Method for calculating transient response of offshore wind power structure under ship collision

Abstract

A transient response calculation method for an offshore wind power structure under ship collision is characterized by adopting a transient response calculation method of Lapalce transformation and modal truncation and comprising the following steps of: calculating the transient response of the offshore wind power structure under ship collision; s1, vibration decoupling of the offshore wind power structure; s2, Laplace transformation of a decoupling equation is carried out; s3, modal response solving is carried out; s4, modal truncation and vibration response solving: decoupling a vibration control equation by adopting a modal matrix, solving vibration response under a modal coordinate system in a Laplace domain, solving the problem that time domain integration depends on calculation of time step length, analyzing contribution of each order of modal to total vibration response, providing a modal truncation method, and solving the vibration response in the Laplace domain; therefore, an efficient and accurate offshore wind power structure transient response calculation method is constructed.

Description

Technical Field

[0001] The present invention relates to the field of marine engineering, and in particular to a method for calculating transient response of an offshore wind power structure under a ship collision. Background Art

[0002] Offshore wind power structures occupy an important position in the field of wind resource development. They are tall flexible structures with large mass components installed on the top. The stability of offshore wind power structures is mainly manifested in the dynamic response of the tower top cabin under external loads. When hit by a ship collision, it often causes large displacement and acceleration responses. When the cabin displacement response is large, it will cause instability during the rotation of the wind rotor blades, thereby affecting the power generation efficiency. At the same time, the large cabin shaking acceleration may cause large vibrations of internal rotors, drive shafts and other devices. Therefore, analyzing the transient response of offshore wind power structures under ship collisions is of great significance to the safe operation of wind power structures.

[0003] The collision between a ship and an offshore wind turbine structure is a transient process, and the time domain integration method is usually used to calculate its transient response. When analyzing the transient response of an offshore wind turbine structure, a smaller calculation time step is often required. At the same time, the offshore wind turbine structure is huge and has many degrees of freedom, which leads to low calculation efficiency of the time domain method and even memory overflow. Summary of the invention

[0004] In order to solve the above problems, the present technical solution provides a method for calculating the transient response of offshore wind power structures under ship collision.

[0005] To achieve the above purpose, the technical solution is as follows:

[0006] A transient response calculation method for offshore wind power structures under ship collision, using Lapalce transformation and modal truncation transient response calculation method, comprising the following steps;

[0007] S1, offshore wind turbine structure vibration decoupling;

[0008] S2, Laplace transform of decoupled equation;

[0009] S3, modal response solution;

[0010] S4, modal truncation and vibration response solution.

[0011] In some embodiments, the step S1 further includes the following steps:

[0012] S101, the collision between a ship and an offshore wind power structure is a transient process, and the collision motion equation is:

[0013]

[0014] Where M is the mass matrix, C is the damping matrix, K is the stiffness matrix, x(t), are the displacement, velocity and acceleration of the offshore wind power structure, F is the collision load, and H is the hourglass viscous damping force matrix;

[0015] S102, after the ship collides with the wind turbine structure, the energy is transferred to the wind turbine structure, and an initial velocity is given to the collision point according to the momentum theorem, so that the entire wind turbine structure vibrates. At this time, the vibration equation of the offshore wind turbine structure is:

[0016]

[0017] S103, using modal coordinates to represent the displacement response of offshore wind power structures:

[0018] x(t)=Φy(t);

[0019] Φ is the vibration modal matrix of the offshore wind turbine structure, and y is the modal space displacement response;

[0020] S104, bring the formula of step S103 into step S102, and multiply it by Φ on the left T ,get:

[0021]

[0022] S105, since M and K are positive definite matrices, the damping adopts the Rayleigh damping model, that is, C = αM + βK, and the formula of step S104 is diagonalized to obtain:

[0023]

[0024] In the formula, m i 、c i , k i They are modal mass, modal damping and modal stiffness respectively, and N is the number of degrees of freedom of the offshore wind turbine structure.

[0025] In some embodiments, step S2 further includes the following steps:

[0026] S201, assuming that the ship collision node is L, and the speed after the collision is v0, at this time, only the jth element of the offshore wind power structure velocity vector is non-zero, and we get:

[0027]

[0028] S202, since the modal matrix is ​​an orthogonal matrix, the initial velocity of the offshore wind power structure in the modal coordinate system after the collision is:

[0029]

[0030] S203, the wind power structure has only a non-zero velocity at node L. Substituting the formula of step S201 into step S202, we get:

[0031]

[0032] In the formula, φ ji is the Lth row and ith column element of the modal matrix Φ;

[0033] S204, perform Laplace transformation on step S105 to obtain:

[0034]

[0035] In the formula, for y i (t) is Laplace transform, s is Laplace variable;

[0036] S205, at the moment of collision of the offshore wind power structure, the initial displacement of each node is zero, and the Laplace transform of the displacement response in the modal coordinate system obtained according to step S203 and step S204 is:

[0037]

[0038] In the formula, ω 0i and i are the natural frequency and damping ratio respectively;

[0039] S206, according to step S205, the i-th order vibration after the offshore wind power structure collides with the ship is only related to the frequency, damping ratio and natural frequency of the i-th order vibration.

[0040] In some embodiments, step S3 further includes the following steps:

[0041] S301, rewrite step S205 into extreme value and residue form to obtain:

[0042]

[0043] In the formula, i is the imaginary unit, and it can be seen that both the extreme value and the residue are conjugate complex numbers;

[0044] S301, perform inverse Laplace transform on the formula and obtain the displacement response:

[0045]

[0046] S302, according to Euler's formula, simplify the formula of step S301 to obtain:

[0047]

[0048] S303, from step S302, it can be known that the vibration response under the modal coordinates is a decaying cosine function. As the modal order increases, the natural frequency increases successively, the vibration amplitude decreases, and the decay speed becomes faster.

[0049] In some embodiments, step S4 further includes the following steps:

[0050] S401, substitute step S302 into step S103, and obtain the displacement response of the wind turbine structure after the ship collides with the offshore wind turbine structure:

[0051]

[0052] It can be seen from the formula that the offshore wind power structure is composed of the superposition of various order responses in the modal coordinate system, and the contribution of each order response includes three parts;

[0053] Amplitude:

[0054]

[0055] Attenuation term:

[0056]

[0057] Cosine term:

[0058]

[0059] S402, as the modal order increases, the modal solid frequency increases, and the damping ratio does not change significantly, so that the amplitude becomes smaller, the attenuation becomes faster, and the contribution to the structural displacement response becomes smaller. The mode is truncated. For the offshore wind power structure to be analyzed, the amplitude term in step S401, when the amplitude term is less than 0.01 times the maximum value of the previous orders, the subsequent modes are truncated to improve the calculation efficiency.

[0060] The beneficial effects of this application are:

[0061] For step S1, the present invention uses a modal matrix to decouple the vibration control equation of the offshore wind power structure under the ship collision, so that the coupled vibration equation of the large degree of freedom structure is converted into a series of single degree of freedom vibration equations in the modal coordinate system, thereby simplifying the transient response solution process;

[0062] For step S2, the present invention transforms the decoupled vibration equation into the Laplace domain, calculates the solution of the modal space response of the ship under collision in the Laplace domain, and lays the foundation for solving the dynamic response;

[0063] For step S3, the present invention converts the solution of the decoupling equation in Laplace into an extreme value-residue form, and obtains the modal coordinate time domain response through an inverse Laplace transform, thereby avoiding the calculation error of the time domain integration;

[0064] For step S4, the present invention analyzes the contribution of the modal response and proposes a modal truncation method, which greatly improves the calculation efficiency of the transient response. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for describing the embodiments are briefly introduced below.

[0066] Figure 1 is a finite element model diagram of an embodiment of the present invention;

[0067] Figure 2 is a vibration amplitude diagram of each order model of an embodiment of the present invention;

[0068] Figure 3 : is a comparison diagram of vibration displacements calculated by the Newmark-β method of an embodiment of the present invention and the method of the present invention;

[0069] Figure 4 is a comparison diagram of calculation results at different time intervals according to an embodiment of the present invention;

[0070] Figure 5 It is a comparison chart of calculation results of the Newmark-β method at different time intervals according to an embodiment of the present invention. DETAILED DESCRIPTION

[0071] In order to make the technical problems, technical solutions and beneficial effects solved by the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0072] Please refer to Figure 1-5 As shown, in order to solve the above problems, the present invention provides a method for calculating the transient response of an offshore wind power structure under a ship collision, which adopts a modal matrix to decouple the vibration control equation, solves the vibration response in the modal coordinate system in the Laplace domain, solves the problem that the time domain integral depends on the calculation time step, analyzes the contribution of each order mode to the total vibration response, and proposes a modal truncation method, thereby constructing an efficient and accurate method for calculating the transient response of an offshore wind power structure.

[0073] The following is a step-by-step analysis of this solution:

[0074] Vibration decoupling of offshore wind turbine structures:

[0075] The collision between a ship and an offshore wind turbine structure is a transient process, and the collision motion equation can be expressed as

[0076]

[0077] Where M is the mass matrix, C is the damping matrix, K is the stiffness matrix, x(t), are the displacement, velocity and acceleration of the offshore wind turbine node, F is the collision load, and H is the hourglass viscous damping force matrix.

[0078] When a ship collides with a wind turbine structure, it transfers energy to the wind turbine structure, which is equivalent to giving the collision point an initial velocity according to the momentum theorem, causing the entire wind turbine structure to vibrate. At this time, the vibration equation of the offshore wind turbine structure becomes:

[0079]

[0080] The displacement response of offshore wind power structures is expressed using modal coordinates, namely:

[0081] x(t)=Φy(t) (3)

[0082] Where Φ is the vibration modal matrix of the offshore wind turbine structure, and y is the modal space displacement response.

[0083] Substitute equation (3) into equation (2) and multiply on the left by Φ T ,get:

[0084]

[0085] Since M and K are positive definite matrices, the damping adopts the Rayleigh damping model, that is, C = αM + βK. Equation (4) can be diagonalized, that is:

[0086]

[0087] In the formula, m i 、c i , k i They are modal mass, modal damping and modal stiffness respectively, and N is the number of degrees of freedom of the offshore wind turbine structure.

[0088] Decouple the equation Laplace transform:

[0089] Assume that the ship collision node is L and the speed after the collision is v0. At this time, only the jth element of the offshore wind power structure velocity vector is non-zero, that is:

[0090]

[0091] Since the modal matrix is ​​an orthogonal matrix, the initial velocity of the offshore wind power structure in the modal coordinate system after the collision is:

[0092]

[0093] The velocity of the wind turbine structure is non-zero only at the node L. Substituting equation (6) into equation (7), the initial velocity in the modal coordinate system can be further simplified, namely:

[0094]

[0095] In the formula, φ ji is the Lth row and i-th column element of the modal matrix Φ.

[0096] Performing Laplace transform on equation (5) yields:

[0097]

[0098] In the formula, for y i (t) is the Laplace transform, and s is the Laplace variable.

[0099] At the moment of collision, the initial displacement of each node of the offshore wind turbine structure is zero. According to equations (8) and (9), the Laplace transform of the displacement response in the modal coordinate system is obtained as follows:

[0100]

[0101] In the formula, ω 0i and i are the natural frequency and damping ratio respectively.

[0102] It can be seen from formula (10) that the i-th order vibration after the offshore wind turbine structure collides with the ship is only related to the inherent properties of the i-th order vibration, such as frequency, damping ratio and natural frequency.

[0103] Modal response solution:

[0104] Rewriting equation (10) into the extreme value-residue form, we obtain:

[0105]

[0106] In the formula, i is the imaginary unit, and it can be seen that both the extreme value and the residue are conjugate complex numbers.

[0107] Performing inverse Laplace transform on equation (12), the displacement response is:

[0108]

[0109] According to Euler's formula, equation (12) can be further simplified as:

[0110]

[0111] It can be seen from formula (13) that the vibration response in modal coordinates is a decaying cosine function. With the increase of the modal order, the natural frequency increases successively, the vibration amplitude decreases, and the decay speed becomes faster.

[0112] Modal truncation and vibration response solution:

[0113] Substituting equation (13) into equation (3), we can obtain the displacement response of the wind turbine structure after the ship collides with the offshore wind turbine structure:

[0114]

[0115] It can be seen from the formula that the offshore wind power structure is composed of the superposition of various order responses in the modal coordinate system. The contribution of each order response includes three parts, namely, amplitude Attenuation term and cosine terms

[0116]

[0117] As the modal order increases, the modal solid frequency increases, and the damping ratio does not change significantly, which makes the amplitude smaller, the attenuation faster, and the contribution to the structural displacement response smaller, providing the possibility of modal truncation. For the offshore wind power structure to be analyzed, the amplitude term in formula (14) is calculated. When the amplitude term is less than 0.01 times the maximum value of the previous orders, the subsequent modes are truncated to improve the calculation efficiency.

[0118] Offshore wind power structures are huge and have many degrees of freedom. When performing transient analysis on them under the action of ship collision, it is often necessary to use a smaller calculation time step to ensure that smaller transient responses are captured. However, under large degrees of freedom conditions, a smaller time step leads to low efficiency in time domain analysis calculations and even memory overflow. The present invention solves the displacement response in the modal coordinate system in Laplace, avoiding the problem that the accuracy of time domain calculations depends on the calculation time step. At the same time, it analyzes the contribution of each modal response to the total response of the structure, and proposes a modal truncation method, which greatly improves the calculation efficiency.

[0119] In specific implementation, the fixed jacket offshore wind power structure supports a 5MW wind turbine in a sea area with a water depth of 50m. The four pile legs of the wind turbine support structure are fixed to the seabed by grouting. The fixing stiffness is large, and the degree of freedom of the fixed point can be considered to be zero. The upper part of the jacket is a concrete structure with dimensions of 4×9.6×9.6m and a mass of 666t. The offshore wind power structure of the embodiment includes 85 nodes, corresponding to 486 degrees of freedom. The structural finite element model is shown in the attached figure. Figure 1 shown.

[0120] The mass matrix, damping matrix and stiffness matrix of the offshore wind turbine structure are obtained by finite element software, and the vibration frequencies and vibration modes of the wind turbine structure are obtained by eigenvalue analysis. Assuming that the collision point of the ship is as shown in the attached figure Figure 1 , the horizontal velocity of the given collision node after the collision is 1m / s. The vibration equation decoupling under the ship collision condition is completed by using the method of the present invention, and the vibration amplitudes of each order are obtained as shown in the attached figure. Figure 2As shown in the figure, it can be seen that after the modal order exceeds 150, its vibration response contributes little to the total vibration and can be ignored. The present invention uses the first 150 orders to calculate the vibration response of the fan position under the ship collision, and compares it with the calculation results of the Newmark-β method. Figure 3 As shown. From the comparison chart, it can be seen that the two are in good agreement, which shows the correctness of the method of the present invention. When calculating the vibration response, the time step used is 0.001s, and the calculation time is 50s. On the computing platform with CPU model i7-12700KF, the calculation time of the method of the present invention and Newmark-β are 1.1406s and 41.9688s respectively. It can be seen that the calculation efficiency of the method of the present invention is much higher than that of the traditional time domain integration method, and it can avoid the memory overflow problem. The calculation time step is set to 0.05s, 0.01s and 0.001s, and the method of the present invention and the Newmark-β method are used to calculate the position displacement response of the wind turbine under ship collision, and the results are compared as shown in the attached figure. Figure 4 and 5 As shown, it can be seen that the calculation accuracy of the method of the present invention is not significantly affected by the calculation time step, and has better robustness.

[0121] The above description is only a preferred embodiment of the present application and is not intended to limit the scope of implementation of the present application. Other principles and basic structures that are the same or similar to those of the present application are within the protection scope of the present application.

Claims

1. A method for calculating the transient response of an offshore wind power structure under a ship collision, characterized in that: The transient response calculation method using Lapalce transformation and modal truncation includes the following steps: S1, offshore wind turbine structure vibration decoupling; S2, Laplace transform of decoupled equation; S3, modal response solution; S4, modal truncation and vibration response solution.

2. The method for calculating transient response of offshore wind power structures under ship collision according to claim 1, characterized in that: The step S1 also includes the following steps: S101, the collision between a ship and an offshore wind power structure is a transient process, and the collision motion equation is: Where M is the mass matrix, C is the damping matrix, K is the stiffness matrix, x(t), are the displacement, velocity and acceleration of the offshore wind power structure, F is the collision load, and H is the hourglass viscous damping force matrix; S102, after the ship collides with the wind turbine structure, the energy is transferred to the wind turbine structure, and an initial velocity is given to the collision point according to the momentum theorem, so that the entire wind turbine structure vibrates. At this time, the vibration equation of the offshore wind turbine structure is: S103, using modal coordinates to represent the displacement response of offshore wind power structures: x(t)=Φy(t); Φ is the vibration modal matrix of the offshore wind turbine structure, and y is the modal space displacement response; S104, bring the formula of step S103 into step S102, and multiply it by Φ on the left T ,get: S105, since M and K are positive definite matrices, the damping adopts the Rayleigh damping model, that is, C = αM + βK, and the formula of step S104 is diagonalized to obtain: In the formula, m i 、c i , k i They are modal mass, modal damping and modal stiffness respectively, and N is the number of degrees of freedom of the offshore wind turbine structure.

3. The method for calculating transient response of offshore wind power structures under ship collision according to claim 2, characterized in that: The step S2 also includes the following steps: S201, assuming that the ship collision node is L, and the speed after the collision is v0, at this time, only the jth element of the offshore wind power structure velocity vector is non-zero, and we get: S202, since the modal matrix is ​​an orthogonal matrix, the initial velocity of the offshore wind power structure in the modal coordinate system after the collision is: S203, the wind power structure has only a non-zero velocity at node L. Substituting the formula of step S201 into step S202, we get: In the formula, φ ji is the Lth row and ith column element of the modal matrix Φ; S204, perform Laplace transformation on step S105 to obtain: In the formula, for y i (t) is Laplace transform, s is Laplace variable; S205, at the moment of collision of the offshore wind power structure, the initial displacement of each node is zero, and the Laplace transform of the displacement response in the modal coordinate system obtained according to step S203 and step S204 is: In the formula, ω 0i and i are the natural frequency and damping ratio respectively; S206, according to step S205, the i-th order vibration after the offshore wind power structure collides with the ship is only related to the frequency, damping ratio and natural frequency of the i-th order vibration.

4. The method for calculating transient response of offshore wind power structures under ship collision according to claim 3 is characterized by: The step S3 also includes the following steps: S301, rewrite step S205 into extreme value and residue form to obtain: In the formula, i is the imaginary unit, and it can be seen that both the extreme value and the residue are conjugate complex numbers; S301, perform inverse Laplace transform on the formula and obtain the displacement response: S302, according to Euler's formula, simplify the formula of step S301 to obtain: S303, from step S302, it can be known that the vibration response under the modal coordinates is a decaying cosine function. As the modal order increases, the natural frequency increases successively, the vibration amplitude decreases, and the decay speed becomes faster.

5. The method for calculating transient response of offshore wind power structure under ship collision according to claim 4, characterized in that: The step S4 further comprises the following steps: S401, substitute step S302 into step S103, and obtain the displacement response of the wind turbine structure after the ship collides with the offshore wind turbine structure: It can be seen from the formula that the offshore wind power structure is composed of the superposition of various order responses in the modal coordinate system, and the contribution of each order response includes three parts; Amplitude: Attenuation term: Cosine term: S402, as the modal order increases, the modal solid frequency increases, and the damping ratio does not change significantly, so that the amplitude becomes smaller, the attenuation becomes faster, and the contribution to the structural displacement response becomes smaller. The mode is truncated. For the offshore wind power structure to be analyzed, the amplitude term in step S401, when the amplitude term is less than 0.01 times the maximum value of the previous orders, the subsequent modes are truncated to improve the calculation efficiency.

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