CN112434428B - Ship transverse-swinging nonlinear dynamics analysis method in regular wave - Google Patents

Abstract

The invention discloses a ship transverse throwing nonlinear dynamics analysis method in regular waves, which comprises the following steps: establishing a bow-rolling motion differential equation of the ship in a regular wave; determining the boundary of a stable domain and an unstable domain of the ship in the transverse throwing motion according to a nonlinear dynamics theory, obtaining a stable domain schematic diagram of a ship yawing motion differential equation solution, and obtaining a theoretical critical value of a parameter excitation term coefficient in the yawing motion differential equation according to the stable domain schematic diagram; calculating the bifurcation characteristic of the ship heading motion by adopting a numerical method based on a bifurcation nonlinear dynamics theory to obtain a bifurcation diagram of the ship heading angle along with the wave height so as to determine the reliability of a theoretical critical value of a parameter excitation term coefficient; and determining the critical condition of the ship for the transverse throwing according to the stability domain schematic diagram. The method adopts a nonlinear dynamics analysis method to analyze the stability region of the safe navigation of the ship for the transverse throwing motion of the ship in the regular wave, and provides an analysis method and a safe navigation basis for the safe navigation of the ship.

Description

A nonlinear dynamic analysis method for ship lateral flutter in regular waves

technical field

The invention relates to nonlinear motion analysis of ships, in particular to a nonlinear dynamic calculation and analysis method for ships to laterally sling under the excitation of regular waves.

Background technique

The ship's wave-riding/slinging motion is one of the failure modes in the second-generation intact stability of ships. The nonlinear dynamic characteristics of the ship in the process of riding the wave/swinging motion are the most significant in the mode of ship instability. The ship roll motion instability mode means that when the ship sails in the waves, the rudder loses the control effect on the ship, and the ship turns sharply, and the ship may roll sharply during this process.

Numerical analysis methods are used in most studies on the lateral flutter motion of ships in regular waves. This method is directly calculated and can consider more complex factors in the model, but it can only consider one working condition at a time, and it is not easy to draw general conclusions. Therefore, seeking an efficient and accurate computational research method is beneficial to improve the understanding of the law of the ship's lateral fling motion in regular waves. Numerous studies have shown that the nonlinear dynamic method has the advantage of being accurate, simple and fast in calculation, and can intuitively obtain the stability domain of the ship's lateral sway motion in regular waves. However, there are few applications of nonlinear dynamics such as bifurcations to this problem.

SUMMARY OF THE INVENTION

The purpose of the present invention is to solve the limitation of the numerical method in the nonlinear sway motion of ships in regular waves, and proposes a nonlinear dynamic analysis method, which adopts nonlinear dynamics analysis for the sway motion of ships in regular waves. Methods The stability domain of the safe navigation of ships is analyzed, and the analysis method and safe navigation basis are provided for the safe navigation of ships.

The technical scheme adopted by the present invention is: a nonlinear dynamic analysis method for ship lateral flutter in regular waves, comprising the following steps:

Step 1, establish the differential equation of the ship's yaw motion in regular waves, and determine the coefficients in the differential equation of the ship's yaw motion;

Step 2: According to the nonlinear dynamics theory, determine the boundary of the stable domain and the unstable domain where the ship has lateral sway motion, and obtain a schematic diagram of the stability domain of the solution of the differential equation of the ship's yaw motion. The theoretical critical value of the coefficient of the parameter excitation term in the differential equation of yaw motion is obtained from the schematic diagram of the domain;

Step 3: Based on the bifurcation nonlinear dynamics theory, numerical methods are used to calculate the bifurcation characteristics of the ship's yaw motion, and the bifurcation diagram of the ship's yaw angle with the wave height is obtained, and the numerical wave height is obtained according to the bifurcation diagram of the ship's yaw angle with the wave height. critical value to determine the reliability of the theoretical critical value of the parameter excitation term coefficient obtained in step 2;

Step 4: According to the stability domain diagram of the solution of the differential equation of the ship's yaw motion obtained in step 2, determine the critical condition for the ship to roll and make a reasonable forecast for the stability of the ship's yaw motion in waves.

Further, in step 1, the differential equation of the bow motion is:

I表示船体艏摇转动惯量，M表示作用在船体上的诱导力矩系数，N表示船体艏摇运动的阻尼系数；In the formula, ψ is the heading angle, F is the wave moment in the direction of the ship's yaw motion, δ is the rudder angle, K and T are the ship's maneuverability index, where,

I represents the moment of inertia of the hull yaw, M represents the induced moment coefficient acting on the hull, and N represents the damping coefficient of the hull yaw motion;

The coefficients in the differential equation of yaw motion are the moment of inertia I of hull yaw motion, the damping coefficient N of hull yaw motion, the coefficient of induced moment M acting on the hull, and the wave moment in the direction of yaw motion that the ship is subjected to. F, rudder angle δ, and ship maneuverability indices K, T;

Among them, the ship maneuverability indices K and T are obtained according to the empirical formula;

The rudder angle δ is shown in formula (2):

where k ₁ and k ₂ are rudder control parameters, and ψ _r is the target heading angle;

The wave moment F in the direction of the yaw motion experienced by the ship is determined according to the following method: the hydrodynamic calculation software SESAM is used to calculate the yaw wave moment of different waves downwards, given the encounter frequency of the ship in the actual sea state, the difference between the wave moment and the wave moment is calculated. The result is interpolated to obtain the first-order bowing wave moment corresponding to the downward direction of multiple waves at this encounter frequency. The wave moment is arranged according to the wave direction angle from small to large, and the wave moment is fitted, and the slope is the coefficient F ₀ The corresponding value, the wave moment F is fitted into the form shown in equation (3):

F=F ₀ ψcos(ω _e t) (3)

where ω _e is the encounter frequency and t is the time.

Further, step 2 further includes:

Substitute equations (2) and (3) into equation (1) to get:

According to the nonlinear dynamics theory, the yaw deviation angle ψ _△ is introduced, that is, ψ _△ =ψ-ψ _r , then the formula (4) is transformed into the following form:

为艏摇运动类固有频率；

为阻尼项的系数；

为参数激励项的系数，对于给定的船舶，h为和波高有关的一个量；

为外激励项的系数；In the formula,

is the natural frequency of yaw motion;

is the coefficient of the damping term;

is the coefficient of the parameter excitation term, and for a given ship, h is a quantity related to the wave height;

is the coefficient of the external incentive term;

The time scale τ=ω ₀ t is introduced, and the following expression is obtained by substituting τ=ω ₀ t into equation (5):

为频率比；

为变换后的阻尼项的系数；

为变换后的外激励项的系数；In the formula,

is the frequency ratio;

is the coefficient of the transformed damping term;

is the coefficient of the transformed external excitation term;

Introducing the small parameter ε, rearrange the formula (6) to get:

To study the subharmonic resonance of the bow motion, let the frequency ratio Ω satisfy Ω≈2, and introduce the frequency ratio tuning factor σ to describe the approximation degree between the frequency ratio Ω and 2, let:

Substituting equation (8) into equation (7), we get:

Suppose the solution of equation (9) is:

ψ _△ =ψ ₀ (T ₀ ,T ₁ )+εψ ₁ (T ₀ ,T ₁ ) (10)

In the formula, ψ _n is the n-order perturbation solution, n=0, 1, 2...; T ₀ =τ, is the variable representing the fast time scale; T ₁ =ετ, is the variable representing the slow time scale;

The calculation formula of the classical multi-scale method is introduced:

均表示对时间尺度求偏导数；In the formula,

Both represent partial derivatives with respect to the time scale;

Substitute equations (10), (11) and (12) into equation (9), and expand them according to the zero-order and first-order terms of ε, the partial differential equations shown in equations (13) and (14) are obtained Group:

Let the expression of the solution of Equation (13) be:

In the formula, A is a composite function; i is an imaginary unit;

Substitute equation (15) into equation (14) to get:

根据消除永年项条件，令式(16)中的永年项为零，如式(17)所示：In the formula,

According to the condition of eliminating the permanent year term, let the permanent year term in equation (16) be zero, as shown in equation (17):

After eliminating the Yongnian term, the first-order approximate solution of Equation (9) is obtained as:

In the formula, θ is a variable representing the phase, and the variable θ and the variable r are determined by equations (19) and (20):

Because considering equation (21):

Substitute equation (17) into equation (21) to get:

The approximate solution of formula (22) is

A=B _r +iB _i ε (23)

In the formula, B _r and B _i are both represented as real numbers. After substituting Equation (23) into Equation (22), and separating the real and imaginary parts of the equation, we get:

Let the solutions of equation (24) be:

In the formula, b _r and b _i are both constants, and υ is the boundary of the stable domain and the unstable domain. Substitute equation (25) into equation (24), and set the small parameter ε = 1, we get:

According to formula (26), take the frequency ratio Ω as the abscissa and the coefficient h of the parameter excitation term as the ordinate, draw the boundary of the stable domain and the unstable domain where the ship has lateral sway motion. The boundary of the stable domain and the unstable domain is A curve, the curve and the upper area of the curve are the unstable domain of the solution of the differential equation of the ship's yaw motion, and the lower area of the curve is the stable domain of the solution of the differential equation of the ship's yaw motion;

For a certain sea state, the encounter frequency ω _e of the ship is determined, and at the same time, for the ship, the natural frequency ω ₀ of the bowing class is also determined, then, in the determined sea state, the value of the frequency ratio Ω is determined; The coordinates of the lowest point of the curve shown by the boundary of the stable domain and the unstable domain where the ship has lateral swaying motion are obtained as (x, y), then, x is the value of the frequency ratio Ω in this sea state, and y is the parameter The theoretical critical value of the excitation term coefficient h.

Further, step 3 further comprises:

First, the wave height of the wave is selected as the bifurcation parameter, and the calculation range of the wave height is determined. For each wave height, the Runge-Kutta method is used to solve the differential equation of the ship's yaw motion in regular waves, and the equations of the yaw angle and the yaw angular velocity are obtained. Time history diagram, in which time is the abscissa, and the ship's yaw angle and yaw angular velocity are the ordinate;

Secondly, select a piece of data in the middle part of the time history graph of the ship's yaw angle and yaw angular velocity, the ordinate is the ship's yaw angular velocity, the abscissa is the ship's yaw angle, and the ship's motion phase diagram is obtained;

Then, according to the obtained ship motion phase diagram, select the section where the ship's yaw angular velocity is zero, and obtain the bifurcation diagram of the ship's yaw angle with the wave height. In the bifurcation diagram, when the wave height is lower than a certain value, the ship's is a stable periodic yaw motion, then at this wave height, a closed circle can be drawn on the bifurcation diagram; when the wave height is equal to a certain value, the ship's yaw motion begins to diverge, and it is no longer a stable back and forth Reciprocating periodic bow motion, at this time, a closed circle can no longer be drawn on the bifurcation diagram, then this value is the critical value of the numerical wave height;

Finally, according to the relationship between the coefficient h of the parameter excitation term and the wave height, the numerical critical value of the parameter excitation term coefficient corresponding to the critical value of the numerical wave height is obtained. According to the calculation results, the theoretical critical value of the parameter excitation term coefficient and the parameter excitation term coefficient The numerical critical value of is equal, which proves that the theoretical critical value of the parameter excitation term coefficient obtained in step 2 is reliable.

Further, in step 4, the critical condition for the ship to be laterally thrown is: when the parameter excitation term coefficient h reaches a value near the theoretical critical value of the parameter excitation term coefficient, the ship's laterally thrown and unstable motion will occur.

The beneficial effects of the present invention are:

1. A nonlinear dynamic calculation and analysis method for ships under the excitation of regular waves of the present invention can accurately predict the motion instability conditions of ships in regular waves, and solves the problem of solving the motion instability conditions of transverse waves. problem;

2. The present invention is based on modern nonlinear dynamic theory methods such as bifurcation, and the calculation result can directly obtain the stability domain of the ship's lateral sway motion in regular waves, with high solution accuracy and high efficiency;

3. The nonlinear dynamic calculation and analysis method of ships under the excitation action of regular waves of the present invention is suitable for various ship types and has strong versatility;

4. The present invention is used for the analysis theory and method of ship motion in waves, and is used in both ship design and ship navigation. This method is used to improve ship design and guide ships to overcome the risks of sailing in wind and waves to ensure navigation. Safety.

Description of drawings

Fig. 1: The flow chart of the nonlinear dynamic analysis method of ship lateral fling in regular waves according to the present invention;

Figure 2: The first-order wave moment transfer function of bowing;

Figure 3: a schematic diagram of the stability domain of the solution to the equation of motion of the ship's lateral throwing motion obtained by the present invention;

Figure 4: The bifurcation diagram of the ship's bow angle with wave height obtained by the present invention.

Detailed ways

In order to further understand the content of the invention, features and effects of the present invention, the following embodiments are exemplified and described in detail with the accompanying drawings as follows:

The invention combines the ship motion theory with the nonlinear dynamics theory, proposes a new measurement index and a new concept of ship motion instability, and establishes a nonlinear dynamics analysis method and analysis process.

As shown in Fig. 1, a nonlinear dynamic analysis method for ship lateral fling in regular waves includes the following steps:

1. First, establish the differential equation of the ship's yaw motion in regular waves:

I表示船体艏摇转动惯量，M表示作用在船体上的诱导力矩系数，N表示船体艏摇运动的阻尼系数。In the formula, ψ is the heading angle, F is the wave moment in the direction of the ship's yaw motion, δ is the rudder angle, K and T are the ship's maneuverability index, where,

I represents the moment of inertia of the hull yaw, M represents the induced moment coefficient acting on the hull, and N represents the damping coefficient of the hull yaw motion.

Secondly, determine the coefficients in the differential equation of the ship's yaw motion: the hull's yaw moment of inertia I, the damping coefficient N of the hull's yaw motion, the induced moment coefficient M acting on the hull, and the yaw motion in the direction of the ship's yaw motion. Wave moment F, rudder angle δ, and ship maneuverability indices K, T.

Among them, the ship maneuverability index K and T are obtained according to the empirical formula ^[1] .

The rudder angle δ is shown in formula (2):

In the formula, k ₁ and k ₂ are the rudder control parameters, and ψ _r is the target heading angle.

The wave moment F in the yaw motion direction of the ship is calculated by the hydrodynamic calculation software SESAM to calculate the yaw wave moment of different wave downwards, as shown in Fig. 2. Given the encounter frequency of the ship in the actual sea state, the result of the wave moment is interpolated to obtain the first-order yaw wave moment corresponding to multiple waves downward at this encounter frequency, and the wave moment is from small to large according to the wave direction angle. Arrange and fit the wave moment, the slope is the value corresponding to the coefficient F ₀ , and the wave moment F is fitted into the form shown in equation (3):

F=F ₀ ψcos(ω _e t) (3)

where ω _e is the encounter frequency and t is the time.

2. According to the nonlinear dynamics theory, determine the boundary of the stable domain and the unstable domain where the ship has lateral sway motion, and obtain the schematic diagram of the stability domain of the solution of the differential equation of the ship's yaw motion. The schematic diagram obtains the theoretical critical value of the coefficient of the parameter excitation term in the differential equation of the yaw motion. Specifically include:

Substitute equations (2) and (3) into equation (1) to get:

According to the nonlinear dynamics theory, the yaw deviation angle ψ _△ is introduced, that is, ψ _△ =ψ-ψ _r , then the formula (4) can be transformed into the following form:

为艏摇运动类固有频率；

为阻尼项的系数；

为参数激励项的系数，对于给定的船舶，h为和波高有关的一个量；

为外激励项的系数。In the formula,

is the natural frequency of yaw motion;

is the coefficient of the damping term;

is the coefficient of the parameter excitation term, and for a given ship, h is a quantity related to the wave height;

is the coefficient of the external excitation term.

The time scale τ=ω ₀ t is introduced, and the following expression is obtained by substituting τ=ω ₀ t into equation (5):

为频率比；

为变换后的阻尼项的系数；

为变换后的外激励项的系数。In the formula,

is the frequency ratio;

is the coefficient of the transformed damping term;

is the coefficient of the transformed extrinsic term.

To introduce the small parameter ε, it is necessary to set the small parameter ε = 1 after the calculation is completed and before the formula (26) is obtained, and rearrange the formula (6) to obtain:

To study the subharmonic resonance of the yaw motion, let the ratio of the encounter frequency to the natural frequency of the yaw motion satisfy Ω≈2, and introduce the frequency ratio tuning factor σ to describe the approximation degree between the frequency ratio Ω and 2, let:

Substituting equation (8) into equation (7), we get:

Suppose the solution of equation (9) is:

ψ _△ =ψ ₀ (T ₀ ,T ₁ )+εψ ₁ (T ₀ ,T ₁ ) (10)

In the formula, ψ _n is the n-order perturbation solution, n=0, 1, 2...; T ₀ =τ, is the variable representing the fast time scale; T ₁ =ετ, is the variable representing the slow time scale;

The calculation formula of the classical multi-scale method is introduced:

均表示对时间尺度求偏导数。In the formula,

Both represent partial derivatives with respect to the time scale.

Substitute equations (10), (11) and (12) into equation (9), and expand according to the zero-order term and first-order term of ε, the partial differential shown in equations (13) and (14) can be obtained equation set:

Let the expression of the solution of Equation (13) be:

In the formula, A is a composite function; i is an imaginary unit.

Substitute equation (15) into equation (14) to get:

根据消除永年项条件，令式(16)中的永年项为零，如式(17)所示：In the formula, cc represents the comprehensive term added up by the conjugate terms of the previous terms, that is,

According to the condition of eliminating the permanent year term, let the permanent year term in equation (16) be zero, as shown in equation (17):

After eliminating the Yongnian term, the first-order approximate solution of equation (9) can be obtained as ^[2] :

In the formula, θ is a variable representing the phase, and the variable θ and the variable r are determined by equations (19) and (20):

Because considering equation (21):

Substituting equation (17) into equation (21) can get:

The approximate solution of formula (22) is

A=B _r +iB _i ε (23)

In the formula, B _r and B _i are both represented as real numbers. After substituting Equation (23) into Equation (22), and separating the real and imaginary parts of the equation, we can get:

Let the solutions of equation (24) be:

In the formula, b _r and b _i are both constants, and υ is the boundary of the stable domain and the unstable domain. Substitute equation (25) into equation (24), and set the small parameter ε = 1, we get:

Equation (26) is to use the multi-scale method to solve the ship's yaw motion equation, to determine the stable and unstable domains of the ship's roll motion, and to obtain the boundaries of the stable and unstable domains.

According to Equation (26), taking the frequency ratio Ω as the abscissa and the coefficient h of the parameter excitation term as the ordinate, draw the boundary of the stable domain and the unstable domain where the ship has lateral sway motion, and obtain the stable domain of the solution of the ship's lateral sway motion equation A schematic diagram is shown in Figure 3. The boundary of the stable domain and the unstable domain is a curve, the curve and the upper area of the curve are the unstable domain of the solution of the differential equation of the ship's bow motion, that is, the conditions for the instability of the ship's rolling motion, and the lower area of the curve is the ship's bow. Stability domain for solutions to differential equations of shaking motion.

As can be seen from Figure 3, the coordinates of the lowest point of the curve are (x, y). For a certain sea state, the encounter frequency ω _e of the ship is determined, and at the same time, for the ship, the natural frequency ω ₀ of the bow class is also determined, then, in the determined sea state, the value of the frequency ratio Ω is determined, then, x is the value of the frequency ratio Ω in this sea state, and y is the theoretical critical value of the parameter excitation term coefficient h.

3. Based on the bifurcation nonlinear dynamics theory, numerical methods are used to calculate the bifurcation characteristics of the ship's bow motion, and the bifurcation diagram of the ship's bow angle with the wave height is obtained. According to the bifurcation diagram of the ship's bow angle with the wave height, the numerical wave height criticality is obtained. value to determine the reliability of the theoretical critical value of the parameter excitation term coefficient obtained in step 2. Specifically include:

First, the wave height of the wave is selected as the bifurcation parameter, and the calculation range of the wave height is determined. For each wave height, the Runge-Kutta method is used to solve the differential equation of the ship's yaw motion in regular waves, and the equations of the yaw angle and the yaw angular velocity are obtained. Time history diagram, in which time is the abscissa, and the ship's yaw angle and yaw rate are the ordinate.

Secondly, select a section of data in the middle part of the time history graph of the ship's yaw angle and yaw angular velocity, the ordinate is the ship's yaw angular velocity, the abscissa is the ship's yaw angle, and the ship's motion phase diagram is obtained.

Then, according to the obtained ship motion phase diagram, the section where the ship's yaw angular velocity is zero is selected, and the bifurcation diagram of the ship's yaw angle with wave height is obtained, as shown in Figure 4. In drawing the bifurcation diagram, when the wave height is lower than a certain value, the ship is in a stable periodic yaw motion, then under this wave height, a closed circle can be drawn on the bifurcation diagram; when the wave height is equal to At a certain value, the bow motion of the ship begins to diverge, and it is no longer a stable reciprocating periodic bow motion. At this time, a closed circle can no longer be drawn on the bifurcation diagram, so the value is Numerical wave height threshold.

Finally, according to the relationship between the coefficient h of the parameter excitation term and the wave height, the numerical critical value of the parameter excitation term coefficient corresponding to the critical value of the numerical wave height is obtained. According to the calculation results, the theoretical critical value of the parameter excitation term coefficient and the parameter excitation term coefficient The numerical critical value of is equal, which proves that the theoretical critical value of the parameter excitation term coefficient obtained in step 2 is reliable.

4. According to the stability domain diagram of the solution of the differential equation of the ship's yaw motion obtained in step 2, determine the critical condition of the ship's yaw motion, and make a reasonable forecast for the stability of the ship's yaw motion in waves.

As shown in Figure 3, the coordinates (x, y) of the lowest point of the curve are expressed as, when the frequency ratio Ω is x, the parameter excitation term h in the ship's bow motion equation reaches a value near y (y is as shown above, is the theoretical critical value of the parameter excitation term coefficient), the ship's yaw motion will occur, and at other frequency ratios, the ship's yaw motion is not easy to become unstable, that is, it is difficult to appear yaw. Through the stability analysis of the solution, the critical conditions for the occurrence of lateral fling can be determined. Through the schematic diagram of the stability domain of the solution of the equation of motion of the ship's lateral throw, the critical condition of the ship's lateral throw under a certain frequency ratio can be clearly seen, which proves that the result is convenient and easy to implement. method.

With the above methods, a reasonable forecast can be made for the stability of the ship's yaw motion in waves and the occurrence of yaw.

To sum up, the present invention proposes a nonlinear dynamic analysis method for ship lateral sway in regular waves based on the hydrodynamics and nonlinear dynamics theory of ships and marine engineering, and realizes the rapid solution of unstable motion conditions of ships through nonlinear dynamics. the goal of. Aiming at the nonlinear problem of the ship's sway motion in regular waves, the unstable dynamic conditions of the ship's sway are determined by the combination of numerical analysis and nonlinear dynamic theory, and the possible motion risk of the ship can be predicted. At present, there is no such analysis method at home and abroad.

references:

[1] Li Zongbo, Zhang Xianku, Zhang Yang. Prediction of ship maneuverability index K and T based on SPSS technology [J]. Navigation Technology, 2007(5): 2-5.

[2] Liu Zheng. Research on nonlinear dynamic characteristics of ships riding waves and swaying and pure loss of stability [D]. Tianjin University, 2020.

Although the preferred embodiments of the present invention have been described above with reference to the accompanying drawings, the present invention is not limited to the above-mentioned specific embodiments. Under the inspiration of the present invention, without departing from the spirit of the present invention and the protection scope of the claims, personnel can also make many forms, which all fall within the protection scope of the present invention.

Claims (5)

1. a nonlinear dynamic analysis method for ship lateral fling in a regular wave, is characterized in that, comprises the following steps: Step 1, establish the differential equation of the ship's yaw motion in regular waves, and determine the coefficients in the differential equation of the ship's yaw motion; Step 2: According to the nonlinear dynamics theory, determine the boundary of the stable domain and the unstable domain where the ship has lateral sway motion, and obtain a schematic diagram of the stability domain of the solution of the differential equation of the ship's yaw motion. The theoretical critical value of the coefficient of the parameter excitation term in the differential equation of yaw motion is obtained from the schematic diagram of the domain; Step 3: Based on the bifurcation nonlinear dynamics theory, numerical methods are used to calculate the bifurcation characteristics of the ship's yaw motion, and the bifurcation diagram of the ship's yaw angle with the wave height is obtained, and the numerical wave height is obtained according to the bifurcation diagram of the ship's yaw angle with the wave height. critical value to determine the reliability of the theoretical critical value of the parameter excitation term coefficient obtained in step 2; Step 4: According to the stability domain diagram of the solution of the differential equation of the ship's yaw motion obtained in step 2, determine the critical condition for the ship to roll and make a reasonable forecast for the stability of the ship's yaw motion in waves. 2. The nonlinear dynamic analysis method for ship lateral throwing in regular waves according to claim 1, is characterized in that, in step 1, described yaw motion differential equation is:

In the formula, ψ is the heading angle, F is the wave moment in the direction of the ship's yaw motion, δ is the rudder angle, K and T are the ship's maneuverability index, where,

I represents the moment of inertia of the hull yaw, M represents the induced moment coefficient acting on the hull, and N represents the damping coefficient of the hull yaw motion; The coefficients in the differential equation of yaw motion are the moment of inertia I of hull yaw motion, the damping coefficient N of hull yaw motion, the coefficient of induced moment M acting on the hull, and the wave moment in the direction of yaw motion that the ship is subjected to. F, rudder angle δ, and ship maneuverability indices K, T; Among them, the ship maneuverability indices K and T are obtained according to the empirical formula; The rudder angle δ is shown in formula (2):

where k ₁ and k ₂ are rudder control parameters, and ψ _r is the target heading angle; The wave moment F in the direction of the yaw motion experienced by the ship is determined according to the following method: the hydrodynamic calculation software SESAM is used to calculate the yaw wave moment of different waves downwards, given the encounter frequency of the ship in the actual sea state, the difference between the wave moment and the wave moment is calculated. The result is interpolated to obtain the first-order bowing wave moment corresponding to the downward direction of multiple waves at this encounter frequency. The wave moment is arranged according to the wave direction angle from small to large, and the wave moment is fitted, and the slope is the coefficient F ₀ The corresponding value, the wave moment F is fitted into the form shown in equation (3): F=F ₀ ψcos(ω _e t) (3) where ω _e is the encounter frequency and t is the time. 3. The nonlinear dynamic analysis method of ship transverse flutter in regular waves according to claim 2, is characterized in that, step 2 further comprises: Substitute equations (2) and (3) into equation (1) to get:

According to the nonlinear dynamics theory, the yaw deviation angle ψ _△ is introduced, that is, ψ _△ =ψ-ψ _r , then the formula (4) is transformed into the following form:

In the formula,

is the natural frequency of yaw motion;

is the coefficient of the damping term;

is the coefficient of the parameter excitation term, and for a given ship, h is a quantity related to the wave height;

is the coefficient of the external incentive term; The time scale τ=ω ₀ t is introduced, and the following expression is obtained by substituting τ=ω ₀ t into equation (5):

In the formula,

is the frequency ratio;

is the coefficient of the transformed damping term;

is the coefficient of the transformed external excitation term; Introducing the small parameter ε, rearrange the formula (6) to get:

To study the subharmonic resonance of the bow motion, let the frequency ratio Ω satisfy Ω≈2, and introduce the frequency ratio tuning factor σ to describe the approximation degree between the frequency ratio Ω and 2, let:

Substituting equation (8) into equation (7), we get:

Suppose the solution of equation (9) is: ψ _△ =ψ ₀ (T ₀ ,T ₁ )+εψ ₁ (T ₀ ,T ₁ ) (10) In the formula, ψ _n is the n-order perturbation solution, n=0, 1, 2...; T ₀ =τ, is the variable representing the fast time scale; T ₁ =ετ, is the variable representing the slow time scale; The calculation formula of the classical multi-scale method is introduced:

In the formula,

Both represent partial derivatives with respect to the time scale; Substitute equations (10), (11) and (12) into equation (9), and expand them according to the zero-order and first-order terms of ε, the partial differential equations shown in equations (13) and (14) are obtained Group:

Let the expression of the solution of Equation (13) be:

In the formula, A is a composite function; i is an imaginary unit; Substitute equation (15) into equation (14) to get:

In the formula,

According to the condition of eliminating the permanent year term, let the permanent year term in equation (16) be zero, as shown in equation (17):

After eliminating the Yongnian term, the first-order approximate solution of Equation (9) is obtained as:

In the formula, θ is a variable representing the phase, and the variable θ and the variable r are determined by equations (19) and (20):

Because considering equation (21):

Substitute equation (17) into equation (21) to get:

The approximate solution of formula (22) is A=B _r +iB _i ε (23) In the formula, B _r and B _i are both represented as real numbers. After substituting Equation (23) into Equation (22), and separating the real and imaginary parts of the equation, we get:

Let the solutions of equation (24) be:

In the formula, b _r and b _i are both constants, and υ is the boundary of the stable domain and the unstable domain. Substitute equation (25) into equation (24), and set the small parameter ε = 1, we get:

According to formula (26), take the frequency ratio Ω as the abscissa and the coefficient h of the parameter excitation term as the ordinate, draw the boundary of the stable domain and the unstable domain where the ship has lateral sway motion. The boundary of the stable domain and the unstable domain is A curve, the curve and the upper area of the curve are the unstable domain of the solution of the differential equation of the ship's yaw motion, and the lower area of the curve is the stable domain of the solution of the differential equation of the ship's yaw motion; For a certain sea state, the encounter frequency ω _e of the ship is determined, and at the same time, for the ship, the natural frequency ω ₀ of the bowing class is also determined, then, in the determined sea state, the value of the frequency ratio Ω is determined; The coordinates of the lowest point of the curve shown by the boundary of the stable domain and the unstable domain where the ship has lateral swaying motion are obtained as (x, y), then, x is the value of the frequency ratio Ω in this sea state, and y is the parameter The theoretical critical value of the excitation term coefficient h. 4. The nonlinear dynamic analysis method of ship transverse flutter in regular waves according to claim 1, is characterized in that, step 3 further comprises: First, the wave height of the wave is selected as the bifurcation parameter, and the calculation range of the wave height is determined. For each wave height, the Runge-Kutta method is used to solve the differential equation of the ship's yaw motion in regular waves, and the equations of the yaw angle and the yaw angular velocity are obtained. Time history diagram, in which time is the abscissa, and the ship's yaw angle and yaw angular velocity are the ordinate; Secondly, select a piece of data in the middle part of the time history graph of the ship's yaw angle and yaw angular velocity, the ordinate is the ship's yaw angular velocity, the abscissa is the ship's yaw angle, and the ship's motion phase diagram is obtained; Then, according to the obtained ship motion phase diagram, select the section where the ship's yaw angular velocity is zero, and obtain the bifurcation diagram of the ship's yaw angle with the wave height. In the bifurcation diagram, when the wave height is lower than a certain value, the ship's is a stable periodic yaw motion, then at this wave height, a closed circle can be drawn on the bifurcation diagram; when the wave height is equal to a certain value, the ship's yaw motion begins to diverge, and it is no longer a stable back and forth Reciprocating periodic bow motion, at this time, a closed circle can no longer be drawn on the bifurcation diagram, then this value is the critical value of the numerical wave height; Finally, according to the relationship between the coefficient h of the parameter excitation term and the wave height, the numerical critical value of the parameter excitation term coefficient corresponding to the critical value of the numerical wave height is obtained. According to the calculation results, the theoretical critical value of the parameter excitation term coefficient and the parameter excitation term coefficient The numerical critical value of is equal, which proves that the theoretical critical value of the parameter excitation term coefficient obtained in step 2 is reliable. 5. The nonlinear dynamic analysis method for ship lateral sling in regular waves according to claim 1, characterized in that, in step 4, the critical condition for the lateral slinging of the ship is: the parameter excitation term coefficient h reaches the parameter When the value of the excitation term coefficient is near the theoretical critical value, the ship's lateral flutter buckling motion will occur.

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