CN109101752B - Method for calculating natural vibration frequency of local structure of complex hydraulic structure - Google Patents

Method for calculating natural vibration frequency of local structure of complex hydraulic structure Download PDF

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CN109101752B
CN109101752B CN201811006818.9A CN201811006818A CN109101752B CN 109101752 B CN109101752 B CN 109101752B CN 201811006818 A CN201811006818 A CN 201811006818A CN 109101752 B CN109101752 B CN 109101752B
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local structure
vibration frequency
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CN109101752A (en
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欧阳金惠
耿峻
许亮华
林文华
郭胜山
钟红
张翠然
涂劲
王静
林文峰
胡海虹
李金伟
任绍成
姜明利
温占营
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China Institute of Water Resources and Hydropower Research
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/13—Architectural design, e.g. computer-aided architectural design [CAAD] related to design of buildings, bridges, landscapes, production plants or roads

Abstract

The invention relates to a method for calculating the natural vibration frequency of a local structure of a complex hydraulic building. The method can simulate the actual rigidity of the local monomer structure with high precision and simulate the actual participation quality of the vibration mode of the local monomer structure with high precision, can greatly improve the solving precision of the natural vibration frequency of the local structure of the complex hydraulic structure, can avoid the generation of severe vibration and resonance when being used for carrying out the dynamic design of the complex hydraulic structure, ensures the self safety of the hydraulic structure, the safety of instruments and equipment and the health safety of workers, and has great potential economic benefit, social benefit and environmental benefit.

Description

Method for calculating natural vibration frequency of local structure of complex hydraulic structure
Technical Field
The invention relates to the technical field of hydraulic buildings, in particular to a method for calculating the natural frequency of a local structure of a complex hydraulic building.
Background
For solving the natural frequency of the local monomer structure of the complex hydraulic structure, the first method is to solve the natural frequency of the whole structure of the complex hydraulic structure. The method solves the equation set uniformly by the rigidity matrix and the mass matrix of all the nodes of the whole structure to obtain the natural vibration frequency and the vibration mode of the whole structure and each local structure, and the solving method is simple and is generally used for solving the natural vibration characteristic and the vibration mode of the dam. However, for complex hydraulic buildings, the method is often not effective for solving. Taking a large hydropower house as an example: the plant sections of the general power station are adjacent, the selection of the boundary conditions has great influence on the natural vibration frequency of the whole structure of the plant, and the plant does not cause the strong vibration of the whole structure of the plant but the strong vibration of the local structure when the unit operates. Therefore, solving the natural vibration frequency and the vibration mode of the whole structure of a single unit block factory building has no practical engineering significance for the problems of vibration and the like, and the natural vibration frequency and the vibration mode of a local structure should be accurately analyzed. However, due to the complexity of the large power plant structure, the vibration modes of the local structures (such as columns, floors, etc.) are often coupled with each other due to the structural characteristics, and it is difficult to distinguish the natural frequency of which local structure a certain frequency belongs to from the vibration modes. Therefore, the method is not suitable for solving the natural vibration frequency and the vibration mode of the complex hydraulic structure.
The second method is to independently model and solve the local monomer structure needing to be solved in the complex hydraulic structure, so that the method is simple and convenient to model and small in solving scale. However, the disadvantages of this method are: the constraint conditions of the independent local monomer structure model (i.e. the rigidity of the local monomer structure) are difficult to be consistent with or even far from those of the local monomer structure in the whole model. Still taking the column of the large hydropower station plant as an example, if fixed constraints are applied to two ends of the column, since the constraint stiffness of the column is much greater than that of the column in the whole structure, the calculated frequency is more than 50% higher than the actual frequency. If the two ends of the upright post adopt simple support constraints, the constraint rigidity of the upright post is smaller than that of the integral structure, so that the calculated frequency is lower than the actual frequency by more than 30%. The vibration mode participation mass of the independent local monomer structure model is smaller than that of the local monomer structure in the whole model. The column finite element model independent from the plant structure does not consider the mass of the building with both ends participating in the constraint when solving the frequency and the vibration mode, so the participating mass of the vibration mode is smaller. Therefore, the second method often brings large errors and even wrong results for solving the natural vibration frequency of the local monomer structure in the complex hydraulic structure.
The third method is to solve the natural vibration frequency of a local monomer structure in a complex integral structure by referring to a method for solving the natural vibration frequency of a dam without a mass foundation. Still taking the hydropower station factory building structure as an example, the method has the advantage that the actual rigidity of the two ends of the upright post P1 (shown in FIG. 4) can be effectively simulated, so that the calculation result precision obtained by the method is greatly improved compared with that obtained by the method II. However, the disadvantages of this method are: when the frequency and the vibration mode of the upright post P1 are solved, the mass of the building with both ends participating in constraint is not considered, and the mass participating in the vibration mode is smaller, so the natural vibration frequency calculated by the method is usually larger, and the larger proportion even exceeds 30%.
Disclosure of Invention
The invention aims to provide a method for calculating the natural frequency of the local structure of the complex hydraulic structure, and solve the problem that the calculation result of the natural frequency of the local single structure of the complex hydraulic structure is not accurate.
The technical scheme for solving the technical problems is as follows: a method for calculating the natural vibration frequency of a local structure of a complex hydraulic structure comprises the following steps:
s1, creating a three-dimensional CAD model of the hydraulic structure;
s2, giving material attributes to the local structure to be solved, assigning the elastic modulus and Poisson ratio of other structures according to actual parameters, and giving a density value of 0;
s3, dividing the three-dimensional CAD model into a plurality of finite element meshes through tetrahedral units or hexahedral units;
s4, applying viscoelastic boundary conditions to the three-dimensional CAD model;
s5, calculating the first-order natural vibration frequency f of the local structure by a finite element method1；
S6, selecting a finite element mesh of a part adjacent to the density-assigned structure, and assigning a value according to the actual density of the part;
s7, calculating the first-order natural vibration frequency f of the local structure under the condition of the step S6 by a finite element method2；
S8, first-order natural vibration frequency f1And first order natural frequency f2If the relative error is greater than the threshold value, returning to the step S6, otherwise, entering the step S9;
s9, converting the first-order natural vibration frequency f2As the natural frequency of the local structure.
On the basis of the technical scheme, the invention can be further improved as follows.
Further, the calculation formula of the first-order natural frequency f is as follows:
|[K]-ω2[M]|＝0 (1)
Figure BDA0001782657640000031
in the above formula, [ K ] is a stiffness matrix, [ M ] is a mass matrix, and ω is a circular frequency.
Further, it is characterized byThe resistance coefficient K of the elastic boundary condition in the step S4bAnd damping coefficient CbThe calculation formula of (2) is as follows:
Figure BDA0001782657640000032
Cb＝ρcs(4)
in the above formula, G is the shear modulus of the foundation, rbIs the distance from the wave source to the calculation point, p is the ground deformation mode, csEither shear wave velocity or compressional wave velocity.
Further, the material properties include density, poisson's ratio, and elastic modulus.
Further, the threshold is 5%.
Further, the size of the finite element mesh is less than or equal to 1/3 of the sectional size of the local structure to be solved.
The invention has the beneficial effects that: the method can simulate the actual rigidity of the local monomer structure with high precision and simulate the actual participation quality of the vibration mode of the local monomer structure with high precision, can greatly improve the solving precision of the natural vibration frequency of the local structure of the complex hydraulic structure, can avoid the generation of severe vibration and resonance when being used for carrying out the dynamic design of the complex hydraulic structure, ensures the self safety of the hydraulic structure, the safety of instruments and equipment and the health safety of workers, and has great potential economic benefit, social benefit and environmental benefit.
Drawings
FIG. 1 is a general flow chart of the present invention;
FIG. 2 is a schematic diagram of a finite element mesh of a hydraulic structure according to an embodiment of the present invention;
FIG. 3 is a schematic representation of a viscoelastic boundary of a hydraulic structure in an embodiment of the invention;
fig. 4 is a schematic diagram illustrating selection of a frequency resolution area according to an embodiment of the present invention.
Detailed Description
The principles and features of this invention are described below in conjunction with the following drawings, which are set forth by way of illustration only and are not intended to limit the scope of the invention.
As shown in fig. 1, a method for calculating the natural frequency of the local structure of the complex hydraulic structure includes the following steps:
and S1, creating a three-dimensional CAD model of the hydraulic structure.
And S2, giving material attributes to the local structure to be solved, wherein the material attributes comprise density, Poisson 'S ratio and elastic modulus, and assigning the Poisson' S ratio and elastic modulus of the other structures according to actual parameters, but giving the density value of 0.
S3, as shown in FIG. 2, dividing the three-dimensional CAD model into a plurality of finite element meshes through tetrahedral units or hexahedral units, and when the calculation result does not need to pay attention to the static stress or dynamic stress of the hydraulic structure, the tetrahedral units can be used for dividing the meshes, but the tetrahedral units are adopted to influence the selection of unit ranges in the subsequent work; when the calculation result needs to consider the static stress or dynamic stress of the hydraulic structure, the hexahedral unit and the degenerated triangular prism unit thereof are adopted, so that the selection of the subsequent unit range is facilitated, and the unit node scale is smaller than that of the tetrahedral unit.
S4, fig. 3, applying viscoelastic boundary conditions to the three-dimensional CAD model, the hydraulic structure is generally built on a foundation, which is capable of transmitting and dissipating vibrational energy. The method can reduce the calculation scale and effectively simulate the transmission and dissipation of the vibration energy in the remote area.
S5, calculating the first-order natural vibration frequency f of the local structure by a finite element method1。
And S6, selecting the finite element meshes of the parts adjacent to the structure with the given density, and assigning values according to the actual density of the parts. As shown in fig. 4, when the natural vibration characteristic of the upright post P1 is solved, the cells a and B at the two ends of the upright post P1 are selected and given actual densities during the first return solution, the cells in the range of 1-1 are selected and given actual densities during the second return solution, the cells in the range of 2-2 are selected and given actual densities during the 3 rd return solution, and so on, so that the selection range can be continuously expanded.
S7, calculating the first-order natural vibration frequency f of the local structure under the condition of the step S6 by a finite element method2。
S8, first-order natural vibration frequency f1And first order natural frequency f2If the relative error is larger than the threshold value (5%), the process returns to step S6, otherwise, the process proceeds to step S9.
S9, converting the first-order natural vibration frequency f2As the natural frequency of the local structure.
Further, the calculation formula of the first-order natural frequency f is as follows:
|[K]-ω2[M]|＝0 (1)
Figure BDA0001782657640000051
in the above formula, [ K ] is a stiffness matrix, [ M ] is a mass matrix, and ω is a circular frequency.
Further, the resistance coefficient K of the elastic boundary condition in the step S4bAnd damping coefficient CbThe calculation formula of (2) is as follows:
Figure BDA0001782657640000052
Cb＝ρcs(4)
in the above formula, G is the shear modulus of the foundation, rbIs the distance from the wave source to the calculation point, p is the ground deformation mode, csEither shear wave velocity or compressional wave velocity.
In the embodiment of the present invention, the dimension of the finite element mesh is equal to or less than 1/3 (preferably not more than 1/4) of the cross-sectional dimension of the local structure to be solved, taking a vertical column of the hydropower station building structure as an example, if the size of the vertical column is 1m × 1m, the size of the unit of the vertical column along the cross-sectional direction and the size of the floor at two ends of the vertical column preferably do not exceed 0.25 m.
In another embodiment of the present invention, the steps S3 and S4 can be reversed, but the difficulty of imparting material properties to the local structure is increased.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (5)

1. A method for calculating the natural vibration frequency of a local structure of a complex hydraulic structure is characterized by comprising the following steps:
s1, creating a three-dimensional CAD model of the hydraulic structure;
s2, giving material attributes to the local structure to be solved, assigning the elastic modulus and Poisson ratio of other structures according to actual parameters, and giving a density value of 0;
s3, dividing the three-dimensional CAD model into a plurality of finite element meshes through tetrahedral units or hexahedral units;
1/3, the size of the finite element mesh is less than or equal to the sectional size of the local structure to be solved;
s4, applying viscoelastic boundary conditions to the three-dimensional CAD model;
s5, calculating the first-order natural vibration frequency f of the local structure by a finite element method1；
S6, selecting a finite element mesh of a part adjacent to the density-assigned structure, and assigning a value according to the actual density of the part;
s7, calculating the first-order natural vibration frequency f of the local structure under the condition of the step S6 by a finite element method2；
S8, first-order natural vibration frequency f1And first order natural frequency f2If the relative error is greater than the threshold value, returning to the step S6, otherwise, entering the step S9;
s9, converting the first-order natural vibration frequency f2As the natural frequency of the local structure.
2. The method for calculating the natural frequency of the local structure of the complex hydraulic structure according to claim 1, wherein the calculation formula of the first-order natural frequency is as follows:
|[K]-ω2[M]|＝0 (1)
Figure FDA0002575108220000011
in the above formula, [ K ] is a stiffness matrix, [ M ] is a mass matrix, [ omega ] is a circular frequency, and f represents a first-order natural frequency.
3. The method for calculating the natural frequency of the local structure of the complex hydraulic structure as claimed in claim 1, wherein the coefficient of resistance K of the viscoelastic boundary condition in the step S4bAnd damping coefficient CbThe calculation formula of (2) is as follows:
Figure FDA0002575108220000021
Cb＝ρcs(4)
in the above formula, G is the shear modulus of the foundation, rbIs the distance from the wave source to the calculation point, p is the ground deformation mode, csEither shear wave velocity or compressional wave velocity.
4. The method of calculating the natural frequency of vibration of the local structure of the complex hydraulic structure as claimed in claim 1, wherein the material properties include density, poisson's ratio and elastic modulus.
5. The method for calculating the natural frequency of the local structure of the complex hydraulic structure as claimed in claim 1, wherein the threshold is 5%.
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