Impact load hydroelastic response analysis method considering time effect

Abstract

The invention discloses an impact load hydroelastic response analysis method considering a time effect, and relates to the field of ship structure safety, the method is based on a hydroelastic theory, a time domain hydroelastic response equation in a convolution form of a maritime work structure under the effect of a transient impact external load is constructed, and the time domain hydroelastic response equation is calculated. An external load item in the time domain hydroelastic response equation under the action of the transient impact external load further comprises a load item of the transient impact external load, and then converting a frequency domain hydroelastic calculation result into a time domain to obtain a generalized additional mass matrix, a time delay function matrix and a time domain generalized wave exciting force in an indirect time domain hydroelastic method; the time domain hydroelastic response equation is solved by combining the transient impact external load, the motion response and the external load response of the maritime work structure of any structure under any wave condition under the action of any transient impact external load can be analyzed, the technical vacancy of the industry is made up, and the application range is wide.

Description

Technical Field

[0001] The present application relates to the field of ship structure safety, and in particular to an analysis method for hydroelastic response of impact loads taking into account time effects. Background Art

[0002] In the case of sea-based rocket launches, collision accidents of marine structures, etc., marine structures will be subjected to extremely large transient impact external loads, which will affect their structural safety. Studying the impact of transient impact external loads on marine structures can be used to evaluate the structural safety of marine structures. However, with the development of offshore technology, marine structures have the characteristics of large-scale structures, complex configurations, and new materials, which leads to very complex problems. At present, there is no good method to analyze the impact of transient impact external loads on marine structures. Summary of the invention

[0003] In view of the above problems and technical requirements, this application proposes a method for analyzing the hydroelastic response of impact loads taking into account the time effect. The technical solution of this application is as follows:

[0004] A method for analyzing water elastic response of impact load taking into account time effect, the method comprising:

[0005] Conduct finite element analysis on offshore structures to determine their elastic modal vibration shapes;

[0006] Frequency domain hydroelastic calculation is performed based on the elastic modal vibration shape of the offshore structure combined with the structural characteristic parameters of the offshore structure and the sea condition parameters of the sea area where the offshore structure is located, and the frequency domain generalized added mass, frequency domain generalized added damping and frequency domain generalized wave excitation force are obtained;

[0007] The generalized added mass matrix [A ∞ ] and the time delay function matrix [K′(t)], the frequency domain generalized wave excitation force is transformed into the time domain generalized wave excitation force {F(t)};

[0008] The convolution form of the time-domain hydroelastic response equation of the marine structure under the transient impact external load is constructed. The external load term in the time-domain hydroelastic response equation under the transient impact external load also includes the load term of the transient impact external load; the generalized additional mass matrix [A ∞ ], the time-delay function matrix [K′(t)], the time-domain generalized wave excitation force {F(t)} and the transient impact external load {S(t)} of the offshore structure are substituted into the constructed time-domain hydroelastic response equation to solve it, and the hydroelastic response result of the offshore structure subjected to transient impact external load in the sea area is obtained.

[0009] A further technical solution is that the time-domain hydroelastic response equation of the marine structure under the transient impact external load is:

[0010]

[0011] Wherein, [a] is the generalized mass matrix of the offshore structure, [b] is the generalized damping matrix of the offshore structure, [c] is the generalized stiffness matrix of the offshore structure, {q(t)} is the principal coordinate response of the offshore structure, τ is the time parameter, {K(t)} is the generalized hydrostatic restoring force of the offshore structure, and {Q(t)} is the generalized gravity of the offshore structure.

[0012] A further technical solution is that the wave condition in the sea area where the offshore structure is located is still water, the calculated time-domain generalized wave excitation force {F(t)} on the offshore structure is 0, and the constructed time-domain hydroelastic response equation is solved to obtain the hydroelastic response result of the offshore structure when it is subjected to a transient impact external load in still water; or, the wave condition in the sea area where the offshore structure is located is regular waves, the calculated time-domain generalized wave excitation force {F(t)} on the offshore structure is the regular wave time-domain generalized wave excitation force, and the constructed time-domain hydroelastic response equation is solved to obtain the hydroelastic response result of the offshore structure when it is subjected to a transient impact external load in regular waves; or, the wave condition in the sea area where the offshore structure is located is irregular waves, the calculated time-domain generalized wave excitation force {F(t)} on the offshore structure is the irregular wave time-domain generalized wave excitation force, and the constructed time-domain hydroelastic response equation is solved to obtain the hydroelastic response result of the offshore structure when it is subjected to a transient impact external load in irregular waves.

[0013] A further technical solution is to transform the generalized additional mass matrix [A ∞ ] and the delay function matrix [K′(t)] include:

[0014] According to the mutually orthogonal r-order mode and k-order mode in the frequency domain generalized additional damping at the wave frequency ω e Frequency domain additional damping under according to The additional damping B of the rth and kth modes at infinite frequency is calculated. ∞rk , and the impulse response function K of the rth and kth modes r ' k (t);

[0015] According to the mutually orthogonal r-order mode and k-order mode in the generalized added mass in the frequency domain at the wave frequency ω e The frequency domain additional mass under The impulse response function K combining the rth mode and the kth mode r 'k (t), according to The additional mass A of the rth and kth modes at infinite frequency is calculated. ∞rk , where C r ' k is the coefficient of restoring force caused by the speed of the marine structure;

[0016] The additional mass A of each mode at infinite frequency ∞rk The generalized added mass matrix [A ∞ ], the impulse response function K of each mode is integrated r ' k (t) obtain the delay function matrix [K′(t)].

[0017] A further technical solution is that the impact load hydroelastic response analysis method further includes:

[0018] The time domain motion curve of the offshore structure Substitute the expression of the generalized radiation force of the rth mode in the time domain into Get Among them, q k is the time domain displacement amplitude of the offshore structure, ω e is the wave frequency in the sea area where the offshore structure is located, i is the imaginary unit, t is the time, and m is the total modal order;

[0019] Determine the radiation force expression of the rth order mode in the frequency domain as follows:

[0020]

[0021] make get

[0022] A further technical solution is that the marine engineering structure is in a no-speed state or a speed state.

[0023] The beneficial technical effects of this application are:

[0024] The present application discloses a method for analyzing the hydroelastic response of an impact load taking into account the time effect. The method is based on the hydroelasticity theory and establishes a time-domain hydroelastic response equation of a marine structure under a transient impact external load in a convolution form. By transforming the frequency-domain hydroelasticity calculation result into the time domain and substituting it into the solution, the motion response and external load response of the marine structure in still water, regular waves and irregular waves can be analyzed under any transient impact external load. This fills the technical gap in the industry, solves the problem of analyzing the flow-solid coupling response of the marine structure under the transient impact external load under arbitrary wave conditions, and realizes the application of the time-domain hydroelastic response analysis method under transient impact external load in the calculation of a type of launch platform.

[0025] This method can be applied to marine structures of any shape, any form of transient impact external loads and any wave conditions, and has a wide range of applications. In addition, this method is an indirect time-domain hydroelastic method. The generalized added mass matrix, time delay function matrix and time-domain generalized wave excitation force in the indirect time-domain hydroelastic method are obtained through frequency domain transformation. The frequency domain only needs to be calculated once, so the calculation speed is faster than other time domain methods. This method is very effective for engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a method flow chart of a method for analyzing hydroelastic response to impact load according to an embodiment of the present application.

[0027] Figure 2 This is an application scenario diagram of an offshore structure being subjected to impact loads during a rocket launch.

[0028] Figure 3 yes Figure 2 In the example, the heave response comparison results of the marine structure before and after being subjected to transient impact external load in still water are obtained using the impact load hydroelastic response analysis method of the present application.

[0029] Figure 4 yes Figure 2 In the example, the comparison results of the pitch response of the marine structure before and after being subjected to a transient impact external load in still water are obtained using the impact load hydroelastic response analysis method of the present application.

[0030] Figure 5 yes Figure 2 In the example, the heave response comparison results of the marine structure before and after being subjected to transient impact external loads in regular waves are obtained using the impact load hydroelastic response analysis method of the present application.

[0031] Figure 6 yes Figure 2 In the example, the comparison results of the pitch response of the marine structure before and after being subjected to transient impact external loads in regular waves are obtained using the impact load hydroelastic response analysis method of the present application.

[0032] Figure 7 yes Figure 2 In the example, the heave response comparison results of the marine structure before and after being subjected to transient impact external loads in irregular waves are obtained using the impact load hydroelastic response analysis method of the present application.

[0033] Figure 8 yes Figure 2 In the example, the comparison results of the pitch response of the marine structure before and after being subjected to transient impact external loads in irregular waves are obtained using the impact load hydroelastic response analysis method of the present application. DETAILED DESCRIPTION

[0034] The specific implementation of the present application is further described below in conjunction with the accompanying drawings.

[0035] This application discloses a method for analyzing the hydroelastic response of impact loads taking into account the time effect. The method is based on the hydroelastic theory of the modal superposition method to analyze the hydroelastic response of marine structures when they are subjected to external impact loads in the sea area. It can take into account the elastic influence of marine structures, so as to make a unified analysis of the operational response and structural load of marine structures in waves. Please refer to Figure 1 As shown in the flowchart, the impact load hydroelastic response analysis method includes the following steps:

[0036] Step 1: Perform finite element analysis on the offshore structure to determine the elastic modal vibration type of the offshore structure. The following overall dynamic equation of the offshore structure is used when solving the elastic modal vibration type:

[0037]

[0038] Wherein, [M] is the total mass matrix of the offshore structure, [C] is the total damping matrix of the offshore structure, [K] is the total stiffness matrix of the offshore structure, {U} is the total node displacement matrix of the offshore structure after discretization, is the first derivative of {U}, It is the second derivative of {U}, and the other subsequent parameters are expressed in the same way. {F} is the external force on the offshore structure. Taking {F} as 0, the characteristic analysis of the offshore structure can be performed to obtain the elastic modal vibration shape, including the natural frequency / natural period and vibration shape of the offshore structure.

[0039] Step 2: Perform frequency domain hydroelastic calculation based on the elastic modal vibration mode of the offshore structure combined with the structural characteristic parameters of the offshore structure and the sea condition parameters of the sea area where the offshore structure is located to obtain the frequency domain generalized added mass, frequency domain generalized added damping and frequency domain generalized wave excitation force. The following frequency domain linear hydroelastic motion equation is used in the frequency domain hydroelastic calculation of this step:

[0040]

[0041] Wherein, [a] is the generalized mass matrix of the offshore structure, [b] is the generalized damping matrix of the offshore structure, and [c] is the generalized stiffness matrix of the offshore structure. [A(ω)] is the frequency domain generalized added mass and includes the frequency domain added mass at different frequencies. [B(ω)] is the frequency domain generalized added damping and includes the frequency domain added damping at different frequencies. [C] is the generalized fluid restoring force matrix with the restoring force coefficient as the matrix element. {p(ω)} is the generalized principal coordinate matrix at different frequencies of the offshore structure. {Z} is the generalized surface distributed force matrix, {Δ} is the generalized concentrated force matrix, and {Q} is the generalized volume force matrix.

[0042] The specific frequency-domain hydroelasticity calculation method can refer to the existing method, and this application will not introduce it in detail. After the frequency-domain hydroelasticity calculation, the frequency-domain generalized added mass at different frequencies and the frequency-domain generalized additional damping at different frequencies can be obtained, and the amplitude and phase of the frequency-domain generalized wave excitation force at different frequencies and different wave directions and the motion response amplitude of the marine structure can be calculated.

[0043] Step 3: transform the frequency domain generalized added mass and frequency domain generalized added damping to obtain the generalized added mass matrix [A ∞ ] and the time delay function matrix [K′(t)], the frequency domain generalized wave excitation force is transformed into the time domain generalized wave excitation force {F(t)}.

[0044] First, it is determined that the time domain motion curve of the offshore structure can be expressed by simple harmonic motion as follows:

[0045]

[0046] Among them, q k is the time domain displacement amplitude of the offshore structure, ω e is the wave frequency in the sea area where the offshore structure is located, i is the imaginary unit, and t is the time.

[0047] Substitute the above-mentioned time-domain motion curve of the marine engineering structure into the following expression of the generalized radiation force of the r-th order mode in the time domain:

[0048]

[0049] get:

[0050]

[0051] Here, m is the total number of modal orders.

[0052] The radiation force expression of the rth order mode corresponding to the frequency domain is determined as:

[0053]

[0054] make get:

[0055]

[0056] in, is the mutually orthogonal r-order mode and k-order mode in the generalized added mass in the frequency domain at the wave frequency ω e The additional quality in the frequency domain is given by is the mutually orthogonal r-order mode and k-order mode in the generalized additional damping in the frequency domain at the wave frequency ω e The frequency domain additional damping is shown in Figure 2. ∞rk is the additional mass of the rth and kth modes at infinite frequency, B ∞rk is the additional damping of the rth and kth modes at infinite frequency. ∞rk and B ∞rk They are only related to the inherent properties and motion state of the marine structure, and have nothing to do with time and frequency. ∞rk and B ∞rk The inherent properties of offshore structures include the geometric shape of offshore structures, which affects A ∞rk and B ∞rk The motion state of the offshore structure includes the ship speed, motion mode and deformation mode. r ' k (t) is the impulse response function K of the rth and kth modes over time t r ' k (t) C r ' k It is the restoring force coefficient caused by the speed of the offshore structure.

[0057] It can be seen from this that the method of the present application can be applied to the analysis of marine structures under the conditions of speed and no speed. When the marine structure has no speed, B can be directly taken. ∞rk =0 and C r ' k = 0. When the marine structure has a speed, the frequency domain hydroelastic calculation should be performed in combination with the speed of the marine structure in the above step 2 to obtain the restoring force coefficient caused by the corresponding speed.

[0058] All frequency-dependent parts are included in K r ' k (t) and there is:

[0059]

[0060] According to the frequency domain additional damping according to The additional damping B at infinite frequency can be calculated ∞rk, and the impulse response function K r ' k (t). Further in accordance with Calculate the additional mass A at infinite frequency ∞rk .

[0061] Finally, the additional mass A of each mode at infinite frequency is ∞rk The generalized added mass matrix [A ∞ ], the impulse response function K of each mode is integrated r ' k (t) to obtain the time delay function matrix [K′(t)]. The method of transforming the frequency domain generalized wave excitation force to obtain the time domain generalized wave excitation force {F(t)} can refer to the existing method, which is not elaborated in this application.

[0062] Step 4, construct a convolution form of the time-domain hydroelastic response equation of the marine structure under the transient impact external load, in which the external load term also includes the load term of the transient impact external load. The convolution form of the time-domain hydroelastic response equation of the marine structure under the transient impact external load is:

[0063]

[0064] Among them, {q(t)} is the principal coordinate response of the offshore structure, τ is the time parameter, {K(t)} is the generalized hydrostatic restoring force of the offshore structure, and {Q(t)} is the generalized gravity of the offshore structure.

[0065] Then the generalized additional mass matrix [A ∞ ], the time delay function matrix [K′(t)] and the time domain generalized wave excitation force {F(t)} are substituted into the constructed time domain hydroelastic response equation, and the transient impact external load {S(t)} to which the marine structure is subjected is substituted into the constructed time domain hydroelastic response equation. The determination method of other items in the above time domain hydroelastic response equation can refer to the existing time domain hydroelastic response analysis method, which will not be described in detail in this embodiment. Then, the above time domain hydroelastic response equation is solved to obtain the hydroelastic response result of the marine structure when it is subjected to transient impact external load in the sea area.

[0066] The above-mentioned time-domain hydroelastic response equation constructed in the present application adds the load term {S(t)} of the transient impact external load, and considers the time effect in the form of convolution, so that the method can be applied to the hydroelastic response analysis of marine structures under any wave conditions, and any wave conditions include still water, regular waves and irregular waves, that is:

[0067] When the wave condition in the sea area where the offshore structure is located is still water, the calculated time-domain generalized wave excitation force {F(t)} on the offshore structure is 0. By solving the constructed time-domain hydroelastic response equation through the above steps, the hydroelastic response result of the offshore structure when it is subjected to transient impact external load in still water can be obtained.

[0068] When the wave condition in the sea area where the offshore structure is located is a regular wave, the calculated time-domain generalized wave excitation force {F(t)} on the offshore structure is the regular wave time-domain generalized wave excitation force. The constructed time-domain hydroelastic response equation is solved by the above steps to obtain the hydroelastic response result of the offshore structure when it is subjected to transient impact external loads in regular waves.

[0069] When the wave condition in the sea area where the offshore structure is located is irregular wave, the calculated time-domain generalized wave excitation force {F(t)} on the offshore structure is the irregular wave time-domain generalized wave excitation force. The hydroelastic response result of the offshore structure subjected to transient impact external load in irregular waves is obtained by solving the constructed time-domain hydroelastic response equation through the above steps.

[0070] Therefore, the versatility of the method of the present application is very high, and it can be applied to the hydroelastic response results of various structures of marine engineering structures under various wave conditions when subjected to transient impact external loads. In addition, it can be seen that the present application obtains the generalized additional mass matrix [A] in the time domain hydroelastic method by transforming the frequency domain hydroelastic calculation results. ∞ ], the time-delay function matrix [K′(t)] and the time-domain generalized wave excitation force {F(t)} only need to be calculated once in the frequency domain, so the calculation speed is faster than other time-domain calculation methods. This indirect time-domain hydroelastic method has a fast solution speed and is very suitable for engineering applications.

[0071] In the case of a sea-based launch platform, such as Figure 2 As shown, a rocket 2 is arranged at the stern of the marine structure 1. When the rocket 2 is launched, the marine structure 1 will be subjected to an impact external load with a short action time and a very large load. Due to the complexity of solving the problem, there is no effective calculation method so far. However, by using the method of the present application, the time curve of the load term {S(t)} of the transient impact external load acting on the marine structure 1 when the rocket 2 is launched can be predicted in advance through data collection and analysis, and then the hydroelastic response results of the marine structure under different wave conditions when subjected to the above-mentioned transient impact external load can be obtained according to the method of the present application. This example takes the marine structure 1 in a zero-speed state as an example, and the comparison results of the heave response of the marine structure in still water when it is not subjected to the transient impact external load and when it is subjected to the transient impact external load are shown as follows. Figure 3 The comparison results of pitch response are shown in Figure 4The comparison results of the heave response of the offshore structure in regular waves without transient impact external load and with transient impact external load are shown in Figure 5 The comparison results of pitch response are shown in Figure 6 The comparison results of the heave response of the offshore structure in irregular waves without transient impact external load and with transient impact external load are shown in Figure 7 The comparison results of pitch response are shown in Figure 8 shown.

[0072] The above is only a preferred embodiment of the present application, and the present application is not limited to the above embodiments. It is understood that other improvements and changes directly derived or associated by those skilled in the art without departing from the spirit and concept of the present application should be considered to be included in the protection scope of the present application.

Claims

1. A method for analyzing hydroelastic response of impact loads taking into account time effects, characterized in that: The impact load hydroelastic response analysis method comprises: Performing finite element analysis on the offshore structure to determine the elastic modal vibration shape of the offshore structure; Perform frequency domain hydroelastic calculation according to the elastic modal vibration shape of the offshore structure in combination with the structural characteristic parameters of the offshore structure and the sea condition parameters of the sea area where the offshore structure is located, to obtain frequency domain generalized added mass, frequency domain generalized added damping and frequency domain generalized wave excitation force; The generalized added mass matrix [A ∞ ] and the time delay function matrix [K′(t)], the frequency domain generalized wave excitation force is transformed into the time domain generalized wave excitation force {F(t)}; The convolution form of the time-domain hydroelastic response equation of the marine structure under the transient impact external load is constructed. The external load term in the time-domain hydroelastic response equation under the transient impact external load also includes the load term of the transient impact external load; the generalized additional mass matrix [A ∞ ], the time-delay function matrix [K′(t)], the time-domain generalized wave excitation force {F(t)} and the transient impact external load {S(t)} applied to the offshore structure are substituted into the constructed time-domain hydroelastic response equation to solve the hydroelastic response result of the offshore structure when it is subjected to the transient impact external load in the sea area.

2. The method for analyzing the impact load hydroelastic response according to claim 1, characterized in that: The time-domain hydroelastic response equation of the offshore structure under transient impact external load is: Wherein, [a] is the generalized mass matrix of the offshore structure, [b] is the generalized damping matrix of the offshore structure, [c] is the generalized stiffness matrix of the offshore structure, {q(t)} is the principal coordinate response of the offshore structure, τ is the time parameter, {K(t)} is the generalized hydrostatic restoring force of the offshore structure, and {Q(t)} is the generalized gravity of the offshore structure.

3. The method for analyzing the impact load hydroelastic response according to claim 2, characterized in that: The wave condition of the sea area where the offshore structure is located is still water, the calculated time-domain generalized wave excitation force {F(t)} on the offshore structure is 0, and the constructed time-domain hydroelastic response equation is solved to obtain the hydroelastic response result of the offshore structure when it is subjected to a transient impact external load in still water; or, The wave condition of the sea area where the offshore structure is located is a regular wave, the calculated time-domain generalized wave excitation force {F(t)} on the offshore structure is the regular wave time-domain generalized wave excitation force, and the constructed time-domain hydroelastic response equation is solved to obtain the hydroelastic response result of the offshore structure when it is subjected to a transient impact external load in a regular wave; or, The wave condition in the sea area where the offshore structure is located is irregular waves. The calculated time-domain generalized wave excitation force {F(t)} on the offshore structure is the irregular wave time-domain generalized wave excitation force. The constructed time-domain hydroelastic response equation is solved to obtain the hydroelastic response result of the offshore structure when it is subjected to transient impact external loads in irregular waves.

4. The method for analyzing hydroelastic response to impact load according to claim 1, characterized in that: The generalized added mass matrix [A ∞ ] and the delay function matrix [K′(t)] include: According to the mutually orthogonal r-order mode and k-order mode in the frequency domain generalized additional damping at the wave frequency ω e Frequency domain additional damping under according to The additional damping B of the rth and kth modes at infinite frequency is calculated. ∞rk , and the impulse response function K of the rth and kth modes r ' k (t); According to the mutually orthogonal r-order mode and k-order mode in the generalized added mass in the frequency domain at the wave frequency ω e The frequency domain additional mass under The impulse response function K combining the rth mode and the kth mode r ' k (t), according to The additional mass A of the rth and kth modes at infinite frequency is calculated. ∞rk , where C r ' k is the coefficient of restoring force caused by the speed of the marine structure; The additional mass A of each mode at infinite frequency ∞rk The generalized added mass matrix [A ∞ ], the impulse response function K of each mode is integrated r ' k (t) obtain the delay function matrix [K′(t)].

5. The method for analyzing hydroelastic response to impact load according to claim 4, characterized in that: The impact load hydroelastic response analysis method further comprises: The time domain motion curve of the offshore structure Substitute the expression of the generalized radiation force of the rth mode in the time domain into Get Among them, q k is the time domain displacement amplitude of the offshore structure, ω e is the wave frequency in the sea area where the offshore structure is located, i is the imaginary unit, t is the time, and m is the total modal order; Determine the radiation force expression of the rth order mode in the frequency domain as follows: make get 6. The method for analyzing hydroelastic response to impact load according to claim 1, characterized in that: The marine engineering structure is in a no-speed state or a speed state.

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