CN115358121B - Modeling method of fluid sloshing equivalent mechanical model of inclined bottom vertical annular water tank - Google Patents
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Abstract
The invention discloses a modeling method, a modeling system, electronic equipment and a computer-readable storage medium for an equivalent mechanical model of fluid sloshing of an inclined bottom vertical annular water tank, and belongs to the technical field of water tank performance evaluation. The method comprises the steps of establishing a fluid shaking finite element model of fluid in an inclined bottom vertical annular water tank according to structural information of the inclined bottom vertical annular water tank; establishing an equivalent mechanical model of fluid in the inclined bottom vertical annular water tank according to the structural information of the inclined bottom vertical annular water tank and the fluid swaying finite element model; and (5) evaluating the earthquake response performance of the inclined bottom vertical annular water tank according to the equivalent mechanical model. The method can establish an accurate equivalent mechanical model of fluid in the inclined bottom vertical annular water tank, further accurately evaluate the earthquake response performance of the inclined bottom vertical annular water tank, and solve the problem that the fluid model in the inclined bottom vertical annular water tank is not accurate and cannot be effectively evaluated in the prior art.
Description
Technical Field
The application relates to the technical field of water tank performance evaluation, in particular to a modeling method of an equivalent mechanical model of fluid sloshing of an inclined bottom vertical annular water tank.
Background
The statements in this section merely provide background information related to the present application and may not necessarily constitute prior art.
The vertical annular water tank has wide application in nuclear power and aerospace engineering. At present, the roof cooling water tank of the third-generation nuclear power station AP1000 which is built and generates electricity in China and the domestic third-generation nuclear power unit CAP1400 which is built are vertical annular water tanks with the inclined bottoms of 35 degrees, and the consideration of the dynamic response under the earthquake action of fluid-solid coupling is one of the important consideration.
The equivalent mechanical model of the water tank is an important technical means for researching the earthquake response of the liquid storage structure. To avoid complex fluid sloshing calculations, a simplified fluid sloshing equivalent mechanical model needs to be built for modeling the dynamic response of sloshing fluid to the structure. The equivalent mechanical model has the same or nearly the same action effect as the real fluid, including the resultant force and resultant moment of the liquid to the structure.
The equivalent mechanical model simplifies the shaking liquid into a fixed mass m 0 A spring vibrator (m 1 、K 1 ) See FIG. 1, wherein h 0 And h 1 Representing the fixed mass and the height of the spring vibrator relative to the tank floor, respectively. Most of the current research results take water tanks with regular shapes as research objects, such as rectangular water tanks, conical water tanks, upright cylindrical water tanks and the like, and the research work on annular water tanks, particularly inclined bottom upright annular water tanks, is relatively less. The industry has now clarified that the Housner formula is only applicable to regular liquid storage containers such as rectangular or cylindrical, so most of the results are improved based on the equivalent mechanical model of the Housner cylindrical water tank, thereby obtaining a calculation formula for the vertical annular water tank. However, according to the latest research results, whether the rectangular water tank or the upright cylindrical water tank, the approximate solution given by the Housner formula has larger error compared with the accurate solution, so that a relatively accurate earthquake response result cannot be obtained, and a certain potential safety hazard is possibly brought to the structural design of the water tank. Thus, there is a need for more elaborate and intensive research on the liquid sloshing of the sloping-bottom upright annular tank and its fluid-solid coupling problem.
In addition, most of the current research equivalent mechanical models adopt an analysis method, so that the compressibility of the fluid is often ignored, and a certain difference exists between the compressibility and the actual situation.
Disclosure of Invention
In order to solve the defects of the prior art, the modeling method, the system, the electronic equipment and the computer readable storage medium of the fluid swaying equivalent mechanical model of the inclined bottom vertical annular water tank can overcome the problems that the prior method has larger error, does not consider the fluid compressibility, does not have a special inclined bottom vertical annular water tank equivalent mechanical model and the like, fully consider the fluid compressibility, and can be used for deducing the earthquake response results of the inclined bottom vertical annular water tank and other complex-shape water tank equivalent mechanical models, thereby obtaining accurate water tank seismic response results and reducing potential safety hazards.
In a first aspect, the present application provides a modeling method for a fluid sloshing equivalent mechanical model of an inclined bottom upright annular water tank;
a modeling method of an equivalent mechanical model of fluid sloshing of an inclined bottom vertical annular water tank comprises the following steps:
according to the structural information of the inclined bottom vertical annular water tank, a fluid shaking finite element model of fluid in the inclined bottom vertical annular water tank is established;
establishing an equivalent mechanical model of fluid in the vertical annular inclined bottom according to the structural information of the vertical annular inclined bottom water tank and the finite element model;
and (5) evaluating the earthquake response performance of the inclined bottom vertical annular water tank according to the equivalent mechanical model.
In a second aspect, the present application provides a modeling system for fluid sloshing of an inclined bottom upright annular tank;
a modeling system for fluid sloshing of an inclined bottom upright annular water tank, comprising:
the fluid shaking finite element model acquisition module is used for establishing a fluid shaking finite element model of fluid in the inclined bottom vertical annular water tank according to the structural information of the inclined bottom vertical annular water tank;
the equivalent mechanical model acquisition module is used for establishing an equivalent mechanical model of fluid in the inclined bottom vertical annular water tank according to the structural information of the inclined bottom vertical annular water tank and the finite element model;
and the evaluation module of the inclined bottom vertical annular water tank is used for evaluating the earthquake response performance of the inclined bottom vertical annular water tank according to the equivalent mechanical model.
In a third aspect, the present application provides an electronic device;
an electronic device comprising a memory and a processor and computer instructions stored on the memory and running on the processor, which when executed by the processor, perform the steps of the modeling method of the fluid sloshing equivalent mechanical model of the sloping-bottom upright annular water tank.
In a fourth aspect, the present application provides a computer-readable storage medium;
a computer readable storage medium storing computer instructions which, when executed by a processor, perform the steps of the modeling method of the fluid sloshing equivalent mechanical model of the sloping-bottom upright annular water tank.
Compared with the prior art, the beneficial effects of this application are:
1. the inclined bottom vertical annular water tank belongs to a special-shaped liquid storage container, and liquid in the inclined bottom vertical annular water tank shakes very complicated; the method solves the problem of derivation of the equivalent mechanical model of the special-shaped water tank, can well simulate the real situation of liquid shaking, can be used for dynamic analysis considering fluid-solid coupling, can accurately acquire the earthquake response result of the special-shaped water tank, and reduces the potential safety hazard of structural design of the special-shaped water tank;
2. the method can also be used for deducing equivalent mechanical models of water tanks with other complex shapes.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this application, illustrate embodiments of the application and together with the description serve to explain the application and do not constitute an undue limitation to the application.
FIG. 1 is a schematic diagram of an equivalent mechanical model provided in an embodiment of the present application;
FIG. 2 is a schematic structural diagram of a liquid finite element model according to an embodiment of the present application;
FIG. 3 is a schematic cross-sectional view of a liquid finite element model provided in an embodiment of the present application;
fig. 4 is a schematic flow chart of an embodiment of the present application.
Detailed Description
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present application. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments in accordance with the present application. As used herein, unless the context clearly indicates otherwise, the singular forms also are intended to include the plural forms, and furthermore, it is to be understood that the terms "comprises" and "comprising" and any variations thereof are intended to cover non-exclusive inclusions, such as, for example, processes, methods, systems, products or devices that comprise a series of steps or units, are not necessarily limited to those steps or units that are expressly listed, but may include other steps or units that are not expressly listed or inherent to such processes, methods, products or devices.
Embodiments of the invention and features of the embodiments may be combined with each other without conflict.
Example 1
The embodiment provides a modeling method of an equivalent mechanical model of fluid sloshing of an inclined bottom vertical annular water tank. As shown in the figure, the modeling method of the fluid sloshing equivalent mechanical model of the inclined bottom vertical annular water tank comprises the following steps:
according to the structural information of the inclined bottom vertical annular water tank, a fluid shaking finite element model of fluid in the inclined bottom vertical annular water tank is established;
establishing an equivalent mechanical model of fluid in the vertical annular inclined bottom according to the structural information of the vertical annular inclined bottom water tank and the finite element model;
and (5) evaluating the earthquake response performance of the inclined bottom vertical annular water tank according to the equivalent mechanical model.
Further, the first-order shaking frequency natural frequency of the liquid shaking finite element model is the same as that of the equivalent model.
Further, according to the excitation of the horizontal acceleration born by the inclined bottom vertical annular water tank, the resonance response of the equivalent mechanical model is obtained;
and obtaining a fitting formula of the fluid shaking mass in the equivalent mechanical model and a fitting formula of the height of the fluid shaking mass relative to the bottom plate of the inclined bottom vertical annular water tank according to the resonance response, the fluid shaking finite element model and the equivalent mechanical model.
Further, according to the excitation of the horizontal acceleration born by the inclined bottom vertical annular water tank, the resonance response of the equivalent mechanical model is obtained;
and obtaining a fitting formula of the fluid shaking mass in the equivalent mechanical model and a fitting formula of the height of the fluid shaking mass relative to the bottom plate of the inclined bottom vertical annular water tank according to the resonance response, the fluid shaking finite element model and the equivalent mechanical model.
Further, according to excitation of constant acceleration born by the inclined bottom vertical annular water tank, resonance response of the equivalent mechanical model is obtained;
and obtaining a fitting formula of the fluid fixed mass in the equivalent mechanical model and a fitting formula of the height of the fluid fixed mass relative to the bottom plate of the inclined bottom vertical annular water tank according to the resonance response, the fluid swaying finite element model and the equivalent mechanical model.
Further, the equivalent mechanical model comprises a fitting formula of first-order shaking frequency, a fitting formula of fluid fixed mass relative to the height of the inclined bottom vertical water tank bottom plate, a fitting formula of spring stiffness, a fitting formula of fluid shaking mass and a fitting formula of fluid shaking mass relative to the height of the inclined bottom vertical annular water tank bottom plate.
Further, the fitting formula of the first-order shaking frequency is as follows
Wherein g is gravitational acceleration, alpha 1 、α 2 As fitting parameters, H is the fluid depth, and R is the fluid radius;
or,
the fitting formula of the spring stiffness is
Wherein m is 1 For fluid sloshing masses, ω 1 Is the natural frequency of the spring vibrator.
Further, the fitting formula of the fluid sloshing mass is as follows
Where m is the total mass of the fluid, α 3 、α 4 To fit coefficients, m 1 For fluid sloshing mass, R is fluid radius and H is fluid depth.
Or,
the fitting formula of the height of the fluid sloshing mass relative to the bottom plate of the inclined bottom vertical annular water tank is that
Wherein h is 1 Alpha is the height of the fluid sloshing mass relative to the bottom plate of the sloping bottom upright annular water tank 5 ～α 8 For the fitting coefficient, H is the fluid depth, R is the fluid radius;
or,
the fitting formula of the fluid fixed mass is that
Wherein m is 0 For fluid fixed mass, alpha 9 ～α 12 R is the radius of the fluid, and H is the depth of the fluid;
or,
the fitting formula of the fluid fixed mass relative to the height of the inclined bottom vertical water tank bottom plate is that
Wherein h is 0 Alpha is the height of the fluid fixed mass relative to the bottom plate of the sloping bottom upright water tank 13 ～α 20 For the fitting parameters, R is the fluid radius and H is the fluid depth.
Next, a modeling method of a fluid sloshing equivalent mechanical model of an inclined bottom upright annular water tank disclosed in this embodiment will be described in detail with reference to fig. 1 to 3.
Modeling method of fluid sloshing equivalent mechanical model of inclined bottom vertical annular water tank, and solving sloshing mass m by adopting force equation 1 And a fixed mass m 0 Solving the position parameter h according to a moment equation 0 And h 1 The method comprises the steps of carrying out a first treatment on the surface of the Comprising the following steps:
s1, establishing a fluid shaking finite element model of fluid in an inclined bottom vertical annular water tank according to structural information of the inclined bottom vertical annular water tank;
illustratively, pure water finite element models (also referred to as "raw systems") with different depth to diameter ratios H/R are created using Ansys software, as shown in FIG. 2. The density of the fluid is ρ=1000 kg/m3, the volume compression modulus is k=2.067×109Pa, the coefficient of viscosity of the fluid is taken to be 0, i.e. the sloshing damping of the fluid is not considered, and the equivalent mechanical model obtained in this way is conservative for the anti-seismic calculation of the structure. The normal relative displacement constraint of the nodes of the fluid sidewall and bottom position is 0, while the tangential relative displacement is released. At the same time, a main degree of freedom is defined at the free liquid level.
S2, establishing an equivalent mechanical model of fluid in the vertical annular inclined bottom according to the structural information of the vertical annular inclined bottom water tank and the finite element model; comprising the following steps:
s201, establishing an equivalent mechanical model based on the following conditions:
(1) Mass conservation conditions: i.e. the equivalent mass must be equal to the total mass M of the actual liquid;
(2) Centroid conservation condition: for small vibrations, the waveform of the free surface assumes an antisymmetric form, so the vertical position of the actual fluid centroid does not change.
(3) Under the action of external excitation, the modal frequency of the equivalent model, the counter force acting on the water tank structure and the counter moment must be the same as or very close to those of the actual fluid system;
(4) The equivalent model can only be adapted to one excitation condition. Such as horizontal excitation in a certain direction or rotational excitation around a certain axis. The excitation input need not be a sinusoidal function, but the excitation value may be an arbitrary function over time;
the equivalent mechanical model comprises a fitting formula comprising first-order shaking frequency, a fitting formula of fluid fixed mass relative to the height of the inclined bottom vertical water tank bottom plate, a fitting formula of spring stiffness, a fitting formula of fluid shaking mass and a fitting formula of fluid shaking mass relative to the height of the inclined bottom vertical annular water tank bottom plate.
S202, acquiring a fitting formula of first-order shaking frequency;
for example, the first order wobble frequency of the equivalent mechanical model can be assumed as:
wherein g is gravitational acceleration, alpha 1 、α 2 As fitting parameters, H is the liquid depth, and R is the liquid radius;
for n different depths and radii (h j 、R j ) (j=1, 2,3,., n) liquid systems, n first order circular frequencies (ω 1 ) j Ansys (j=1, 2,3,) n. The original system and the equivalent system should have the same natural frequency, and according to equation (1) and the least square method, the following objective function can be established:
the shaking frequency f of the annular liquid with different depth-to-diameter ratios H/R can be obtained by utilizing Ansys software calculation 1 (ω 1 ＝2πf 1 ) According to the least square method, the optimal fitting parameter alpha can be obtained by adopting the objective function 1 、α 2 。
S203, acquiring a fitting formula of flow and liquid shaking quality and a fitting formula of the height of the liquid shaking quality relative to the bottom plate of the inclined bottom vertical annular water tank;
exemplary, first order sloshing mass ratio m 1 M and position parameter h thereof 1 The following form can be assumed for H:
wherein: m is the total mass of the liquid; alpha 3 ～α 8 And (5) the fitting coefficient to be determined.
The vertical annular water tank with a flat bottom bears horizontal accelerationThe horizontal force and moment that the equivalent system acts on the container sidewall can be written as:
wherein: omega 1 Is a spring vibrator (m) 1 ，K 1 ) Is a natural frequency of (c). The equivalent model parameters express the self characteristics of liquid shaking, the parameters are irrelevant to external excitation, the dynamic response of the equivalent system contains the information of the equivalent model parameters, and in order to make m 1 Is separated from the total response, the following positive is selectedString resonance excitation:
wherein: a is excitation amplitude, t 0 For a particular moment, here taken as t 0 ＝kπ/ω 1 K is an integer. The resonance response at the above sinusoidal resonance excitation of equations (5) and (6) is:
by formulae (8) and (9), when t>t 0 ＝kπ/ω 1 When there will be no fixed mass m 0 Is to leave only the wobble mass m 1 The equivalent system response is just a simple spring vibrator that is free to vibrate. F can be obtained by substituting the formulas (3) and (4) into the formulas (8) and (9) L (t) and M L The fitting formula for (t) is shown below:
the finite element software Ansys software is utilized to calculate, the best fitting coefficient is obtained by utilizing the principle of a least square method, namely the calculation result of the equivalent model is consistent with the calculation result of Ansys, thereby obtaining the coefficient alpha in the equivalent model 3 ～α 8 。
When t>t 0 When the fluid is in the state of sine curve, the horizontal force and moment time of the fluid to the container are all sine curve according to the result of finite element calculationThe three-dimensional finite element model is adopted, so that the extraction of the counter force is greatly different from that of the two-dimensional model, the invention carries out technical improvement on programming, and the sum of all counter forces of the side wall of the three-dimensional model container in the x direction is extracted. The magnitude of the curve may be expressed as |FL| j Ansys |ML| j Ansys Wherein the moment is calculated taking into account the effect of the entire wet boundary, including the bottom boundary. Using the amplitude data, the best fit coefficient alpha can be calculated 3 ～α 8 That is to say, m is determined 1 And h 1 Is a fitting formula of (2).
S204, acquiring a fitting formula of the spring stiffness;
by way of example, the spring rate of an equivalent mechanical model can be expressed as: k (K) 1 ＝m 1 ω 1 2 The above m is taken as 1 And omega 1 The formula of (2) is carried in.
S205, acquiring a fitting formula of liquid fixed mass and a fitting formula of the height of the liquid fixed mass relative to the bottom plate of the inclined bottom vertical water tank;
exemplary, m 0 Represents a fixed mass, h 0 Representing the height of the fixed mass relative to the tank floor, see in detail figure 1, m 0 And h 0 The fitting formula of (a) can be assumed to be of the form:
α 9 ～α 22 and (5) the fitting coefficient to be determined. To obtain a fixed mass m 0 A constant acceleration stimulus may be selected, namely:
wherein A is a constant; t is t 0 Is a special point in time. Substituting equation (14) into equations (5) and (6), the horizontal force and moment response of the equivalent system is:
F L (t)＝-(m 0 +m 1 )A+m 1 Acosω 1 t，0≤t≤t 0 (15)
M L (t)＝-(m 0 h 0 +m 1 h 1 )A+m 1 Acosω 1 t，0≤t≤t 0 (16)
using the same n finite element models in S1, they were subjected to the applied excitation of formula (14), where a=0.1 m/S 2 Taking the time endpoint t 0 ＝2kπ/ω 1 (k is an integer), the liquid finite element model has a series of sinusoids in response to both the horizontal force and moment of the container. The absolute value of the mean value of the horizontal force and the moment curve can be respectively calculated to be |F L,mean | j Ansys |M L,mean | j Ansys (j=1, 2,3, …, n) these results should be equal to the absolute value of the mean value in formula (15), formula (16), i.e., | (m) 0 +m 1 ) A|and| (m) 0 h 0 +m 1 h 1 ) A is the same as the above. Can obtain the optimal fitting coefficient alpha 9 ～α 22 Thereby determining m 0 And h 0 Is a fit to the expression of (c).
S3, obtaining an earthquake response result of the inclined bottom vertical annular water tank according to the equivalent mechanical model.
Example two
The embodiment discloses modeling system of equivalent mechanical model of fluid sloshing of vertical annular water tank of sloping bottom, includes:
the fluid shaking finite element model acquisition module is used for establishing a fluid shaking finite element model of fluid in the inclined bottom vertical annular water tank according to the structural information of the inclined bottom vertical annular water tank;
the equivalent mechanical model acquisition module is used for establishing an equivalent mechanical model of fluid in the inclined bottom vertical annular water tank according to the structural information of the inclined bottom vertical annular water tank and the finite element model;
and the evaluation module of the inclined bottom vertical annular water tank is used for evaluating the earthquake response performance of the inclined bottom vertical annular water tank according to the equivalent mechanical model.
It should be noted that, the liquid sloshing finite element model obtaining module, the equivalent mechanical model obtaining module and the inclined bottom vertical annular water tank evaluating module correspond to the steps in the first embodiment, and the above modules are the same as the examples and application scenarios implemented by the corresponding steps, but are not limited to the disclosure of the first embodiment. It should be noted that the modules described above may be implemented as part of a system in a computer system, such as a set of computer-executable instructions.
Example III
The third embodiment of the invention provides an electronic device, which comprises a memory, a processor and a computer instruction stored on the memory and running on the processor, wherein the computer instruction is executed by the processor to complete the modeling method of the fluid sloshing equivalent mechanical model of the inclined bottom vertical annular water tank.
Example IV
The fourth embodiment of the invention provides a computer readable storage medium for storing computer instructions, which when executed by a processor, complete the steps of the modeling method of the fluid sloshing equivalent mechanical model of the inclined bottom vertical annular water tank.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The foregoing embodiments are directed to various embodiments, and details of one embodiment may be found in the related description of another embodiment.
The foregoing description is only of the preferred embodiments of the present application and is not intended to limit the same, but rather, various modifications and variations may be made by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application should be included in the protection scope of the present application.
Claims (8)
1. A modeling method of an equivalent mechanical model of fluid sloshing of an inclined bottom vertical annular water tank is characterized by comprising the following steps:
according to the structural information of the inclined bottom vertical annular water tank, a fluid shaking finite element model of fluid in the inclined bottom vertical annular water tank is established;
establishing an equivalent mechanical model of fluid in the vertical annular inclined bottom according to the structural information of the vertical annular inclined bottom water tank and the finite element model;
according to an equivalent mechanical model, evaluating the earthquake response performance of the inclined bottom vertical annular water tank;
the equivalent mechanical model comprises a fitting formula of first-order shaking frequency, a fitting formula of fluid fixed mass relative to the height of the inclined bottom vertical water tank bottom plate, a fitting formula of spring stiffness, a fitting formula of fluid shaking mass and a fitting formula of fluid shaking mass relative to the height of the inclined bottom vertical annular water tank bottom plate;
the fitting formula of the fluid sloshing mass is as follows
Where m is the total mass of the fluid, α 3 -α 4 To fit coefficients, m 1 The fluid sloshing mass is R, the fluid radius is R, and the fluid depth is H;
the fitting formula of the height of the fluid sloshing mass relative to the bottom plate of the inclined bottom vertical annular water tank is that
Wherein h is 1 Alpha is the height of the fluid sloshing mass relative to the bottom plate of the sloping bottom upright annular water tank 5 -α 8 For the fitting coefficient, H is the fluid depth, R is the fluid radius;
the fitting formula of the fluid fixed mass is that
Wherein m is 0 For fluid fixed mass, alpha 9 ～α 12 R is the radius of the fluid, and H is the depth of the fluid;
the fitting formula of the fluid fixed mass relative to the height of the inclined bottom vertical water tank bottom plate is that
Wherein h is 0 Alpha is the height of the fluid fixed mass relative to the bottom plate of the sloping bottom upright water tank 13 ～α 20 For the fitting parameters, R is the fluid radius and H is the fluid depth.
2. The modeling method of a fluid sloshing equivalent mechanical model of an inclined bottom upright annular water tank according to claim 1, wherein the first order sloshing frequency natural frequency of the fluid sloshing finite element model and the equivalent model is the same.
3. The modeling method of the fluid sloshing equivalent mechanical model of the inclined bottom vertical annular water tank according to claim 2, wherein the resonance response of the equivalent mechanical model is obtained according to the excitation of the horizontal acceleration born by the inclined bottom vertical annular water tank;
and obtaining a fitting formula of the fluid shaking mass in the equivalent mechanical model and a fitting formula of the height of the fluid shaking mass relative to the bottom plate of the inclined bottom vertical annular water tank according to the resonance response, the fluid shaking finite element model and the equivalent mechanical model.
4. The modeling method of the fluid sloshing equivalent mechanical model of the inclined bottom vertical annular water tank according to claim 1, wherein the resonance response of the equivalent mechanical model is obtained according to the excitation of constant acceleration born by the inclined bottom vertical annular water tank;
and obtaining a fitting formula of the fluid fixed mass in the equivalent mechanical model and a fitting formula of the height of the fluid fixed mass relative to the bottom plate of the inclined bottom vertical annular water tank according to the resonance response, the fluid swaying finite element model and the equivalent mechanical model.
5. The modeling method of the fluid sloshing equivalent mechanical model of the inclined bottom upright annular water tank according to claim 1, wherein the fitting formula of the first-order sloshing frequency is that
Wherein g is gravitational acceleration, alpha 1 、α 2 As fitting parameters, H is the fluid depth, and R is the fluid radius;
or,
the fitting formula of the spring stiffness is
Wherein m is 1 For fluid sloshing masses, ω 1 Is the natural frequency of the spring vibrator.
6. A modeling system for fluid sloshing of an inclined bottom upright annular water tank, comprising:
the fluid shaking finite element model acquisition module is used for establishing a fluid shaking finite element model of fluid in the inclined bottom vertical annular water tank according to the structural information of the inclined bottom vertical annular water tank;
the equivalent mechanical model acquisition module is used for establishing an equivalent mechanical model of fluid in the inclined bottom vertical annular water tank according to the structural information of the inclined bottom vertical annular water tank and the finite element model;
the inclined bottom vertical annular water tank evaluation module is used for evaluating the earthquake response performance of the inclined bottom vertical annular water tank according to the equivalent mechanical model;
the equivalent mechanical model comprises a fitting formula of first-order shaking frequency, a fitting formula of fluid fixed mass relative to the height of the inclined bottom vertical water tank bottom plate, a fitting formula of spring stiffness, a fitting formula of fluid shaking mass and a fitting formula of fluid shaking mass relative to the height of the inclined bottom vertical annular water tank bottom plate;
the fitting formula of the fluid sloshing mass is as follows
Where m is the total mass of the fluid, α 3 -α 4 To fit coefficients, m 1 Is fluidSloshing mass, R is fluid radius, H is fluid depth;
the fitting formula of the height of the fluid sloshing mass relative to the bottom plate of the inclined bottom vertical annular water tank is that
Wherein h is 1 Alpha is the height of the fluid sloshing mass relative to the bottom plate of the sloping bottom upright annular water tank 5 -α 8 For the fitting coefficient, H is the fluid depth, R is the fluid radius;
the fitting formula of the fluid fixed mass is that
Wherein m is 0 For fluid fixed mass, alpha 9 ～α 12 R is the radius of the fluid, and H is the depth of the fluid;
the fitting formula of the fluid fixed mass relative to the height of the inclined bottom vertical water tank bottom plate is that
Wherein h is 0 Alpha is the height of the fluid fixed mass relative to the bottom plate of the sloping bottom upright water tank 13 ～α 20 For the fitting parameters, R is the fluid radius and H is the fluid depth.
7. An electronic device comprising a memory and a processor and computer instructions stored on the memory and running on the processor, which when executed by the processor, perform the steps of the method of any of claims 1-5.
8. A computer readable storage medium storing computer instructions which, when executed by a processor, perform the steps of the method of any of claims 1-5.
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| CN106950853A (en) * | 2017-04-19 | 2017-07-14 | 北京空间飞行器总体设计部 | The modeling method of liquid sloshing under a kind of spherical tank microgravity environment |
| CN113553661A (en) * | 2021-06-30 | 2021-10-26 | 航天科工火箭技术有限公司 | Method for obtaining rocket propellant shaking parameters and computer-readable storage medium |
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