A fast calculation method for dynamic response of offshore structures based on discontinuous load segmentation

Abstract

The present invention relates to the field of marine engineering technology, and provides a method for quickly calculating the dynamic response of an offshore structure based on discontinuous load segmentation. The external load of the offshore structure is discontinuously segmented to obtain a discontinuous segmented external load time history; the transfer function of the offshore structure in the Laplace domain is determined, and a polar residue model of the offshore structure transfer function is constructed based on the transfer function of the offshore structure; based on the discontinuous segmented external load time history and the polar residue model of the offshore structure, the Laplace domain polar residue method is used to calculate the dynamic response of the offshore structure under each discontinuous segmented external load time history to obtain the segmented dynamic response of the offshore structure; all the segmented dynamic responses of the offshore structure obtained are superimposed to obtain the total response of the offshore structure.

Description

Technical Field

[0001] The invention relates to the technical field of marine engineering, and in particular to a method for quickly calculating the dynamic response of a marine structure based on discontinuous segmentation of loads. Background Art

[0002] The dynamic analysis of offshore structures is a key task in the early design and operation and maintenance of structures during service. It is of great significance for evaluating and predicting the dynamic performance of structures and implementing structural vibration control. At present, the dynamic analysis of offshore structures is mainly carried out in the frequency domain, time domain and Laplace domain, each of which has its own advantages and disadvantages. Specifically, the frequency domain method has high computational efficiency, but it can only calculate steady-state responses and cannot obtain transient responses; the time domain method can obtain time-varying responses with high accuracy, but it requires a large number of numerical integration operations, especially for long-term dynamic analysis of large offshore structures, the calculation is very time-consuming; the Laplace domain method is based on the extreme residue theory, which characterizes both external loads and structures into extreme residue models, and uses the extreme residue operation rules and Laplace transform technology to calculate the analytical solution of the transient response of the structure, which has high accuracy and leads the development direction of dynamic analysis of offshore structures.

[0003] The Laplace domain extreme residue method uses the complex exponential decomposition method to construct the extreme residue model of the external load. Considering the time-consuming and inefficient complex exponential decomposition of long-term external load signals, some scholars have tried to continuously segment the external load and reduce the time-consuming construction of the extreme residue model of the long-term load signal through segmented calculation. This approach has improved the calculation efficiency to a certain extent, but the continuous segmentation of the load has caused new problems in solving the structural natural vibration response. Specifically, since the response is calculated continuously in segments, the non-zero initial motion conditions of the structure caused by the previous segment response must be considered in the calculation of the current segment response, which introduces new problems in the calculation of the structural natural vibration response. In particular, when there are many segments, the natural vibration response needs to be solved multiple times, which has an adverse effect on the overall analysis efficiency of the structure. In addition, the continuous segmented solution of the load causes the subsequent response solution to be limited by the calculation accuracy of the previous segment response results, which is easy to cause a significant cumulative error amplification effect, thereby affecting the calculation accuracy. Summary of the invention

[0004] The purpose of the present invention is to solve the above technical problems and provide a method for rapid calculation of dynamic response of marine structures based on discontinuous segmentation of loads.

[0005] In order to achieve the above object, in some embodiments of the present invention, the following technical solutions are provided:

[0006] A method for rapid calculation of dynamic response of offshore structures based on discontinuous segmentation of loads comprises the following steps:

[0007] S1: External loads on offshore structures Perform discontinuous segmentation to obtain discontinuous segment external load time history ;

[0008] S2: Determine the transfer function of offshore structures in the Laplace domain , and based on the transfer function of offshore structures Constructing the extreme residue model of transfer function of offshore structures ;

[0009] S3: Extreme residue model based on discontinuous segmented external load time history and offshore structures , using the Laplace domain pole residue method, calculate the time history of each discontinuous segment external load The dynamic response of offshore structures under the action of ;

[0010] S4: The segmented dynamic responses of all offshore structures obtained in step S3 are Superposition to obtain the total response of the offshore structure .

[0011] In some embodiments of the present invention, step S1 includes:

[0012] S11: Obtaining time intervals for offshore structures Discrete external load signal , according to the discrete external load signal , and divide it equally into Each of them includes multiple discrete external load signals, and each discrete external load signal is defined as a segmented time course of the external load. :

[0013] ;

[0014] in, , , is the time point number, is the number of time points, subscript Represents the segment number of the external load, which is an integer. , the duration of each continuous external load time history is ;

[0015] S12: Segmented time history based on each external load , build The segment duration is Discontinuous external load segmentation, The external load is recorded as :

[0016] ;

[0017] The load segment Total duration and external load of equal length, Medium The values ​​of the remaining elements are all zero.

[0018] In some embodiments of the present invention, step S2 includes:

[0019] S21: Determine the governing equations of motion for offshore structures:

[0020] ;

[0021] in, For the quality of offshore structures, is the damping of offshore structures, is the stiffness matrix of the offshore structure, for A symmetric matrix; is the motion acceleration of the offshore structure, is the movement speed of the offshore structure, is the displacement vector of the offshore structure, 、 、 Both A vector of is the external load vector, A vector of is the number of degrees of freedom of motion of the offshore structure;

[0022] S22: Introducing the state variable vector , the offshore structure motion control equation obtained in step S21 is written as an offshore structure state space model:

[0023] ;

[0024] in, and for The symmetric matrix is ​​expressed as:

[0025] ;

[0026] ;

[0027] yes The external load vector in the state space is expressed as:

[0028] ;

[0029] S23: Determine a state space model of the offshore structure, and determine a pole residue model of a transfer function of the offshore structure based on the state space model:

[0030] Based on the state space model of offshore structures, the generalized eigenvalue equation of offshore structures is obtained:

[0031] ;

[0032] in, is the eigenvalue, which is 2 N scalar; is the characteristic vector of the offshore structure, with dimension ; Motion modes of offshore structures The following relationship exists:

[0033] ;

[0034] in, is the first n eigenvalues; It corresponds to the offshore structure n Eigenvalues The eigenvector of It is the first offshore structure order mode; is the subscript, ;

[0035] According to the orthogonality of symmetric matrices A and B, we can get hour:

[0036] , ;

[0037] in, It is the first r eigenvalues, is the first s eigenvalues, , , superscript Represents a matrix transpose operation;

[0038] Define the complex modal matrix , define the transformation relationship between physical coordinates and modal coordinates of offshore structures , transforming the state space model of offshore structures into The decoupled modal motion equations are:

[0039] ;

[0040] in, is the state space solution of the offshore structure, It corresponds to The state-space solution of the order mode, ;

[0041] , For offshore structures The coefficients of the modal motion equations are, For offshore structures External loads for the modal equations of motion, where:

[0042] ;

[0043] Based on the decoupled modal motion equation of the offshore structure, the corresponding equation in the Laplace domain of the offshore structure can be obtained. The transfer function of the first mode :

[0044] .

[0045] in, is the first poles, s is the Laplace variable, ;

[0046] According to the modal superposition principle, based on the Modal transfer function , we get the pole residue model of the transfer function of the offshore structure:

[0047] ;

[0048] in, is the pole residue model of the transfer function of offshore structures, subscript and They represent the load input coordinates and motion output coordinates of the offshore structure respectively. For the corresponding pole The remainder of:

[0049] ;

[0050] in, and Offshore structures First Mode No. elements and elements, , .

[0051] In some embodiments of the present invention, step S3 includes:

[0052] S31: Divide non-continuous external loads into segments It can be expressed as a Fourier series:

[0053] ;

[0054] in: For the discrete frequency values, is the frequency number, is the frequency resolution, It corresponds to The complex coefficients of External load Length of time, is the maximum value of the discrete frequency sequence number, is an imaginary number;

[0055] Segmentation of non-continuous external loads Performing Laplace transform, we get Laplace transform of for:

[0056] ;

[0057] in, For function The poles, complex coefficients for The residue of

[0058] S32: Pole residue model based on transfer function of offshore structures , using the Laplace domain residue method, we can calculate External loads on degrees of freedom The offshore structures caused by Motion response of degrees of freedom for:

[0059] ;

[0060] Will Written in extreme residue form:

[0061] ;

[0062] For the corresponding pole The response residue of For the corresponding pole The response residues are expressed as:

[0063] ;

[0064] ;

[0065] S33: Yes Perform inverse Laplace transform to obtain the segmented dynamic response of the offshore structure :

[0066] .

[0067] In some embodiments of the present invention, step S4 includes:

[0068] Load of each segment Induced segmental dynamic response Add together to get the external load on the offshore structure The total response under the action of:

[0069] .

[0070] The method for rapid calculation of dynamic response of marine structures based on discontinuous load segmentation proposed in the present invention has the technical effects of high efficiency and high precision compared with the prior art. Specifically, the beneficial effects of the technical solution of the present invention are:

[0071] 1. The calculation method of non-continuous load segmentation is adopted to solve the problem of solving the self-vibration response component generated by the load continuous segmentation pole residue method when solving the dynamic response, as well as the problem that there are many continuous segments and multiple calculations are required, which significantly improves the calculation efficiency of the dynamic response of offshore structures;

[0072] 2. The present invention avoids the problem of cumulative propagation of numerical errors caused by the load continuous segmentation method, and the calculation accuracy is guaranteed. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0074] Figure 1 To invent a flow chart of a method for rapid calculation of dynamic response of marine structures based on non-continuous segmentation of loads;

[0075] Figure 2 The external load in the present invention Timeline diagram;

[0076] Figure 3 The first non-continuous load of the present invention Timeline diagram;

[0077] Figure 4 The discontinuous second load section of the present invention Timeline diagram;

[0078] Figure 5 The present invention discontinuous first section load Response of offshore structures to Schematic diagram;

[0079] Figure 6 The present invention discontinuous first section load Response of offshore structures to Schematic diagram;

[0080] Figure 7 This is a comparison chart of the total response of the offshore structure obtained by the calculation method of the present invention and the calculation results of the time domain method. DETAILED DESCRIPTION

[0081] In order to make the technical problems, technical solutions and beneficial effects to be 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.

[0082] The present invention proposes a method for quickly calculating the dynamic response of an offshore structure based on discontinuous segmentation of loads, which includes the following steps.

[0083] S1: External loads on offshore structures Perform discontinuous segmentation to obtain discontinuous segment external load time history .

[0084] In some embodiments of the present invention, the specific execution steps of step S1 are as follows.

[0085] S11: Obtaining time intervals for offshore structures Discrete external load signal For example, the discrete external load signal can be obtained by discrete sampling method , sampling duration and sampling interval Determines the number of discrete external load signals obtained.

[0086] According to the discrete external load signal , and divide it equally into Each portion includes multiple discrete external load signals.

[0087] Define each discrete external load signal as an external load segment time series :

[0088] ;

[0089] in, , , is the time point number, is the number of time points, subscript Represents the segment number of the external load, which is an integer. , the duration of each continuous external load time history is .

[0090] For example, if there are 100 discrete external load signals, they can be divided into 10 parts, and each part has 10 discrete external load signals. The first to tenth discrete external load signals are used, and so on. The sampling duration and time interval can be determined according to the number of groups to be grouped, the number of data in each group, and other information.

[0091] S12: Segmented time history based on each external load , build The segment duration is Discontinuous external load segmentation, The external load is recorded as :

[0092] ;

[0093] The load segment Total duration and external load of equal length, Medium The values ​​of the remaining elements are all zero.

[0094] S2: Determine the transfer function of offshore structures in the Laplace domain , and based on the transfer function of offshore structures Constructing the extreme residue model of transfer function of offshore structures .

[0095] In some embodiments of the present invention, the specific execution steps of step S2 are as follows.

[0096] S21: Determine the governing equations of motion for offshore structures:

[0097] ;

[0098] in, For the quality of offshore structures, is the damping of offshore structures, is the stiffness matrix of the offshore structure, for A symmetric matrix; is the motion acceleration of the offshore structure, is the movement speed of the offshore structure, is the displacement vector of the offshore structure, 、 、 Both A vector of is the external load vector, A vector of It is the number of degrees of freedom of motion of offshore structures.

[0099] S22: Introducing the state variable vector , the offshore structure motion control equation obtained in step S21 is written as an offshore structure state space model:

[0100] ;

[0101] in, and for The symmetric matrix is ​​expressed as:

[0102] ;

[0103] ;

[0104] yes The external load vector in the state space is expressed as:

[0105] .

[0106] S23: Determine a state space model of the offshore structure, and determine a pole residue model of a transfer function of the offshore structure based on the state space model:

[0107] Based on the state space model of offshore structures, the generalized eigenvalue equation of offshore structures is obtained:

[0108] ;

[0109] in, is the eigenvalue, which is 2 N scalar; is the characteristic vector of the offshore structure, with dimension ; Motion modes of offshore structures The following relationship exists:

[0110] ;

[0111] in, It is the first n eigenvalues; It corresponds to the offshore structure n Eigenvalues The eigenvector of It is the first offshore structure order mode; is the subscript, Among them, the means for determining the generalized eigenvalue equation of the offshore structure belongs to the prior art in this field.

[0112] According to the orthogonality of symmetric matrices A and B, we can get hour:

[0113] , ;

[0114] in, It is the first r eigenvalues, is the first s eigenvalues, , , superscript Represents a matrix transpose operation;

[0115] Define the complex modal matrix , define the transformation relationship between physical coordinates and modal coordinates of offshore structures , transforming the state space model of offshore structures into The decoupled modal motion equations are:

[0116] ;

[0117] in, is the state space solution of the offshore structure, It corresponds to The state-space solution of the order mode, ;

[0118] , For offshore structures The coefficients of the modal motion equations are, For offshore structures External loads for the modal equations of motion, where:

[0119] ;

[0120] Based on the decoupled modal motion equation of the offshore structure, the corresponding equation in the Laplace domain of the offshore structure can be obtained. The transfer function of the first mode :

[0121] ;

[0122] in, To satisfy the generalized eigenvalue equation of offshore structures poles, s is the Laplace variable, ;

[0123] According to the modal superposition principle, based on the Modal transfer function , we get the pole residue model of the transfer function of the offshore structure:

[0124] ;

[0125] in, is the pole residue model of the transfer function of offshore structures, subscript and They represent the load input coordinates and motion output coordinates of the offshore structure respectively. For the corresponding pole The remainder of:

[0126] ;

[0127] in, and Offshore structures First Mode No. elements and elements. Among them, , .

[0128] S3: Extreme residue model based on discontinuous segmented external load time history and offshore structures , using the Laplace domain pole residue method, calculate the time history of each discontinuous segment external load The dynamic response of offshore structures under the action of .

[0129] In some embodiments of the present invention, the specific execution steps of step S3 are as follows.

[0130] S31: Divide non-continuous external loads into segments It can be expressed as a Fourier series:

[0131] ;

[0132] in: For the discrete frequency values, is the frequency number, is the frequency resolution, It corresponds to The complex coefficients of External load Length of time, is the maximum value of the discrete frequency sequence number, is an imaginary number;

[0133] Segmentation of non-continuous external loads Performing Laplace transform, we get Laplace transform of for:

[0134] ;

[0135] in, For function The poles, complex coefficients for The remainder of .

[0136] S32: Pole residue model based on transfer function of offshore structures , using the Laplace domain residue method, we can calculate External loads on nodes The offshore structures caused by The motion response of each node for:

[0137] ;

[0138] Will Written in extreme residue form:

[0139] ;

[0140] For the corresponding pole The response residue of For the corresponding pole The response residues are expressed as:

[0141] ;

[0142] ;

[0143] S33: Yes Perform inverse Laplace transform to obtain the segmented dynamic response of the offshore structure :

[0144] .

[0145] S4: The segmented dynamic responses of all offshore structures obtained in step S3 are Superposition to obtain the total response of the offshore structure .

[0146] In some embodiments of the present invention, the specific execution steps of step S4 are as follows.

[0147] Load of each segment Induced segmental dynamic response Add together to get the external load on the offshore structure The total response under the action of:

[0148] .

[0149] Hereinafter, a single-degree-of-freedom marine engineering structure is taken as an example to illustrate the specific implementation effect of the method provided by the present invention.

[0150] The governing equations of structural motion are as follows:

[0151] ;

[0152] in, , , , , The duration is 30 seconds and the sampling interval is 0.01 seconds. According to the modal analysis theory, the poles of the structure are calculated. 0.1+0.6245 , 0.1 0.6245 ;residue , ,in Is an imaginary number.

[0153] During the implementation, the external load lasts for 30 seconds. Divide into two segments, each 15 seconds long. Figure 2 is an external load Schedule, Figure 3 and Figure 4 It is the first load history of the non-continuous division and the second load history Assuming that the system is initially in a static state, the first load is calculated using the method of the present invention. Structural response under action , and the second load Dynamic response of offshore structures under , see Figure 5 and Figure 6 .

[0154] Will and Add together to get the total response of the structure , and the comparison with the time domain results is shown in Figure 7 The two have good consistency, which confirms the effectiveness of the present invention.

[0155] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. It should be pointed out that for those skilled in the art, any modification, equivalent replacement and improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the patent application shall be based on the protection scope of the attached claims.

Claims

1. A fast calculation method for dynamic response of marine structures based on discontinuous segmentation of loads, characterized in that: The following steps are involved: S1: External loads on offshore structures Perform discontinuous segmentation to obtain discontinuous segment external load time history ; S2: Determine the transfer function of offshore structures in the Laplace domain , and based on the transfer function of offshore structures Constructing the extreme residue model of transfer function of offshore structures ; S3: Extreme residue model based on discontinuous segmented external load time history and offshore structures , using the Laplace domain pole residue method, calculate the time history of each discontinuous segment external load The dynamic response of offshore structures under the action of ; S4: The segmented dynamic responses of all offshore structures obtained in step S3 are Superposition to obtain the total response of the offshore structure ; The step S2 comprises: S21: Determine the governing equations of motion for offshore structures: ； in, For the quality of offshore structures, is the damping of offshore structures, is the stiffness matrix of the offshore structure, for A symmetric matrix; is the motion acceleration of the offshore structure, is the movement speed of the offshore structure, is the displacement vector of the offshore structure, 、 、 Both A vector of is the external load vector, A vector of is the number of degrees of freedom of motion of the offshore structure; S22: Introducing the state variable vector , the offshore structure motion control equation obtained in step S21 is written as an offshore structure state space model: ； in, and for The symmetric matrix is ​​expressed as: ； ； yes The external load vector in the state space is expressed as: ； S23: Determine a state space model of the offshore structure, and determine a pole residue model of a transfer function of the offshore structure based on the state space model: Based on the state space model of offshore structures, the generalized eigenvalue equation of offshore structures is obtained: ； in, is the eigenvalue, which is 2 N scalar; is the characteristic vector of the offshore structure, with dimension ; Motion modes of offshore structures The following relationship exists: ； in, It is the first n eigenvalues; Corresponding to the offshore structure n Eigenvalues The eigenvector of It is the first offshore structure order mode; is the subscript, ; According to the orthogonality of symmetric matrices A and B, we can get hour: ， ； in, It is the first r eigenvalues, is the first s eigenvalues, , , superscript Represents a matrix transpose operation; Define the complex modal matrix , define the transformation relationship between physical coordinates and modal coordinates of offshore structures , transforming the state space model of offshore structures into The decoupled modal motion equations are: ； in, is the state space solution of the offshore structure, It corresponds to The state-space solution of the order mode, ; , For offshore structures The coefficients of the modal motion equations are, For offshore structures External loads for the modal equations of motion, where: ； Based on the decoupled modal motion equation of the offshore structure, the corresponding equation in the Laplace domain of the offshore structure can be obtained. The transfer function of the first mode : ； in, To satisfy the generalized eigenvalue equation of offshore structures poles, s is the Laplace variable, ; According to the modal superposition principle, based on the Modal transfer function , we get the pole residue model of the transfer function of the offshore structure: ； in, is the pole residue model of the transfer function of offshore structures, subscript and They represent the load input coordinates and motion output coordinates of the offshore structure respectively, For the corresponding pole The remainder of: ； in, and Offshore structures First Mode No. elements and elements, among which , .

2. The method for rapid calculation of dynamic response of marine structures based on non-continuous load segmentation according to claim 1, characterized in that: Step S1 includes: S11: Obtaining time intervals for offshore structures Discrete external load signal , according to the discrete external load signal , and divide it equally into Each of them includes multiple discrete external load signals, and each discrete external load signal is defined as a segmented time course of the external load. : ； in, , , is the time point number, is the number of time points, subscript Represents the segment number of the external load, which is an integer. , the duration of each continuous external load time history is ; S12: Segmented time history based on each external load , build The segment duration is Discontinuous external load segmentation, The external load is recorded as : ； The load segment Total duration and external load of equal length, Medium The values ​​of the remaining elements are all zero.

3. The method for rapid calculation of dynamic response of marine structures based on non-continuous load segmentation according to claim 1, characterized in that: Step S3 includes: S31: Divide non-continuous external loads into segments It can be expressed as a Fourier series: ； in: For the discrete frequency values, is the frequency number, is the frequency resolution, It corresponds to The complex coefficients of External load Length of time, is the maximum value of the discrete frequency sequence number, is an imaginary number; Segmentation for non-continuous external loads Performing Laplace transform, we get Laplace transform of for: ； in, For function The poles, complex coefficients for The residue of S32: Pole residue model based on transfer function of offshore structures , using the Laplace domain residue method, we can calculate External loads on nodes The offshore structures caused by The motion response of each node for: ； Will Written in extreme residue form: ； For the corresponding pole The response residue of For the corresponding pole The response residues are expressed as: ； ； S33: Yes Perform inverse Laplace transform to obtain the segmented dynamic response of the offshore structure : 。 4. The method for rapid calculation of dynamic response of marine structures based on non-continuous load segmentation according to claim 3 is characterized in that: Step S4 includes: Load of each segment Induced segmental dynamic response Add together to get the external load on the offshore structure The total response under the action of: 。

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