing the Green function G (p)j,qj) About point pjPartial derivatives in the vertical direction; phi () is a velocity potential;
Figure FDA0003009010520000013
representing point qjVelocity potential phi (q)j) About point qjPartial derivative in the vertical direction;
green function G (p)j,qj) The expression of (a) is:
Figure FDA0003009010520000014
wherein f iskIs a wave regulatory factor; h. λ and μ are constants;
Figure FDA0003009010520000015
Figure FDA0003009010520000016
J0() Is a Bessel function;
the expression for the velocity potential φ () is:
φ(x,y,z)＝Re[φI(x,y,z)e-iωt+φD(x,y,z)e-iωt+φR(x,y,z)e-iωt]
wherein phi isI(x, y, z) represents the incident potential,. phi.,D(x, y, z) represents the diffraction potential,. phiR(x, y, z) represents the radiation potential;
and step 3: calculating a hydrodynamic coefficient of the double-floating-body platform in a j-th motion state;
Figure FDA0003009010520000021
Figure FDA0003009010520000022
Figure FDA0003009010520000023
Figure FDA0003009010520000024
wherein k isAjThe moving direction of the first floating body is the moving direction of the double-floating-body platform in the moving state j; k is a radical of formulaBjThe motion direction of the second floating body is the motion direction of the double floating body platform in the motion state j;
and 4, step 4: calculating the predicted value f of the wave excitation force received by the first floating body of the double-floating-body platformexAThe predicted value f of the wave excitation force to which the second floating body is subjectedexB；
Figure FDA0003009010520000025
Figure FDA0003009010520000026
And 5: calculating the predictive value RAO of the first float motion response of a dual float platformAThe predicted value RAO of the motion response of the second floating bodyB；
Figure FDA0003009010520000027
Figure FDA0003009010520000028
ξAAnd xiBSolving according to the motion equation to obtain:
(-ω2(MAj+aAA)-iωbAA+CA)ξA+(-ω2aAB-iωbAB)ξB＝fexA+FLAj
(-ω2aBA-iωbBA)ξA+(-ω2(MBj+aBB)-iωbBB+CB)ξB＝fexB+FLBj
wherein M isAjThe mass of the first floating body is the mass of the double-floating-body platform in the motion state j; m is a group ofBjThe mass of the second floating body when the double-floating-body platform is in the motion state j; cAIs the hydrostatic restoring force of the first floating body; cBIs the hydrostatic restoring force of the second floating body; when j is {1,2,3}, i.e., the dual-float platform is in a state of sway, surge or heave motion, FLAjRepresenting the force of the connection means between the first and second float on the first float, FLBjRepresenting the acting force of the connecting device between the first floating body and the second floating body on the second floating body; when j is {4,5,6}, namely the double-floater platform is in a rolling, pitching or yawing motion state, FLAjRepresenting the moment of action of the connection means between the first and second float on the first float, FLBjThe moment of action of a connecting device between the first floating body and the second floating body on the second floating body is represented; fLAjAnd FLBjEqual in size and opposite in direction.
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Publication number Priority date Publication date Assignee Title
CN114880619B (en) * 2022-05-10 2023-10-27 中国海洋大学 Floating ocean structure random dynamic response analysis and calculation method
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Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2009042043A (en) * 2007-08-08 2009-02-26 Shimizu Corp Sound field analyzer
CN109325309A (en) * 2018-10-23 2019-02-12 哈尔滨工程大学 The Three-dimensional Numerical Simulation Method of ship large-amplitude roll movement
CN109344531A (en) * 2018-10-23 2019-02-15 哈尔滨工程大学 Forecast the three-dimensional frequency domain value method of more float structure object wave drift load
CN109472065A (en) * 2018-10-23 2019-03-15 哈尔滨工程大学 Forecast the three-dimensional numerical method of Low Speed Full Ships Added Resistance under severe sea condition
CN109657257A (en) * 2017-10-12 2019-04-19 中国船舶重工集团公司第七六研究所 Labyrinth radiated sound field calculation method in a kind of ocean acoustic channel
CN112182995A (en) * 2020-10-27 2021-01-05 中国海洋大学 Viscous potential flow theory analysis method

Family Cites Families (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2008032646A1 (en) * 2006-09-12 2008-03-20 Osaka University Numerical simulation device of time dependent schrodinger equation
CN109446634B (en) * 2018-10-23 2022-07-15 哈尔滨工程大学 Ship motion forecasting method based on Taylor expansion boundary element method
CN110532685B (en) * 2019-08-29 2023-02-07 山东交通学院 Response forecasting method for floating structure swaying motion

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2009042043A (en) * 2007-08-08 2009-02-26 Shimizu Corp Sound field analyzer
CN109657257A (en) * 2017-10-12 2019-04-19 中国船舶重工集团公司第七六研究所 Labyrinth radiated sound field calculation method in a kind of ocean acoustic channel
CN109325309A (en) * 2018-10-23 2019-02-12 哈尔滨工程大学 The Three-dimensional Numerical Simulation Method of ship large-amplitude roll movement
CN109344531A (en) * 2018-10-23 2019-02-15 哈尔滨工程大学 Forecast the three-dimensional frequency domain value method of more float structure object wave drift load
CN109472065A (en) * 2018-10-23 2019-03-15 哈尔滨工程大学 Forecast the three-dimensional numerical method of Low Speed Full Ships Added Resistance under severe sea condition
CN112182995A (en) * 2020-10-27 2021-01-05 中国海洋大学 Viscous potential flow theory analysis method

Non-Patent Citations (7)

* Cited by examiner, † Cited by third party
Title
Microwave Signatures of Snow Cover Using Numerical Maxwell Equations Based on Discrete Dipole Approximation in Bicontinuous Media and Half-Space Dyadic Green"s Function;Shurun Tan等;《 IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing》;20170602;第10卷(第11期);4686-4702 *
Wave Loading on a Group of Cylinders in Fairly Perfect Fluid;Lin Cui等;《 Journal of Coastal Research》;20200706;第103卷;288–292 *
基于三维辐射能量法的船舶波浪增阻计算分析;洪亮等;《船舶力学》;20180731;第22卷(第7期);807-817 *
基于改进自由面格林函数的FMM-BEM算法研究;姬铭泽;《中国优秀博硕士学位论文全文数据库(硕士)基础科学辑》;20220315(第3期);A010-207 *
岛礁环境下的波浪运动研究;陈彧超;《中国优秀博硕士学位论文全文数据库(硕士)工程科技Ⅱ辑》;20160315(第3期);C034-882 *
气泡上浮碰撞油滴过程的格子Boltzmann方法模拟及实验研究;陈航宇;《中国优秀博硕士学位论文全文数据库(硕士)工程科技Ⅰ辑》;20200115(第1期);B027-1717 *
波浪与浮体相互作用的边界元法研究;刘梦超;《中国优秀博硕士学位论文全文数据库(硕士)基础科学辑》;20190915(第9期);A010-28 *

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