CN104850688A - Method for determining elastic ship body load responding model in irregular wave - Google Patents
Method for determining elastic ship body load responding model in irregular wave Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 42
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- 239000012530 fluid Substances 0.000 claims abstract description 15
- 238000013016 damping Methods 0.000 claims abstract description 11
- 239000011159 matrix material Substances 0.000 claims description 38
- 238000006073 displacement reaction Methods 0.000 claims description 17
- 230000004044 response Effects 0.000 claims description 15
- 230000002706 hydrostatic effect Effects 0.000 claims description 11
- 238000005452 bending Methods 0.000 claims description 9
- 238000010008 shearing Methods 0.000 claims description 6
- 230000001133 acceleration Effects 0.000 claims description 3
- 230000002238 attenuated effect Effects 0.000 claims description 3
- 230000005484 gravity Effects 0.000 claims description 3
- 230000002194 synthesizing effect Effects 0.000 claims description 3
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Abstract
The present invention relates to a method for determining an elastic ship body load responding model in an irregular wave. The method comprises the following steps: truncating an integrating range of a ship body time domain delay function at a truncating frequency omega-hat of a high-frequency fluid damping coefficient B(omega) during the determination of the time domain delay function considering the ship body elastic effect and dividing the whole integrating range into two parts (0,omega-hat) and (omega-hat, infinity); dividing the range (0,omega-hat) into a limited number of small ranges, and performing integration in the range to obtain the damping coefficient B(omega) of the range; selecting an exponential decay function for simulating the damping coefficient B( omega) in the range (omega-hat, infinity) so as to obtain an infinite limit integral K<rk>(t) of the ship body time domain delay function. By virtue of the method, the influence on the truncating errors can be eliminated; and the defect of high requirement on hardware because of large calculation quantity of the method in the current method can be solved.
Description
Technical Field
The invention relates to the field of hydrodynamic force of wave load technology of ships and ocean engineering, in particular to a method for determining a response model of elastic hull load in irregular waves.
Background
As is known, the actual sea waves are irregular waves and are formed by stacking a plurality of regular wavelets with different amplitudes and frequencies, so that the influence of different wave frequencies on the result must be considered for predicting the load response under random sea waves. However, most of the traditional load response prediction of the irregular wave only considers the single frequency of the wave main peak, or belongs to a two-dimensional problem, and the influence of the time-varying characteristics of physical quantities such as the amplitude and the frequency of the irregular wave on the result cannot be considered, so that the accuracy of the hull response prediction result in the irregular wave is greatly reduced.
At present, in order to solve the problem, a time domain delay function is generally adopted in the prior art to further account for the influence of different wave frequency components on the result.
However, the … … method in the prior art still has the following problems: 1. for the determination of the high-frequency hydrodynamic coefficient, a global integration method is often adopted, and the problem of high hardware requirement due to overlarge calculated amount can occur; 2. determining the hydrodynamic coefficient of the high frequency by means of a cut-off frequency for increased efficiency makes it difficult to achieve a high degree of accuracy due to the cut-off.
With the increasing of the main dimension of the ship, the coupling effect of the elastic deformation of the structure and the fluid is more obvious, so that the requirement for determining the load response of the elastic ship body under random sea waves in the prior art is more obvious. Therefore, it is necessary to provide a new method for determining a load response model that can take into account the elastic effect of the hull.
Disclosure of Invention
The invention aims to overcome the defects of the existing method and provide a method for determining a load response model of an elastic ship body in irregular waves, so that the load response of the ship body under random sea waves can be determined quickly and accurately, and the requirement on a hardware system is reduced.
In order to solve the above problems, according to an aspect of the present invention, there is provided a method for determining a model of response to loads of an elastic hull in irregular waves, comprising the steps of:
step one, determining an equation hull nonlinear time domain motion equation
Constructing nonlinear time domain motion equation of ship body
In formula (1): [ a ] A],[b],[c]-a structural generalized mass matrix, a generalized damping matrix, a generalized stiffness matrix; [ C ]]-a generalized fluid restoring force coefficient matrix;representing the density of the hull; g-gravitational acceleration;-an object plane normal vector; s (t) -a transient object plane;-representing a displacement vector resulting from an r-th order free motion mode of the resilient hull structure; w is ak-vertical displacement of the hull in the k-th mode; [ mu ] of]-a generalized fluid additional mass matrix when the frequency tends to infinity; [ K (τ)]The time-domain delay function matrix of the system, which depends on the geometry and the time interval of the hull, represents the damping characteristics and hydrodynamic inertia of the waves; fI(t)、FD(t) -incident wave force and diffraction wave force received by the ship body; fslam(t) -the slamming force experienced by the hull; p is a radical ofr(t) -the hull's primary r-th coordinate;
step two, solving a generalized fluid restoring force coefficient matrix
By means of three-dimensional hull instantaneous grid interception, the hydrostatic restoring force is directly calculated by adopting a method of synthesizing the integral of hydrostatic pressure on an instantaneous wet surface S (t) and the gravity of a hull at every moment, and the nonlinear hydrostatic restoring force load on the instantaneous average wet surface of the hull is as follows:
wherein, FGr-gravity under displacement of the hull at the r-th order; fg-hull weight concentration; through which it passes
Matrix w inkTo said generalized fluid restoring force coefficient matrix [ C ]]；
Step three, solving the incident force and the diffraction force;
by means of interception of instantaneous grids of the ship body, the pressure of incident waves and diffracted waves is integrated on the instantaneous wet surface grids at every moment:
step four, calculating the slamming force
By using
Solving a slamming force; wherein x, y represent the x, y coordinates of the hull;
step five, solving a system time domain delay function matrix;
the time domain delay function matrix is <math>
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<mi>K</mi>
<mi>rk</mi>
</msub>
<mrow>
<mo>(</mo>
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<msub>
<mi>B</mi>
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<mo>(</mo>
<mn>6</mn>
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</mrow>
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</math>
Infinite integral at the cut-off frequency for equation (6)The truncation divides the whole integration interval of the delay function formula into (0,) And (a)∞)，To accurately calculate Brk(ω) the limiting frequency, then,
wherein, tau is time, and m is a natural number.
For the interval (0) or (c),) It is divided into n parts, assuming that in each small interval (ω)n,ωn+1) B (omega) ≈ P with linear variation therein0+P1ω wherein in the above formula (I), <math>
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<mn>0</mn>
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</mrow>
</mfrac>
</mrow>
</math>
the first term at the right end of equation (7) is therefore:
for interval (Infinity), selecting an exponential decay function to simulate B (ω), the function being of the formWherein, alpha and beta are undetermined coefficients, and beta is ensured to be more than 0 in order to ensure that B (omega) is attenuated; <math>
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</math>
step six, obtaining the movement of the ship body
Solving the nonlinear time domain motion equation of the ship body to obtain the r-th order principal coordinate p of the ship bodyr(t)；
By utilizing the characteristics of the raw materials, <math>
<mfenced open='{' close=''>
<mtable>
<mtr>
<mtd>
<mi>w</mi>
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obtaining the displacement w (x, t), the bending moment M (x, t) and the shearing force V (x, t) of any cross section on the ship body in the time domain:
wherein, wr(x)、Mr(x)、Vr(x) The natural vibration modes of the displacement, bending moment and shearing force of the hull beam are the r-th order natural vibration modes, wherein r is 1-6 motion modes of a rigid body, and when r is larger than or equal to 7, the motion modes are the elastic vibration modes of the hull.
The method has the advantages of taking the influence of truncation errors into account and solving the problem of high requirement on hardware due to overlarge calculated amount in the prior art.
Drawings
FIG. 1 is a three-dimensional hull instantaneous grid capture;
FIG. 2 shows the result of comparing the midship bending moment of a ship with a characteristic period 10.877s and the test value of the navigational speed of 24kn, the sense wave height of 8m obtained by different methods;
fig. 3 shows the results of comparing the midship bending moment test values of 30kn, 6m sense wave height and 9.50s characteristic period based on different methods.
Detailed Description
The following specifically describes embodiments of the present invention:
1. determining an equation hull nonlinear time domain equation of motion
Based on a three-dimensional potential flow theory, an elastic body theoretical model with navigational speed hull motion and wave load is constructed, and a hull nonlinear time domain motion equation is in the form as follows:
in the formula: [ a ] A],[b],[c]-a structural generalized mass matrix, a generalized damping matrix, a generalized stiffness matrix; [ C ]]-a matrix of generalized fluid recovery force coefficients,representing the contribution of hydrostatic pressure generated by the vertical displacement of the ship body in the k-th order mode to the r-th order motion mode; rho-seawater density; g-gravitational acceleration;-an object plane normal vector; s (t) -a transient object plane;-representing a displacement vector resulting from an r-th order free motion mode of the resilient hull structure; w is ak-vertical displacement of the hull in the k-th mode; [ mu ] of]-a generalized fluid additional mass matrix when the frequency tends to infinity; [ K (τ)]-a time-domain delay function matrix for the system, which is dependent on the geometry and time interval of the hull, and which embodies the damping characteristics and hydrodynamic inertia of the waves; fI(t)、FD(t) -incident wave force and diffraction wave force received by the ship body; fslam(t) -the slamming force experienced by the hull; p is a radical ofr(t) -the hull's r-th principal coordinate.
The letters in the other formulas that are the same as in formula (1) have the same meaning as the corresponding letters in formula (1), unless otherwise specified.
2. Solving generalized fluid restoring force coefficient matrix [ C ]
In the embodiment, by means of three-dimensional hull instantaneous grid interception, as shown in fig. 1, the hydrostatic restoring force is directly calculated by adopting a method of integrating hydrostatic pressure on an instantaneous wet surface s (t) and synthesizing the gravity of a hull at every moment. This process reflects the most realistic situation, the nonlinear hydrostatic restoring force load F on the instantaneous average wet surface of the hullS(t) is:
wherein, FGr-gravity under displacement of the hull at the r-th order; fg-hull weight concentration.
Through which matrix wkTo said generalized fluid restoring force coefficient matrix [ C ]]. This is widely documented in the prior art and therefore this embodiment will not be described in detail.
3. Determining the incident and diffraction forces
For the calculation of the incident wave force and the diffracted wave force, the incident wave and the diffracted wave pressure are integrated on the instantaneous wet surface grid at each moment by means of interception of instantaneous grids of the ship body:
4. determining the slamming force
Using results from momentum theory <math>
<mrow>
<mi>F</mi>
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</math> And finally, integrating along the surface of the ship to obtain a slamming load expression which is counted into a vibration mode analysis equation:
where x, y represent the x, y coordinates of the hull.
5. Solving a system time domain delay function matrix
In order to improve the calculation efficiency, avoid the requirement of hardware from being too high, and keep higher prediction on the motion of the ship body, the embodiment has the prominent substantive characteristics and remarkably and progressively adopts the following method to solve the time domain delay function matrix [ K (tau) ].
Time domain delay function matrix of systemIt can be known that, in the actual solving process, the hydrodynamic coefficient in the whole frequency domain needs to be calculated, and due to the limitation of numerical methods such as grid scale, number and wave frequency, in the actual solving process, only the hydrodynamic coefficient at a limited number of frequencies can be obtained, and an accurate result cannot be obtained for the hydrodynamic coefficient at the frequency ω → ∞.
First, assume that the integration interval is at the cutoff frequencyThe truncation divides the whole integration interval of the delay function formula into (0,) And (a)∞)，To accurately calculate Brk(ω) the limiting frequency, then,
wherein, tau is time, and m is a natural number.
1. For the interval (0) or (c),) It is divided into n parts, assuming that in each small interval (ω)n,ωn+1) Internally linearly varying
B(ω)≈P0+P1ω(6)
Wherein,
therefore, the first term at the right end of equation (1) is:
wherein, <math>
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2. for interval (Infinity), since B (ω) also approaches 0 when ω → ∞. Therefore, in this region, an exponential decay function can be selected to model B (ω), the function being of the form:
where α and β are both undetermined coefficients, β must be guaranteed to be greater than 0 to ensure that B (ω) is attenuated.
Due to the first derivative of B (omega) at omegan+1The process is maintained continuously and, therefore,
a first guideThe solution can be performed by a "finite difference method". However, in order to ensure better numerical accuracy, the process is divided into two cases:
a) when damping coefficient B (ω))>When 0, taking logarithm at the same time for two sides of the formula (5):at this time, the least square method can be adopted to calculate alpha and beta;
b) when the damping coefficient B (ω) is less than 0 in some modes, α and β can be obtained from the average of the derivatives. At this time, the second half integral of equation (1) can be written as:
substituting the equations (8) and (11) into the equation (5) can obtain the delay function matrix K of the systemrk(τ)。
Cut-off frequencyThe choice of (A) is dependent on the particular hull and can generally be withinTo select between. From the results, it can be seen that the time-domain delay function of the ship hull has the characteristic of rapid attenuation, which is determined by the physical characteristics of the time-domain delay function. For a general ship body, K (t) can be considered to be close to zero when t is between (50-100) without losing regularity, and by utilizing the law, numerical calculation time is greatly saved when numerical calculation of convolution integral in a time domain motion equation is carried out.
6. To obtain movement of the hull
Obtaining a delay function matrix K of the systemrkAfter (tau), solving a nonlinear time domain motion equation (namely shown in the formula 1) of the ship body to obtain the ship body motion. But due to the convolution term in the equation of motionThe solution process is complicated and can cause great difficulty in the later programming. To solve the problem, a fourth-order Runge-Kutta (Runge-Kutta) method is adopted to solve the equation of motionObtaining the r-th order principal coordinate p of the ship bodyr(t), which is an explicit one-step method with 4 th order accuracy.
Obtaining the r-th order principal coordinate p of the ship bodyrAnd (t) obtaining the displacement w (x, t), the bending moment M (x, t) and the shearing force V (x, t) of any cross section on the ship body in the time domain by using a modal superposition principle.
Wherein, wr(x)、Mr(x)、Vr(x) The displacement, bending moment and shearing force of the hull beam are respectively the r-th order natural vibration modes. And r is 1-6 motion mode of rigid body, and when r is more than or equal to 7, the motion mode is elastic vibration mode of the ship body.
The technical scheme of the invention has simple process and easy realization, can take the influence of the elastic deformation of the ship body into consideration, has the test to prove that compared with the prior method, the method has more accurate result and obviously improved calculation efficiency, can be used for load response forecast of the ship body and ocean engineering structures, and has larger application prospect.
In order to verify the superiority of the method of the present invention, midship bending moment of the target ship in the test is calculated by using the conventional method and the method of the present invention, and compared with the test results, see fig. 2 and 3. As can be seen from the above comparison, for the irregular wave, since the acting forces, hydrodynamic coefficients, and the like in the main peak frequency method are calculated based on the main peak frequency, the response characteristic of the irregular wave cannot be expressed. The load response obtained by the method can be well matched with the test result, and meanwhile, the method is proved to be capable of meeting the engineering requirements.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and should not be taken as limiting the scope of the present invention, which is intended to cover any modifications, equivalents, improvements, etc. within the spirit and scope of the present invention.
Claims (2)
1. A method for determining a load response model of an elastic ship body in irregular waves is characterized by comprising the following steps:
step one, determining an equation hull nonlinear time domain motion equation;
solving a coefficient matrix of the generalized fluid restoring force;
step three, solving the incident force and the diffraction force;
step four, calculating the slamming force;
step five, solving a system time domain delay function matrix;
and step six, obtaining the movement of the ship body.
2. A method for determining a load response model of an elastic ship body in irregular waves is characterized by comprising the following steps:
step one, determining an equation hull nonlinear time domain motion equation
Constructing nonlinear time domain motion equation of ship body
In formula (1): [ a ] A],[b],[c]-a structural generalized mass matrix, a generalized damping matrix, a generalized stiffness matrix; [ C ]]-a generalized fluid restoring force coefficient matrix;representing the contribution of hydrostatic pressure generated by the vertical displacement of the ship body in the k-th order mode to the r-th order motion mode; rho-seawater density; g-gravitational acceleration;-an object plane normal vector; s (t) -a transient object plane;-representing a displacement vector resulting from an r-th order free motion mode of the resilient hull structure; w is ak-vertical displacement of the hull in the k-th mode; [ mu ] of]-a generalized fluid additional mass matrix when the frequency tends to infinity; [ K (τ)]The time-domain delay function matrix of the system, which depends on the geometry and the time interval of the hull, represents the damping characteristics and hydrodynamic inertia of the waves; fI(t)、FD(t) -incident wave force and diffraction wave force received by the ship body; fslam(t) -the slamming force experienced by the hull; p is a radical ofr(t) -the hull's primary r-th coordinate;
step two, solving a generalized fluid restoring force coefficient matrix
By means of three-dimensional hull instantaneous grid interception, the hydrostatic restoring force is directly calculated by adopting a method of synthesizing the integral of hydrostatic pressure on an instantaneous wet surface S (t) and the gravity of a hull at every moment, and the nonlinear hydrostatic restoring force load on the instantaneous average wet surface of the hull is as follows:
wherein, FGr-gravity under displacement of the hull at the r-th order; fg-hull weight concentration; through which matrix wkTo said generalized fluid restoring force coefficient matrix [ C ]]；
Step three, solving the incident force and the diffraction force;
by means of interception of instantaneous grids of the ship body, the pressure of incident waves and diffracted waves is integrated on the instantaneous wet surface grids at every moment:
step four, calculating the slamming force
By using
Solving a slamming force; wherein x, y represent the x, y coordinates of the hull;
step five, solving a system time domain delay function matrix;
the time domain delay function matrix is <math>
<mrow>
<msub>
<mi>K</mi>
<mi>rk</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>τ</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>2</mn>
<mi>π</mi>
</mfrac>
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mo>∞</mo>
</msubsup>
<msub>
<mi>B</mi>
<mi>rk</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>ω</mi>
<mo>)</mo>
</mrow>
<mi>cos</mi>
<mrow>
<mo>(</mo>
<mi>ωτ</mi>
<mo>)</mo>
</mrow>
<mi>dω</mi>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>6</mn>
<mo>)</mo>
</mrow>
</mrow>
</math>
Infinite integral at the cut-off frequency for equation (6)Cut off, dividing the whole integral interval of the delay function formula intoAndto accurately calculate Brk(ω) the limiting frequency, then,
wherein, tau is time, and m is a natural number.
For intervalDivide it into n parts, assume that in each small interval (ω)n,ωn+1) B (omega) ≈ P with linear variation therein0+P1ω wherein in the above formula (I), <math>
<mrow>
<msub>
<mi>P</mi>
<mn>0</mn>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mi>B</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>ω</mi>
<mi>n</mi>
</msub>
<mo>)</mo>
</mrow>
<msub>
<mi>ω</mi>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<mi>B</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>ω</mi>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<msub>
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<mi>n</mi>
</msub>
</mrow>
<mrow>
<msub>
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<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
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<mo>-</mo>
<msub>
<mi>ω</mi>
<mi>n</mi>
</msub>
</mrow>
</mfrac>
<mo>;</mo>
<msub>
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<mn>1</mn>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mi>B</mi>
<mrow>
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<msub>
<mi>ω</mi>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>B</mi>
<mrow>
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<msub>
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<mi>n</mi>
</msub>
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</mrow>
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<mrow>
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<mrow>
<mi>n</mi>
<mo>+</mo>
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</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>ω</mi>
<mi>n</mi>
</msub>
</mrow>
</mfrac>
</mrow>
</math> the first term at the right end of equation (7) is therefore:
for intervalB (omega) is simulated by selecting an exponential decay function, e.g. of the formWherein, alpha and beta are undetermined coefficients, and beta is ensured to be more than 0 in order to ensure that B (omega) is attenuated; α ═ B (ω)N+1)； <math>
<mrow>
<mi>β</mi>
<mo>=</mo>
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<mo>;</mo>
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Step six, obtaining the movement of the ship body
Solving the nonlinear time domain motion equation of the ship body to obtain the r-th order principal coordinate p of the ship bodyr(t)；
By utilizing the characteristics of the raw materials, <math>
<mfenced open='{' close=''>
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</mtable>
</mfenced>
</math>
obtaining the displacement w (x, t), the bending moment M (x, t) and the shearing force V (x, t) of any cross section on the ship body in the time domain:
wherein, wr(x)、Mr(x)、Vr(x) Respectively displacement of hull beamsAnd the ith order natural vibration mode of bending moment and shearing force, wherein r is 1-6 motion modes of a rigid body, and when r is more than or equal to 7, the motion mode is the elastic vibration mode of the ship body.
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| CN108763692A (en) * | 2018-05-18 | 2018-11-06 | 中国舰船研究设计中心 | A kind of efficient wave making method for ship numerical tank |
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| 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 |
| CN109726519A (en) * | 2018-11-12 | 2019-05-07 | 中国船舶及海洋工程设计研究院（中国船舶工业集团公司第七0八研究所） | A kind of movement load calculation method of cutter suction dredger under longitudinal buffer effect |
| CN109726519B (en) * | 2018-11-12 | 2023-05-19 | 中国船舶及海洋工程设计研究院（中国船舶工业集团公司第七0八研究所） | Motion load calculation method of cutter suction dredger under longitudinal buffer effect |
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| CN110489918B (en) * | 2019-08-28 | 2022-02-18 | 中国船舶科学研究中心（中国船舶重工集团公司第七0二研究所） | Method for processing elastic displacement of ultra-large floating body in anchoring analysis |
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