KR20120018984A - Method for making nonlinear dynamic analysis model about cabinets of power plants to predict their seismic responses - Google Patents

Abstract

PURPOSE: A non-linear dynamic interpreted model creating method is provided to accurately predict earthquakes with a cabinet by considering model development and non-linearization effects. CONSTITUTION: A cabinet structure selects a non-linear model by using a node weight system and a finite element. A non-linear dynamic motion equation is selected by using the selected non-linear model. The non-linear dynamic motion equation uses a basic vibration mode in order to change the non-linear dynamic motion equations. An analysis model is improved by comparing with experiment materials.

Description

Method for making nonlinear dynamic analysis model about cabinets of power plants to predict their seismic responses}

The present invention relates to a method for preparing a nonlinear dynamic analysis model of a cabinet for predicting an earthquake response to a cabinet of a power plant. More particularly, the present invention relates to an earthquake response to a cabinet for storing electricity, communication, and power equipment of a power plant. In this paper, a non-linear dynamic analysis model of the cabinet is developed to predict and predict the earthquake response of the cabinet, the core equipment of the power plant, efficiently and accurately.

Power plants have many steel cabinets that house electrical or control instrumentation. Most of these are important facilities that are responsible for the safe operation and shutdown of power plants. In addition, they must maintain structural stability in the event of a strong earthquake such as a design earthquake. In addition, the unique functions assigned to each must be performed smoothly without errors. . For this purpose, when the power plant is constructed, the structures must be seismic safe through seismic design, and important equipment and facilities installed inside the structure must be verified by seismic verification.

In particular, commercial operation of nuclear power plants among power plants began in the 1960s. Based on more than 40 years of experience in this industry, we now have more advanced design technologies than in the early days, and our licensing requirements have been strengthened. Since the 1970s, the need to reassess the seismic safety of equipment installed in older nuclear power plants built before the requirements of the seismic design procedure have been comparable. Work is underway to reevaluate stability and improve performance.

Among them, the seismic performance can be evaluated by constructing an analytical model based on the blueprint and analyzing the seismic response. On the other hand, devices can be proved to be shockproof by vibration tests or seismic response analysis. However, since the equipment installed in the operating nuclear power plant is not allowed to be taken out for the purpose of vibration testing, it is not easy to prepare a dynamic analysis model for the seismic response analysis.

Normally, the seismic performance of electrical equipment including relays of nuclear power plants is determined by shaking table test. In this test, the relay is usually mounted directly on the shaking table. The earthquake demand diagram for a relay can usually be expressed as a floor response spectrum at the bottom of the cabinet in which the relay is mounted. In order to obtain the seismic demand for the relay and its corresponding performance value, the amplification of the laminar movement due to the cabinet at the relay mounting position is required, and the seismic tolerance of the relay can be evaluated.

To diagnose the seismic safety of the internal electrical equipment of a nuclear power plant, the dynamic characteristics of them must be analyzed first. In particular, in the case of replacing all or a part of the existing equipment and exercise equipment, it is necessary to prove whether the seismic performance requirements are met before and after the replacement of the components.

However, among the facilities of nuclear power plants, electrical devices such as cabinets or panels are very difficult to accurately determine the rigidity and the contribution mass of such equipment because not only the structural characteristics of the equipment itself but also the connection of the components included therein are very complicated. . Moreover, due to the amplified large seismic loads acting on the cabinet, the cabinet can exhibit complex nonlinearities. Therefore, it is very difficult for this kind of equipment to accurately build dynamic analysis model, and it is not easy to grasp their dynamic characteristics by the existing analysis method.

The present invention proposes a method for producing an accurate nonlinear dynamic analysis model that can reflect the dynamic nonlinearity and dynamic experimental results of a cabinet for a power plant equipment cabinet, which is very difficult to prepare a dynamic analysis model for seismic performance evaluation. I have a problem with doing.

The present invention provides the following steps: 1) the first step of idealizing the cabinet structure into a nonlinear model with finite element and nodal mass system, and 2) the second step of estimating the nonlinear dynamic equation of motion using the idealized cabinet structure model. The third step of converting the nonlinear dynamic equation of motion into the nonlinear equation of motion of a non-linked terminal induction system using the vibration mode, and 4) the fourth step of comparing the experimental data and the analysis model to improve the analysis model. Can be solved.

According to the present invention, it is possible to perform accurate prediction of the earthquake response of the cabinet because the problem solving means can consider the model improvement and nonlinear effects for each mode compared to the seismic response prediction method based on the existing finite element method.

1 is a diagram showing a structure of a cabinet that is an object for calculating a motion equation for nonlinear dynamic behavior analysis;
FIG. 2 illustrates that the cabinet of FIG. 1 is nonlinearly deformed by an earthquake, and the cabinet is manufactured in the same manner as the cabinet of FIG. 1, and the magnitude of the earthquake is increased by shaking table test on the manufactured cabinet. Figure showing the result of signal value separation by measuring the change,
3 is a diagram showing that the restoring force and displacement relationship for the cabinet of FIG.
4 is a view showing a model of the cabinet structure of Figure 1 by a finite element and node mass system;
5 shows a variant of the finite element of FIG. 4, and
FIG. 6 is a diagram showing an example of dynamic characteristics obtained by the finite element model before and after the improvement of FIG. 4. FIG.

Hereinafter, a method for preparing a nonlinear dynamic analysis model of a cabinet for predicting earthquake response of a power plant cabinet will be described in detail.

1. Nonlinear modeling of cabinet structures with finite element and node mass systems

Figure 1 shows the structure of a cabinet as an object for creating a nonlinear dynamic analysis model.

First, in order to estimate that the cabinet of FIG. 1 is nonlinearly deformed by the earthquake, the cabinet is manufactured in the same manner as the cabinet of FIG. 1, and the magnitude of the earthquake is increased by shaking table test on the manufactured cabinet. I measured it.

The result of the single value decompositon according to the measurement is shown in FIG.

The horizontal axis shown in FIG. 2 represents the excitation frequency (f) of the shaking table, the vertical axis represents the magnitude (S (t)) of the acceleration response power spectrum of the cabinet, and the lines of different colors are given for the cabinet. The RMS values of the force exerted through the shaking table (in g) are shown. In FIG. 2, the response points of the maximum size extracted by the PP (peak picking) method are indicated by a rhombus.

As can be seen in the graph of Fig. 2, the actual cabinet produced shows natural frequencies that decrease as the magnitude of the earthquake increases.

This phenomenon is presumed that the actual manufactured cabinet has a softening spring that is not proportional to the restoring force and displacement relationship, rather than linear spring, as shown in FIG. 3. do.

Based on these estimates, the finite element and node mass systems were modeled for the structure of the cabinet of FIG.

The modeled one is shown in FIG. 4. The points shown in FIG. 4 represent the node masses, and the numbers represent the number of finite elements and nodes.

2. Estimate nonlinear dynamic equations using modeled cabinet structures

The cabinet model as shown in FIG. 4 can be regarded as a force-displacement relationship in the form of a duffing to represent the soft form, where the bending stiffness of the beam, which is a component of the cabinet model, Is reduced.

Therefore, the relationship between the viewing stress σ _x and the strain ε _x of the cabinet model may be expressed as Equation 1 below, and the deformation may be illustrated as shown in FIG. 5.

는 각각 탄성계수와 비선형 변형률의 비례계수이다. Where E and

Are proportional coefficients of elastic modulus and nonlinear strain, respectively.

The sum of the finite element moments over the entire cross section of the beam shown in FIG. 5 should be equal to the bending moment M _n .

The bending moment is as shown in Equation 2 below.

In the case where the cross section of the beam is b * h, Equation 2 may be simplified as in Equation 3 below.

이고,

이다.From here

ego,

to be.

Using Equation 4 below, the deflection equation of a beam having nonlinear bending stiffness is given by Equation 5 below.

Displacement energy stored in the beam can be expressed as Equation 6 below.

Based on the above equations, deriving the motion equation for the finite element of one beam is given by the following equation (7).

및

는 다음과 같이 요소변위벡터이고, 그리고

는 다음과 같이 힘벡터이다. 또한,

,

, 및

는 각각 다음 같이 요소 질량 행렬, 선형 요소 강성 행렬 및 비선형 요소 강성 행렬이다.From here,

And

Is the element displacement vector, and

Is the force vector as Also,

,

, And

Are the element mass matrix, the linear element stiffness matrix and the nonlinear element stiffness matrix, respectively, as follows.

Therefore, the motion equation of the beam system of the cabinet structure can be obtained by combining the element matrices as shown in Equation 8 below.

,

,

,

및

는 각각

,

,

,

및

에 대응하는 시스템 행렬이다. here

,

,

,

And

Respectively

,

,

,

And

Is the system matrix corresponding to.

3. Converting nonlinear dynamic equations into nonlinear equations of motion of the non-coupled terminal induction system using the basic vibration mode.

In order to compare the shaking table test results with the analysis results for the cabinet, the analysis vibration mode corresponding to the dominant test vibration mode obtained from the shaking table test should be extracted from the nonlinear dynamic motion equation. The modes should be compared. In order to extract the analysis vibration mode from the nonlinear dynamic equations, it is necessary to convert the nonlinear dynamic equations into the equations of the non-coupled terminal induction system. The first oscillation and nonlinear modes are presented as follows to convert these non-linked equations.

을 이용함으로써 비연계 단자유도계 운동방정식들이 얻어질 수 있다. 물리적 좌표 시스템에서의 변위{U}는, 다음과 같이 모드 좌표 시스템에서 대응 변위{

}와 선형모드행렬을 사용하여 치환될 수 있다.In the case of a linear system, a mode matrix, ie a linear mode matrix

By using, non-connected terminal induction motion equations can be obtained. The displacement {U} in the physical coordinate system is the corresponding displacement {in the mode coordinate system as follows:

} And linear mode matrices.

및

, (i=1,L,n;j=1,L,m)

And

, (i = 1, L, n; j = 1, L, m)

Where n is the number of degrees of freedom of the system and m is the number of system modes.

를 곱함으로써 연계된 비선형방정식이 다음의 수학식 9와 같은 선형시스템에 대해서만 비연계된 비선형 모드 방정식으로 확장된다.On both sides of the equation

By multiplying, the associated nonlinear equations are extended to non-linked nonlinear mode equations only for linear systems such as

로 대각행렬이고, 그리고

로 대각행렬이며, Ω은 가진진동수이다.
From here,

Is a diagonal matrix, and

Is a diagonal matrix, and Ω is the excitation frequency.

In addition, the nonlinear term on the left side of the equation may be converted into a mode coordinate system using the newly defined nonlinear mode as shown in Equation 10 below.

Here, the nonlinear mode is an associated nonlinear form of mode displacements as shown in Equation 11 below.

이이다. here,

This is it.

,i=1, n) 및 제1의 고유진동수(

)에 의해 강력하게 지배된다는 것에 추정을 가지고서, 서로 연계된 (

)은 그들의 비율이 다음과 같은 제1모드 증폭들의 비율로서 고려됨으로써 추정된다.The nonlinear dynamic response of the system is the first eigenmode (

, i = 1, n) and the first natural frequency (

With the presumption that it is strongly dominated by

) Is estimated by considering their ratio as the ratio of first mode amplifications as follows.

Using the above relation, Equation 11 may be expressed as a non-associative nonlinear form of mode displacement as shown in Equation 12 below.

here

Accordingly, the nonlinear term in Equation 9 can be expressed as follows by using Equation 11.

은 대각행렬이 아니다. 하지만

인 경우에 다음의 수학식 13와 같은 대각행렬로 근사된다.From the stomach

Is not a diagonal matrix. However

Is approximated by the diagonal matrix as in Equation (13).

은 제1 고유진동수(

) 주위에서 시스템이 자극을 받을 때의 대각행렬이다.here,

Is the first natural frequency (

) Is the diagonal matrix when the system is stimulated.

Therefore, by combining Equations 9 and 13, the nonlinear equations of motion obtained by a simple diagonal matrix can be obtained as follows, and the analysis model can be improved by comparing with the test results shown in FIG. have.

or

이다.here

to be.

진동수 영역에서 가속도 응답의 크기이며, 청색선은 시혐결과이고, 녹색선은 해석모델의 갱신전의 결과이며, 그리고 적색선은 해석모델의 갱신후의 결과이다.Fig. 6 shows the magnitude in the frequency range of the acceleration response near the natural frequency measured or interpreted at the top of the cabinet as the RMS values of the excited loads increase to 0.2g, 0.4g, 0.6g, 0.8g, 1.0g, 1.2g. Also increase with. In Figure 6 the horizontal axis is the frequency ratio (frequency ratio), the vertical axis is

The magnitude of the acceleration response in the frequency domain, the blue line is the test result, the green line is the result before the update of the analysis model, and the red line is the result after the update of the analysis model.

The analysis results represented by the green and red lines are obtained by applying a numerical method to the nonlinear equations of motion shown in Equation (14).

값을 해석결과와 실험결과 사이의 오차를 최소화하는 방법 등을 적용하여 조절함으로써 비선형 해석모델의 해석결과를 실험결과와 근사시킬 수 있다.
In Figure 6, the natural frequency of the structure before updating the analysis model does not change as the magnitude of the acceleration response increases, but the natural frequency after updating the analysis model decreases as the magnitude of the acceleration response increases, similar to the test results. Since the trends are shown, the results after updating the model tend to be more similar to the test results than the results before updating the model. That is, in the case of a linear analysis model, a change in natural frequency cannot be represented according to the magnitude of an input load, but in the case of a nonlinear analysis model, a change in natural frequency can be represented according to the magnitude of an input load. In the first term

By adjusting the value to minimize the error between the analysis result and the experimental result, the analysis result of the nonlinear analysis model can be approximated with the experimental result.

; 진동수 영역에서 가속도 응답의 크기S (t); The magnitude of the acceleration response power spectrum of the cabinet,

; Magnitude of acceleration response in frequency domain

Claims (3)

1) First step to idealize cabinet structure into nonlinear model with finite element and node mass system,
2) a second step of estimating the nonlinear dynamic equation of motion using the idealized cabinet structure model;
3) a third step of converting the nonlinear dynamic equation of motion into the nonlinear equations of motion of the non-linked terminal induction system using the basic vibration mode; and
4) A method of preparing a nonlinear dynamic analysis model of a cabinet for predicting seismic response to a cabinet of a power plant, comprising a fourth step of improving the analysis model by comparing the experimental data with the analysis model. The method of claim 1,
In the second step, the nonlinear dynamic equation

And
here

,

,

,

And

Are the displacement system matrix, the force system matrix, the mass system matrix, the linear system stiffness matrix, and the nonlinear system stiffness matrix, respectively, and

A nonlinear dynamic analysis model of a cabinet for predicting earthquake response of a cabinet of a power plant, characterized in that. The method of claim 2,
In the third step, the nonlinear equations of motion of the non-

,
here,

Is the displacement,

A nonlinear dynamic analysis model of a cabinet for predicting the seismic response of a cabinet of a power plant, characterized in that the excitation frequency.

Images