A Pole Residue Dynamic Analysis Method for Nonlinear Floating Systems Based on Discontinuous Segmentation

Abstract

The present invention belongs to the field of marine engineering technology, and provides a nonlinear floating system pole residue dynamic analysis method based on discontinuous segmentation. The nonlinear term is separated from the motion control equation of the nonlinear floating system to obtain the motion control equation of the linearized floating system; based on the above linearized motion equation of the floating system, the time-domain external load motion response of the floating system under the excitation of the external load is solved; the time-domain external load motion response of the floating structure is divided into segments of different lengths to obtain the segmented response of the external load of the floating system; the nonlinear external load motion response component caused by the nonlinear external load in the corresponding segmented response is iteratively solved to obtain the nonlinear external load segmented response, which is superimposed with the external load segmented response caused by the external load in step S3 to obtain the nonlinear segmented response of the floating system; the calculation is repeated until the total response of the nonlinear floating system is obtained.

Description

Technical Field

[0001] The invention relates to the technical field of marine engineering, and in particular to a nonlinear floating system pole residue dynamic analysis method based on discontinuous segmentation. Background Art

[0002] Offshore floating systems, such as various ships and offshore platforms, are the main structural forms of current marine resource and energy development. Their dynamic analysis is the key work for the preliminary design and service life operation and maintenance of the system. Actual offshore floating structures are typical nonlinear systems. Common nonlinearities include nonlinear damping, nonlinear mooring force, and nonlinear restoring force. At present, the mainstream method for dynamic analysis of nonlinear floating systems is the time domain stepping method, which has high calculation accuracy. However, this method requires a large number of numerical integration operations to solve the convolution terms and time-varying dynamic responses in the Cummins equation. Especially for the long-term analysis of large floating systems with multiple degrees of freedom, the calculation is very time-consuming and inefficient. In order to improve the efficiency of dynamic analysis of nonlinear floating systems, some scholars applied the Laplace domain pole residue model of linear floating structures to the dynamic analysis of nonlinear floating structures. Combined with the response continuous segmented iterative solution technology, a hybrid time domain-Laplace domain calculation method suitable for the dynamic response of nonlinear floating systems was proposed, which avoided the solution of convolution terms and cumbersome numerical stepping operations in the traditional time domain method, and improved the analysis efficiency to a certain extent. However, when solving the response in segments, this method must take into account the fluid memory effect caused by the previous floating body movement, and also needs to consider the solution of the self-oscillation response under non-zero initial conditions caused by the floating body movement. The calculation theory and numerical implementation are relatively complex, and the theoretical completeness and calculation efficiency still need to be further improved. Summary of the invention

[0003] The purpose of the present invention is to solve the above technical problems and provide a nonlinear floating system pole residue dynamic analysis method based on discontinuous segmentation.

[0004] In order to achieve the above object, in some embodiments of the present invention, the following technical solutions are provided:

[0005] The nonlinear floating system pole residue dynamic analysis method based on discontinuous segmentation includes the following steps:

[0006] S1: determining a motion control equation of a floating system, wherein the motion control equation includes a linear term and a nonlinear term, separating the nonlinear term from the motion control equation, and obtaining a linearized motion control equation of the floating system; the nonlinear term is used as a nonlinear external load of the floating system;

[0007] S2: Based on the linearized motion control equations of the floating system, the external loads are solved using the Laplace domain pole residue method Motion response of floating structures under excitation to external loads in the time domain, including displacement response to external loads in the time domain and the velocity response of the external load in the time domain ;

[0008] S3: From the start time First, the time domain external load motion response of the floating structure is divided into N segments of different lengths. The segment duration is ,in ,get The external load segmented response of the floating system includes the external load segmented response. Segmented displacement response , and the external load Segmented speed response ;in, is the duration of external load action;

[0009] S4: Use the Laplace domain pole residue method to iteratively solve the corresponding In the segmented response, the nonlinear external load motion response component caused by the nonlinear external load is obtained. Segmented response, including nonlinear Segmented displacement response , and nonlinear Segmented speed response , and compare it with the external load in step S3 The external load caused The nonlinear first order of the floating system is obtained by superposing the segmented responses. Segmented response, including floating system nonlinearity Segmented displacement response , and the floating system nonlinear Segmented speed response ;

[0010] S5: Repeat step S4 until n=N, and obtain the total displacement response of the nonlinear floating system and the overall speed response .

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

[0012] S11: Determine the governing equations for the motion of the nonlinear floating system:

[0013] ;

[0014] in, is the mass of the floating system, is the additional mass of the floating system at infinite frequency, is the acceleration of the floating system, is the time delay function of the floating system, is a dummy time variable, is the floating system movement speed, is the hydrostatic restoring stiffness coefficient, is the floating system displacement, is the external load of the floating system, that is, the surface wave force on the floating system. is a generalized nonlinear term, which is the system displacement and speed Function of

[0015] S12: Determine the linearized floating system motion control equations:

[0016] The nonlinear term in the nonlinear floating system motion control equation obtained in step S11 is Move to the right side of the equation and regard it as an equivalent external load term to obtain the linearized floating system motion control equation:

[0017] .

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

[0019] S21: Define nonlinear external load as 0 and calculate external load The displacement response of the floating system Responsiveness :

[0020] S22: External load Perform Fourier decomposition and transform the external load Expressed as a Fourier series:

[0021] ;

[0022] in: For the discrete frequency values, is the frequency number, is the frequency resolution, It corresponds to The complex coefficients of It is the maximum value of discrete frequency sequence number in the process of Fourier decomposition calculation;

[0023] S23: External load Performing Laplace transform, we get Laplace transform of for:

[0024] ;

[0025] in, For function The poles, complex coefficients for The remainder of is a complex variable;

[0026] S24: Determine the polar residue characterization model of the floating structure in the Laplace domain:

[0027] ;

[0028] The Laplace domain pole residue method is used to calculate the external loads on the floating structure. Displacement response of external load under action :

[0029] ;

[0030] in, is the transfer function of the floating structure in the Laplace domain, is the Laplace domain pole, is the residue in the Laplace domain, are the numbers of Laplace domain poles and Laplace domain residues, is the number of Laplace domain poles and Laplace domain residues;

[0031] S25: External load displacement response Written in extreme residue form:

[0032] ;

[0033] in, is the corresponding Laplace domain pole The response residue of For the corresponding pole The response residues are expressed as:

[0034] ;

[0035] ;

[0036] S26: Calculate displacement response to external loads and external load velocity response :

[0037] right Perform inverse Laplace transform to obtain the external load displacement response in the time domain expression:

[0038] ;

[0039] Displacement response to external load in time domain About time Derivative, get the external load velocity response expression

[0040] .

[0041] In some embodiments of the present invention, step S4 includes:

[0042] S41: Define nonlinear The intermediate value of the segmented displacement response is , nonlinear The intermediate value of the segmented speed response is , , is an integer; nonlinear The intermediate quantity of the segmented displacement response and the nonlinear The initial value of the intermediate quantity of the segmented speed response is set to zero: , ;like , execute steps S42 to S44, if , execute steps S45 to S47;

[0043] S42: The external load caused by the external load calculated in step S3 is Segmented displacement response With the nonlinear term Initial value of intermediate displacement of segment Add together and get the floating system The first calculation value of the piecewise nonlinear displacement response , external load Segmented speed response With nonlinear Initial value of intermediate value of segmented speed response Add together and get the floating system First calculation value of piecewise nonlinear velocity response :

[0044] ;

[0045] ;

[0046] The above obtained , Substitute nonlinear external load function In the The first calculated value of the piecewise nonlinear external load term ;

[0047] Based on the said The first calculation value of the piecewise nonlinear external load term is calculated by using the extreme residue method to obtain the second calculation value of the floating structure caused by the nonlinear external load term. Intermediate value of segmented displacement response and speed response intermediate ;

[0048] Calculate the difference between the intermediate values ​​of two adjacent displacement responses and define the nonlinear displacement response error: ,in, Indicates the absolute value operation. To obtain the maximum value of the function;

[0049] S43: If the nonlinear displacement response error Greater than the set threshold , then use the nonlinear Intermediate value of segmented displacement response Instead of the initial value of the intermediate amount of nonlinear displacement response in step S42 , using the nonlinear Segmented speed response intermediate value Replace the initial value of the intermediate amount of nonlinear speed response in S42 Repeat step S42, iterate and calculate to obtain the nonlinear Intermediate value of segmented displacement response And nonlinear Segmented speed response intermediate value The calculated value until the error of two adjacent nonlinear displacement responses is Less than the set threshold , then stop the calculation;

[0050] The nonlinearity of the floating structure calculated at this time Intermediate value of segmented displacement response and nonlinear Segmented speed response intermediate value , as the nonlinear term, the dynamic nonlinearity of the floating system is finally Segmental displacement response components and the nonlinear final Segmented velocity response components ;

[0051] S44: Use external load Segmental displacement response components and the nonlinear final Segmental displacement response components Determine the nonlinearity of the floating system Segmented displacement response:

[0052] ;

[0053] Using external load Segmented velocity response components and the nonlinear final Segmented velocity response components Determine the nonlinearity of the floating system Segmented speed response:

[0054] ;

[0055] The nonlinear floating system Segmented displacement response, nonlinear floating system Segmented velocity response, substituting into nonlinear external load function In the The piecewise nonlinear external load is ;

[0056] S45: The final nonlinearity is determined Segmental displacement response components and the nonlinear final Segmented velocity response components , update the nonlinear The initial value of the intermediate quantity of the segmented displacement response and the nonlinear The initial value of the intermediate quantity of the segmented speed response corresponds to the The value of the segment duration is obtained by updating the nonlinear Initial value of intermediate quantity of segmented displacement response , and nonlinear Initial value of intermediate value of segmented speed response ;

[0057] Will The external load caused by the external load calculated in step S3 Segmented displacement response Add together and get the floating system The first calculation value of the piecewise nonlinear displacement response ,Will The external load caused by the external load calculated in step S3 Segmented speed response Add together and get the floating system The first calculation value of piecewise nonlinear velocity response :

[0058] ;

[0059] ;

[0060] The above obtained , , bringing in the nonlinear external load function In the The first calculated value of the piecewise nonlinear external load term ;

[0061] Based on The first calculation value of the piecewise nonlinear external load term is calculated by using the extreme residue method to obtain the second calculation value of the floating structure caused by the nonlinear external load term. Intermediate value of segmented displacement response and speed response intermediate ;

[0062] Calculate the nonlinear displacement response error: ,in, Indicates the absolute value operation. To obtain the maximum value of the function;

[0063] S46: If the response error Greater than the set threshold , then use the Intermediate value of segmented displacement response Instead of the initial value of the intermediate amount of nonlinear displacement response in step S45 , use the Segmented speed response intermediate value Replace the initial value of the intermediate amount of nonlinear speed response in S45 , repeat step S45 until the two adjacent nonlinear displacement response errors are Less than the set threshold , then stop the calculation;

[0064] The nonlinear first Intermediate value of segmented displacement response and nonlinear Segmented speed response intermediate value , as the nonlinear term, the dynamic nonlinearity of the floating system is finally Segmental displacement response components and the nonlinear final Segmented velocity response components ;

[0065] S47: Use external load Segmental displacement response components and the nonlinear final Segmental displacement response components Determine the nonlinear floating system Segmented displacement response:

[0066] ;

[0067] Using external load Segmented velocity response components and the nonlinear final Segmented velocity response components Determine the nonlinear floating system Segmented speed response:

[0068] ;

[0069] The nonlinear floating system Segmented displacement response, nonlinear floating system Segmented velocity response, substituting into nonlinear external load function In the The piecewise nonlinear external load is .

[0070] In some embodiments of the present invention: step S5 includes:

[0071] Repeat S45, after After calculation, the total displacement response of the nonlinear floating system is obtained:

[0072] ;

[0073] The total velocity response of a nonlinear floating system:

[0074] .

[0075] In some embodiments of the present invention: Pick .

[0076] The present invention proposes a nonlinear floating system pole residue dynamic analysis method based on discontinuous segmentation to solve the technical defects of the current nonlinear floating system dynamic analysis method. Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0077] 1. The present invention is based on the Laplace domain pole residue analysis method of linear floating structure, and introduces the discontinuous response segment solution technology. The segments all start from time zero, avoiding the complex fluid memory effect and non-zero initial condition calculation problems caused by the time-continuous segment calculation response. At the same time, it can solve the technical defects of the existing analysis method such as the need for deconvolution terms, fluid memory effect and self-oscillation response components, and the calculation theory is clearer and more complete, and the calculation efficiency is greatly improved.

[0078] 2. The present invention utilizes the Laplace domain pole residue method to solve the analytical response in segments, thus avoiding the tedious numerical calculations based on small-step time domain step-by-step solutions, improving efficiency while also achieving high computational accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] 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.

[0080] Figure 1 To invent a flow chart of a nonlinear floating system pole residue dynamic analysis method based on discontinuous segmentation;

[0081] Figure 2 The external load in the present invention The displacement response of the linearized system induced result;

[0082] Figure 3 The external load in the present invention The displacement response of the linearized system induced Segmented graph;

[0083] Figure 4 The nonlinear external load is calculated by the method of the present invention The first displacement response induced ;

[0084] Figure 5 The present invention calculates the displacement response of the first segment of the floating system Comparison chart with the calculation results of the time domain method;

[0085] Figure 6 The first piecewise nonlinear external load is obtained by the method of the present invention Schedule;

[0086] Figure 7 This is a comparison chart of the total response of the nonlinear floating system obtained by the method of the present invention and the calculation results of the time domain method. DETAILED DESCRIPTION

[0087] 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.

[0088] The present invention provides a nonlinear floating system pole residue dynamic analysis method based on discontinuous segmentation, comprising the following steps:

[0089] S1: Determine the motion control equation of the floating system. The motion control equation includes linear terms and nonlinear terms. Separate the nonlinear terms from the motion control equation to obtain the linearized motion control equation of the floating system. The nonlinear terms are used as nonlinear external loads of the floating system.

[0090] In some implementations of the present invention, step S1 includes:

[0091] S11: Determine the governing equations for the motion of the nonlinear floating system:

[0092] ;

[0093] in, is the mass of the floating system, is the additional mass of the floating system at infinite frequency, is the acceleration of the floating system, is the time delay function of the floating system, is a dummy time variable, is the floating system movement speed, is the hydrostatic restoring stiffness coefficient, is the floating system displacement, is the external load of the floating system, that is, the surface wave force on the floating system. is a generalized nonlinear term, which is the system displacement and speed Function of

[0094] S12: Determine the linearized floating system motion control equations:

[0095] The nonlinear term in the nonlinear floating system motion control equation obtained in step S11 is Move to the right side of the equation and regard it as an equivalent external load term to obtain the linearized floating system motion control equation:

[0096] .

[0097] S2: Based on the linearized motion control equations of the floating system, the external loads are solved using the Laplace domain pole residue method Motion response of floating structures under excitation to external loads in the time domain, including displacement response to external loads in the time domain and the velocity response of the external load in the time domain .

[0098] In some embodiments of the present invention, step S2 includes:

[0099] S21: Define nonlinear external load as 0 and calculate external load The displacement response of the floating system Responsiveness :

[0100] S22: External load Perform Fourier decomposition and transform the external load Expressed as a Fourier series:

[0101] ;

[0102] in: For the discrete frequency values, is the frequency number, is the frequency resolution, It corresponds to The complex coefficients of It is the maximum value of discrete frequency sequence number in the process of Fourier decomposition calculation;

[0103] S23: External load Performing Laplace transform, we get Laplace transform of for:

[0104] ;

[0105] in, For function The poles, complex coefficients for The remainder of is a complex variable;

[0106] S24: Determine the polar residue characterization model of the floating structure in the Laplace domain:

[0107] ;

[0108] The Laplace domain pole residue method is used to calculate the external loads on the floating structure. Displacement response of external load under action :

[0109] ;

[0110] in, is the transfer function of the floating structure in the Laplace domain, is the Laplace domain pole, is the residue in the Laplace domain, are the numbers of Laplace domain poles and Laplace domain residues, is the number of Laplace domain poles and Laplace domain residues;

[0111] S25: External load displacement response Written in extreme residue form:

[0112] ;

[0113] in, is the corresponding Laplace domain pole The response residue of For the corresponding pole The response residues are expressed as:

[0114] ;

[0115] ;

[0116] S26: Calculate displacement response to external loads and external load velocity response :

[0117] right Perform inverse Laplace transform to obtain the external load displacement response in the time domain expression:

[0118] ;

[0119] Displacement response to external load in time domain About time Derivative, get the external load velocity response expression

[0120] .

[0121] S3: From the start time First, the time domain external load motion response of the floating structure is divided into Segment, The segment duration is ,in ,get The external load segmented response of the floating system includes the external load segmented response. Segmented displacement response , and the external load Segmented speed response ;in, is the duration of external load action.

[0122] Based on the segmentation method of the external load motion response provided by the present invention, the duration of each segment of the external load motion response is different. As the time increases, the duration of the corresponding segment also increases.

[0123] S4: Use the Laplace domain pole residue method to iteratively solve the corresponding In the segmented response, the nonlinear external load motion response component caused by the nonlinear external load is obtained. Segmented response, including nonlinear Segmented displacement response , and nonlinear Segmented speed response , and compare it with the external load in step S3 The external load caused The nonlinear first order of the floating system is obtained by superposing the segmented responses. Segmented response, including floating system nonlinearity Segmented displacement response , and the floating system nonlinear Segmented speed response .

[0124] In some embodiments of the present invention, the specific execution method of step S4 is as follows.

[0125] S41: Define nonlinear The intermediate value of the segmented displacement response is , nonlinear The intermediate value of the segmented speed response is , , is an integer; nonlinear The intermediate quantity of the segmented displacement response and the nonlinear The initial value of the intermediate quantity of the segmented speed response is set to zero: , .

[0126] according to The specific calculation method of step S4 is different. , execute steps S42 to S44, if , execute steps S45 to S47.

[0127] S42: The external load caused by the external load calculated in step S3 is Segmented displacement response With the nonlinear term Initial value of intermediate displacement of segment Add together and get the floating system The first calculation value of the piecewise nonlinear displacement response , external load Segmented speed response With nonlinear Initial value of intermediate value of segmented speed response Add together and get the floating system First calculation value of piecewise nonlinear velocity response :

[0128] ;

[0129] ;

[0130] The above obtained , Substitute nonlinear external load function In the The first calculated value of the piecewise nonlinear external load term ;

[0131] Based on the said The first calculation value of the piecewise nonlinear external load term is calculated by using the extreme residue method to obtain the second calculation value of the floating structure caused by the nonlinear external load term. Intermediate value of segmented displacement response and speed response intermediate ;

[0132] Calculate the difference between the intermediate values ​​of two adjacent displacement responses and define the nonlinear displacement response error: ,in, Indicates the absolute value operation. To obtain the maximum value of the function;

[0133] S43: If the nonlinear displacement response error Greater than the set threshold , then use the nonlinear Intermediate value of segmented displacement response Instead of the initial value of the intermediate amount of nonlinear displacement response in step S42 , using the nonlinear Segmented speed response intermediate value Replace the initial value of the intermediate amount of nonlinear speed response in S42 Repeat step S42, iterate and calculate to obtain the nonlinear Intermediate value of segmented displacement response And nonlinear Segmented speed response intermediate value The calculated value until the error of two adjacent nonlinear displacement responses is Less than the set threshold , then stop the calculation;

[0134] The nonlinear first Intermediate value of segmented displacement response and nonlinear Segmented speed response intermediate value , as the nonlinear term, the dynamic nonlinearity of the floating system is finally Segmental displacement response components and the nonlinear final Segmented velocity response components ;

[0135] S44: Use external load Segmental displacement response components and the nonlinear final Segmental displacement response components Determine the nonlinearity of the floating system Segmented displacement response:

[0136] ;

[0137] Using external load Segmented velocity response components and the nonlinear final Segmented velocity response components Determine the nonlinearity of the floating system Segmented speed response:

[0138] ;

[0139] The nonlinear floating system Segmented displacement response, nonlinear floating system Segmented velocity response, substituting into nonlinear external load function In the The piecewise nonlinear external load is ;

[0140] S45: The final nonlinearity is determined Segmental displacement response components and the nonlinear final Segmented velocity response components , update the nonlinear The initial value of the intermediate quantity of the segmented displacement response and the nonlinear The initial value of the intermediate quantity of the segmented speed response corresponds to the The value of the segment duration is obtained by updating the nonlinear Initial value of intermediate quantity of segmented displacement response , and nonlinear Initial value of intermediate quantity of segmented speed response ;

[0141] Will The external load caused by the external load calculated in step S3 Segmented displacement response Add together and get the floating system The first calculation value of the piecewise nonlinear displacement response ,Will The external load caused by the external load calculated in step S3 Segmented speed response Add together and get the floating system The first calculation value of piecewise nonlinear velocity response :

[0142] ;

[0143] ;

[0144] The above obtained , , bringing in the nonlinear external load function In the The first calculated value of the piecewise nonlinear external load term ;

[0145] Based on The first calculation value of the piecewise nonlinear external load term is calculated by using the extreme residue method to obtain the second calculation value of the floating structure caused by the nonlinear external load term. Intermediate value of segmented displacement response and speed response intermediate ;

[0146] Calculate the nonlinear displacement response error: ,in, Indicates the absolute value operation. To obtain the maximum value of the function;

[0147] S46: If the response error Greater than the set threshold , then use the Intermediate value of segmented displacement response Instead of the initial value of the intermediate amount of nonlinear displacement response in step S45 , use the Segmented speed response intermediate value Replace the initial value of the intermediate amount of nonlinear speed response in S45 , repeat step S45 until the two adjacent nonlinear displacement response errors are Less than the set threshold , then stop the calculation;

[0148] The nonlinearity of the floating structure calculated at this time Intermediate value of segmented displacement response and nonlinear Segmented speed response intermediate value , as the nonlinear term, the dynamic nonlinearity of the floating system is finally Segmental displacement response components and the nonlinear final Segmented velocity response components ;

[0149] S47: Use external load Segmental displacement response components and the nonlinear final Segmental displacement response components Determine the nonlinear floating system Segmented displacement response:

[0150] ;

[0151] Using external load Segmented velocity response components and the nonlinear final Segmented velocity response components Determine the nonlinear floating system Segmented speed response:

[0152] ;

[0153] The nonlinear floating system Segmented displacement response, nonlinear floating system Segmented velocity response, substituting into nonlinear external load function In the The piecewise nonlinear external load is

[0154] The following describes the execution process of steps S45 to S47 by taking the calculation of the second segment as an example.

[0155] S45: Order , the nonlinear final first Segmental displacement response components and the nonlinear final Segmented velocity response components , update the value of the first segment duration in the initial value of the intermediate amount of the nonlinear second segment displacement response and the initial value of the intermediate amount of the nonlinear second segment velocity response, and obtain the updated initial value of the intermediate amount of the nonlinear second segment displacement response , and the initial value of the intermediate value of the nonlinear second segment speed response ;

[0156] Will The external load caused by the external load calculated in step S3 Segmented displacement response Add together and get the floating system The first calculation value of the piecewise nonlinear displacement response ,Will The external load caused by the external load calculated in step S3 Segmented speed response Add together and get the floating system First calculation value of piecewise nonlinear velocity response :

[0157] ;

[0158] ;

[0159] The The first calculated value of the piecewise nonlinear external load term , , bringing in the nonlinear external load function In the The first calculated value of the piecewise nonlinear external load term ;

[0160] Based on this nonlinear external load time history, the pole residue method is used to calculate the floating structure caused by the nonlinear external load term. Intermediate value of segmented displacement response and speed response intermediate ;

[0161] Calculate the error between two consecutive nonlinear displacement responses ,in, Indicates the absolute value operation. To obtain the maximum value of the function;

[0162] S46: If the response error Greater than the set threshold , then use the Intermediate value of segmented displacement response Instead of the initial value of the intermediate amount of nonlinear displacement response in step S45 , use the Segmented speed response intermediate value Replace the initial value of the intermediate amount of nonlinear speed response in S45 , repeat step S45 until the two adjacent nonlinear displacement response errors are Less than the set threshold , then stop the calculation;

[0163] The nonlinearity of the floating structure calculated at this time Intermediate value of segmented displacement response and nonlinear Segmented speed response intermediate value , as the nonlinear term, the dynamic nonlinearity of the floating system is finally Segmental displacement response components and the nonlinear final Segmented velocity response components ;

[0164] S47: Use external load Segmental displacement response components and the nonlinear final Segmental displacement response components Determine the nonlinear floating system Segmented displacement response:

[0165] ;

[0166] Using external load Segmented velocity response components and the nonlinear final Segmented velocity response components Determine the nonlinear floating system Segmented speed response:

[0167] ;

[0168] The nonlinear floating system Segmented displacement response, nonlinear floating system Segmented velocity response, substituting into nonlinear external load function In the The piecewise nonlinear external load is .

[0169] S5: Repeat step S4 until n=N, and obtain the total displacement response of the nonlinear floating system and the overall speed response .

[0170] It should be understood that, by repeating S45, After calculation, the total displacement response of the nonlinear floating system is obtained:

[0171] ;

[0172] The total velocity response of a nonlinear floating system:

[0173] .

[0174] In some embodiments of the present invention: Pick .

[0175] Hereinafter, an analytical nonlinear floating system is taken as an example to illustrate the specific implementation effect of the method provided by the present invention.

[0176] .

[0177] Among them, the mass of the floating structure =2.5, additional mass , recovery stiffness , the delay function has the following analytical expression , the nonlinear term is selected as follows: , external load , The duration is 40 seconds and the sampling interval is 0.01 seconds.

[0178] According to the pole residue theory, the four analytical poles of the transfer function of the floating structure are determined: , , and the corresponding 4 analytical residues , ; At the same time, the two analytical poles of the time delay function of the floating structure are determined: , and the corresponding two analytical residues .

[0179] In the implementation, it is first assumed that the floating structure is initially in a static state, and the external load is calculated by using the present invention. The linearized system dynamic response induced by Figure 2 is the calculated displacement response time history of the external load .Will Divided into two sections, the first section Duration: 20 seconds, second segment The duration is 40 seconds, and all start from time zero. Figure 3 yes Set the iterative convergence threshold , the nonlinear external load is calculated by the method of the present invention The first segment response component induced ,like Figure 4 As shown, the convergence is achieved after 12 iterations. Figure 5 The total response of the first segment is calculated by the present invention Compared with the calculation results of the time domain method (fourth-order Runge-Kutta method), the two are in good agreement.

[0180] According to the calculation results of the first segment response, the first segment nonlinear external load is determined. ,See Figure 6, and update the second segmented nonlinear external load term according to it. Further applying the method of the present invention, the second segmented response of the floating system caused by the nonlinear external load term is calculated. , iterate 15 times to reach convergence, and Add the second segment response of the nonlinear floating system , since there are 2 segments in this example, That is, the total response of the nonlinear system. The comparison between the results calculated by the time domain method and the results of the time domain method is shown in Figure 7 The two are in good agreement, which confirms the effectiveness of the method of the present invention.

[0181] The load segmentation time interval in the present invention is 20 seconds, which is much longer than the 0.01 second time interval used in the numerical step solution of the time domain method, effectively improving the calculation efficiency; in addition, the segmentation of the present invention starts from time zero, avoiding the fluid memory effect and self-oscillation response solution problems caused by continuous segmentation solution, and the calculation efficiency is further improved.

[0182] 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 nonlinear floating system pole residue dynamic analysis method based on discontinuous segmentation, characterized in that: The following steps are involved: S1: determining a motion control equation of a floating system, wherein the motion control equation includes a linear term and a nonlinear term, separating the nonlinear term from the motion control equation, and obtaining a linearized motion control equation of the floating system; the nonlinear term is used as a nonlinear external load of the floating system; S2: Based on the linearized motion control equations of the floating system, the external loads are solved using the Laplace domain pole residue method Motion response of floating structures under excitation to external loads in the time domain, including displacement response to external loads in the time domain and the velocity response of the external load in the time domain ; S3: From the start time First, the time domain external load motion response of the floating structure is divided into N segments of different lengths. The segment duration is ,in ,get The external load segmented response of the floating system includes the external load segmented response. Segmented displacement response , and the external load Segmented speed response ;in, is the duration of external load action; S4: Use the Laplace domain pole residue method to iteratively solve the corresponding In the segmented response, the nonlinear external load motion response component caused by the nonlinear external load is obtained. Segmented response, including nonlinear Segmented displacement response , and nonlinear Segmented speed response , and compare it with the external load in step S3 The external load caused The nonlinear first order of the floating system is obtained by superposing the segmented responses. Segmented response, including floating system nonlinearity Segmented displacement response , and the floating system nonlinear Segmented speed response ; S5: Repeat step S4 until n=N, and obtain the total response of the nonlinear floating system, including the total displacement response of the floating system and the overall speed response of the floating system ; Step S2 includes: S21: Define nonlinear external load as 0 and calculate external load The displacement response of the floating system Responsiveness : S22: External load Perform Fourier decomposition and transform the external load 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 It is the maximum value of discrete frequency sequence number in the process of Fourier decomposition calculation; S23: External load Performing Laplace transform, we get Laplace transform of for: ； in, For function The poles, complex coefficients for The remainder of is a complex variable; S24: Determine the polar residue characterization model of the floating structure in the Laplace domain: ； The Laplace domain pole residue method is used to calculate the external loads on the floating structure. Displacement response of external load under action : ； in, is the transfer function of the floating structure in the Laplace domain, is the Laplace domain pole, is the residue in the Laplace domain, are the numbers of Laplace domain poles and Laplace domain residues, is the number of Laplace domain poles and Laplace domain residues; S25: External load displacement response Written in extreme residue form: ； in, is the corresponding Laplace domain pole The response residue of For the corresponding pole The response residues are expressed as: ； ； S26: Calculate displacement response to external loads and external load velocity response : right Perform inverse Laplace transform to obtain the external load displacement response in the time domain expression: ； Displacement response to external load in time domain About time Derivative, get the external load velocity response expression ； Step S4 includes: S41: Define nonlinear The intermediate value of the segmented displacement response is , nonlinear The intermediate value of the segmented speed response is , , is an integer; nonlinear The intermediate quantity of the segmented displacement response and the nonlinear The initial value of the intermediate quantity of the segmented speed response is set to zero: , ;like , execute steps S42 to S44, if , execute steps S45 to S47; S42: The external load caused by the external load calculated in step S3 is Segmented displacement response With the nonlinear term Initial value of intermediate displacement of segment Add together and get the floating system The first calculation value of the piecewise nonlinear displacement response , external load Segmented speed response With nonlinear Initial value of intermediate value of segmented speed response Add together and get the floating system First calculation value of piecewise nonlinear velocity response : ； ； The above obtained , Substitute nonlinear external load function In the The first calculated value of the piecewise nonlinear external load term ; Based on the said The first calculation value of the piecewise nonlinear external load term is calculated by using the extreme residue method to obtain the second calculation value of the floating structure caused by the nonlinear external load term. Intermediate value of segmented displacement response and speed response intermediate ; Calculate the difference between the intermediate values ​​of two adjacent displacement responses and define the nonlinear displacement response error: ,in, Indicates the absolute value operation. To obtain the maximum value of the function; S43: If the nonlinear displacement response error Greater than the set threshold , then use the nonlinear Intermediate value of segmented displacement response Instead of the initial value of the intermediate amount of nonlinear displacement response in step S42 , using the nonlinear Segmented speed response intermediate value Replace the initial value of the intermediate amount of nonlinear speed response in S42 Repeat step S42, iterate and calculate to obtain the nonlinear Intermediate value of segmented displacement response And nonlinear Segmented speed response intermediate value The calculated value until the error of two adjacent nonlinear displacement responses is Less than the set threshold , then stop the calculation; The nonlinear first Intermediate value of segmented displacement response and nonlinear Segmented speed response intermediate value , as the nonlinear term, the dynamic nonlinearity of the floating system is finally Segmental displacement response components and the nonlinear final Segmented velocity response components ; S44: Use external load Segmental displacement response components and the nonlinear final Segmental displacement response components Determine the nonlinearity of the floating system Segmented displacement response: ； Using external load Segmented velocity response components and the nonlinear final Segmented velocity response components Determine the nonlinearity of the floating system Segmented speed response: ； The nonlinear floating system Segmented displacement response, nonlinear floating system Segmented velocity response, substituting into nonlinear external load function In the The piecewise nonlinear external load is ; S45: The final nonlinearity is determined Segmental displacement response components and the nonlinear final Segmented velocity response components , update the nonlinear The initial value of the intermediate quantity of the segmented displacement response and the nonlinear The initial value of the intermediate quantity of the segmented speed response corresponds to the The value of the segment duration is obtained by updating the nonlinear Initial value of intermediate quantity of segmented displacement response , and nonlinear Initial value of intermediate value of segmented speed response ; Will The external load caused by the external load calculated in step S3 Segmented displacement response Add together and get the floating system The first calculation value of the piecewise nonlinear displacement response ,Will The external load caused by the external load calculated in step S3 Segmented speed response Add together and get the floating system The first calculation value of piecewise nonlinear velocity response : ； ； The above obtained , , bringing in the nonlinear external load function In the The first calculated value of the piecewise nonlinear external load term ; Based on The first calculation value of the piecewise nonlinear external load term is calculated by using the extreme residue method to obtain the second calculation value of the floating structure caused by the nonlinear external load term. Intermediate value of segmented displacement response and speed response intermediate ; Calculate the nonlinear displacement response error: ,in, Indicates the absolute value operation. To obtain the maximum value of the function; S46: If the response error Greater than the set threshold , then use the Intermediate value of segmented displacement response Instead of the initial value of the intermediate amount of nonlinear displacement response in step S45 , use the Segmented speed response intermediate value Replace the initial value of the intermediate amount of nonlinear speed response in S45 , repeat step S45 until the two adjacent nonlinear displacement response errors are Less than the set threshold , then stop the calculation; The nonlinear first Intermediate value of segmented displacement response and nonlinear Segmented speed response intermediate value , as the nonlinear term, the dynamic nonlinearity of the floating system is finally Segmental displacement response components and the nonlinear final Segmented velocity response components ; S47: Use external load Segmental displacement response components and the nonlinear final Segmental displacement response components Determine the nonlinear floating system Segmented displacement response: ； Using external load Segmented velocity response components and the nonlinear final Segmented velocity response components Determine the nonlinear floating system Segmented speed response: ； The nonlinear floating system Segmented displacement response, nonlinear floating system Segmented velocity response, substituting into nonlinear external load function In the The piecewise nonlinear external load is .

2. A nonlinear floating system pole residue dynamic analysis method based on discontinuous segmentation as claimed in claim 1, characterized in that: Step S1 includes: S11: Determine the governing equations for the motion of the nonlinear floating system: ； in, is the mass of the floating system, is the additional mass of the floating system at infinite frequency, is the acceleration of the floating system, is the time delay function of the floating system, is a dummy time variable, is the floating system movement speed, is the hydrostatic restoring stiffness coefficient, is the floating system displacement, is the external load of the floating system, that is, the surface wave force on the floating system. is a generalized nonlinear term, which is the system displacement and speed Function of S12: Determine the linearized floating system motion control equations: The nonlinear term in the nonlinear floating system motion control equation obtained in step S11 is Move to the right side of the equation and regard it as an equivalent external load term to obtain the linearized floating system motion control equation: 。 3. The nonlinear floating system pole residue dynamic analysis method based on discontinuous segmentation according to claim 1 is characterized in that: Step S5 includes: Repeat S45, after After calculation, the total displacement response of the nonlinear floating system is obtained: ； The total velocity response of a nonlinear floating system: 。 4. The nonlinear floating system pole residue dynamic analysis method based on discontinuous segmentation according to claim 1 is characterized in that: Pick .

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