CN109508439B - Time course analysis method for nuclear power plant floor response spectrum - Google Patents
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Abstract
The invention relates to a high-precision time-course analysis method for calculating a floor spectrum of a nuclear power plant; the method comprises the following steps: simplifying nuclear power equipment into a single-degree-of-freedom damping system, establishing a motion equation, and selecting a damping ratio and equipment frequency; secondly, selecting an analysis step length; third, calculating time step by time step, for the ith time step, knowing t i‑1 The displacement and the speed of the moment are calculated by the recursion formula listed in the invention, and t is calculated at the ith time step i Displacement, velocity and absolute acceleration at time; and fourthly, calculating the peak value of the acceleration response curve as the floor spectrum value of the given frequency and damping ratio for drawing the floor spectrum. Compared with the existing floor spectrum calculation software, the time course analysis method has higher solving precision, simple operation steps, easy implementation and very strong engineering application value.
Description
Technical Field
The invention relates to a time course analysis method for a nuclear power plant floor response spectrum.
Background
Along with the rapid development of economy in China, the energy demand is increased rapidly, and meanwhile, the problem of global warming environmental pollution caused by excessive emission of greenhouse gases troubles people, and more people aim at nuclear energy. The advantages of high-efficiency cleaning of nuclear power and the like and the promotion of the national economic development needs of China promote the rapid development of the nuclear power. At the same time, the consequences of nuclear leaks are also extremely severe, with earthquakes being one of the important factors affecting nuclear safety. A violent earthquake of grade 6.8, occurring in the new seikaga county on day 17 of month 7 2007, caused 4 units of the tokyo electric Liu Yu nuclear power plant to shut down. Nuclear power plants operate safely and reliably, and require reliable seismic analysis.
Compared with the common structural seismic design, the nuclear power plant seismic design has particularity, not only comprises the structural seismic design of the reaction shell and the nuclear power plant, but also comprises the seismic design of the support, the connection and the like of nuclear power key equipment, and the seismic design is often the most key factor influencing the safe operation of the nuclear power plant under the action of an earthquake. For earthquake-resistant analysis of subsystems which are not coupled with a main body structure in a nuclear power plant, a floor response spectrum is usually adopted as design earthquake motion input. Therefore, the accuracy of the floor reaction spectrum directly determines the effectiveness of the seismic analysis of the nuclear power equipment.
The existing floor response spectrum calculation method usually adopts a time course analysis method, namely equipment is simplified into a single-degree-of-freedom system, inertia force obtained by the product of floor acceleration and mass is applied to the equipment, acceleration response peak values under the conditions of different damping ratios and different frequencies are calculated by adopting the time course analysis method, and the acceleration response peak values of the equipment with different frequencies are drawn into curves, so that the floor response spectrum corresponding to the specific damping ratio is obtained. The most common floor reaction spectrum analysis software at present is SeismoSignal, and the software adopts a Newmark method to carry out kinetic analysis. However, the method is low in precision, and for a high-frequency region, a reliable acceleration peak value which cannot be calculated by a Newmark method causes curve distortion of a floor response spectrum in a short period section.
Disclosure of Invention
Aiming at the problem that the existing time-course method is insufficient in calculation accuracy of the high-frequency part of the floor response spectrum, the invention aims to provide an accurate time-course analysis method for the floor response spectrum of the nuclear power plant.
The technical scheme of the invention is as follows:
a high-precision time-course analysis method for calculating a floor spectrum of a nuclear power plant comprises the following steps:
the method comprises the steps of firstly, simplifying nuclear power equipment into a single-degree-of-freedom damping system, wherein the mass of the nuclear power equipment is m, the rigidity of the nuclear power equipment is k, the damping of the nuclear power equipment is c, the mass, the rigidity and the damping of the nuclear power equipment can be measured through experiments, and the mass of the nuclear power equipment isThe floor acceleration corresponding to the center position is a f And establishing a motion equation:
ma+cv+ku＝-ma f ；
wherein u, v and a are respectively the particle displacement, velocity and acceleration of the nuclear power equipment, and are obtained by simplification:
a+2ξωv+ω 2 u＝-a f ；
wherein,
is a round frequency->
Is the damping ratio; />
Secondly, selecting a floor spectrum period interval (T) to be calculated 1 ,T 2 ) And a period interval Δ T;
thirdly, calculating a floor spectrum value corresponding to each discrete period T in the period interval;
1) Calculating the circle frequency corresponding to the period T, wherein omega =2 pi/T, and calculating an invariant; theta, alpha 1 ～α 4 And β 1 ～β 4 Are respectively as
θ＝e -ξωΔt
Wherein
Δ t is floor acceleration a f A recording interval of (a);
2) Make the initial displacement u 0 And velocity v 0 The displacement u at each time is calculated in stepwise recursion as follows i Velocity v i Absolute acceleration a i ；
a i ＝-2ξωv i -ω 2 u i
3) Get a i Peak value max | a i L as the value S of the floor response spectrum corresponding to the period T in the period interval a ；
Fourthly, the value S of the value response spectrum corresponding to each discrete period a And connecting the lines to obtain a floor response spectrum.
Compared with the prior art, the invention has the advantages that:
(1) The time course analysis method can accurately calculate the floor response spectrum, is particularly effective for calculating the floor response spectrum in a high-frequency band, and other methods such as a Newmark method can only be converged in the method by a method for subdividing time steps.
(2) The method is an explicit method, each step of calculation of the explicit method does not need to solve a large-scale equation set, only needs to carry out unit-level matrix and vector multiplication operation and integral vector addition operation, has obvious advantages in calculation efficiency, and does not have the problem of incapability of convergence, so the method has inherent advantages in calculating the dynamic response of the building structure under the action of strong earthquake and simulating the strong nonlinear response of complex models such as collapse.
Drawings
FIG. 1 is a schematic view of a floor response spectrum calculation model;
FIG. 2 is a schematic illustration of floor acceleration input;
FIG. 3 is a comparison graph of the floor response spectrum calculated by the method of the present invention and a Newmark method.
Detailed Description
The present invention is further illustrated by the following examples, which are not intended to limit the invention to these embodiments. It will be appreciated by those skilled in the art that the present invention encompasses all alternatives, modifications and equivalents as may be included within the scope of the claims.
The invention will be described in detail with reference to the following drawings, which are provided for illustration purposes and the like:
the dynamic analysis method is specifically explained by taking a single-degree-of-freedom system obtained by simplifying high-frequency nuclear power equipment as an example, wherein the single-degree-of-freedom system is shown in figure 1, and the damping ratio of the single-degree-of-freedom system is 0.02; the power time course analysis method comprises the following steps:
the method comprises the following steps that firstly, a nuclear power device 1 is simplified into a single-degree-of-freedom damping system, the mass of the nuclear power device 1 is m, the rigidity is k, the damping is c, and the mass, the rigidity and the damping of the nuclear power device 1 can be measured through experiments; the floor acceleration corresponding to the mass center position of the nuclear power equipment 1 is a f And establishing a motion equation:
ma+cv+ku＝-ma f
wherein u, v and a are respectively the particle displacement, velocity and acceleration of the nuclear power equipment 1; the simplification results in:
a+2ξωv+ω 2 u＝-a f ；
wherein,
is a round frequency->
Is the damping ratio;
where ξ =0.02, floor acceleration a f The distribution of (c) is shown in fig. 2, and the acceleration recording interval is 0.005s;
secondly, selecting a floor spectrum period interval (T) to be calculated 1 ,T 2 ) And a period interval Δ T;
thirdly, calculating a floor spectrum value corresponding to each discrete period T in the period interval;
1) Calculating the circle frequency corresponding to the period T, taking T =0.02s as an example, and ω =100 pi, and calculating an invariant; theta, alpha 1 ～α 4 And β 1 ～β 4 Are respectively as
θ＝0.939101367424293
α 1 ＝-0.999987232427475
α 2 ＝0.00000200060006841807
α 3 ＝-0.197451312573499
α 4 ＝-1.00001237270939
β 1 ＝-0.104003924224908e-4
β 2 ＝-0.105207602581023e-4
β 3 ＝0.209011466798461e-2
β 4 ＝-0.209211526805928e-2
2) Make the initial displacement u 0 And velocity v 0 The displacement u at each time is calculated in stepwise recursion as follows i Velocity v i Absolute acceleration a i ；
a i ＝-2ξωv i -ω 2 u i
3) Get a i Peak value max | a i L as the value S of the floor response spectrum corresponding to the period T in the period interval a 。
Fourthly, the value S of the value response spectrum corresponding to each discrete period a And connecting the lines to obtain a floor reaction spectrum. As shown in fig. 3. The horizontal axis is the period, and the vertical axis is the floor response spectrum.
In order to show the high efficiency and accuracy of the time course analysis method, the Newmark method is also adopted to calculate the example. The analysis step length delta t =0.005s is selected, and the smaller step length delta t =0.00125s is selected for calculation, and the floor response spectrum is calculated, as shown in fig. 3. By contrast, the calculation result of the method with the Newmark method of delta t =0.00125s is closer to that of the method, and the deviation of the calculation result of the method with the Newmark method of delta t =0.005s is larger. Further indicating the accuracy of the method of the invention.
It should be understood that the steps of the methods described herein are merely exemplary and no particular requirement is placed on the chronological order in which they are performed unless they are themselves necessarily sequential.
While the present invention has been described with reference to a limited number of embodiments and drawings, as described above, various modifications and changes will become apparent to those skilled in the art to which the present invention pertains. Accordingly, other embodiments are within the scope of the following claims and the claims and equivalents thereto.
Claims (1)
1. A time course analysis method for a nuclear power plant floor response spectrum is characterized by comprising the following steps:
the method comprises the steps that firstly, nuclear power equipment is simplified into a single-degree-of-freedom damping system, the mass of the nuclear power equipment is m, the rigidity is k, the damping is c, the mass, the rigidity and the damping of the nuclear power equipment can be measured through experiments, and the floor acceleration corresponding to the mass center position of the nuclear power equipment is a f And establishing a motion equation:
ma+cv+ku＝-ma f ；
wherein u, v and a are respectively the particle displacement, velocity and acceleration of the nuclear power equipment, and are obtained by simplification:
a+2ξωv+ω 2 u＝-a f ；
wherein,
in the form of a circular frequency, the frequency of the circular frequency,
is the damping ratio;
secondly, selecting a floor spectrum period interval (T) to be calculated 1 ,T 2 ) And a period interval Δ T;
thirdly, calculating a floor spectrum value corresponding to each discrete period T in the period interval;
1) Calculating the circle frequency corresponding to the period T, wherein omega =2 pi/T, and calculating an invariant; theta, alpha 1 ～α 4 And beta 1 ～β 4 Are respectively as
θ＝e -ξωΔt
Wherein
Δ t is floor acceleration a f A recording interval of (a);
2) Make the initial displacement u 0 And velocity v 0 The displacement u at each time is calculated in stepwise recursion as follows i Velocity v i Absolute acceleration a i ；
a i ＝-2ξωv i -ω 2 u i
3) Get a i Peak value max | a i L as the value S of the floor response spectrum corresponding to the period T in the period interval a ；
Fourthly, the values corresponding to the discrete periods are reflected to the value S of the spectrum a And connecting the lines to obtain a floor response spectrum.
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Citations (6)
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|---|---|---|---|---|
| JPH0434330A (en) * | 1990-05-31 | 1992-02-05 | Toshiba Corp | Floor response spectrum evaluator |
| JP2008268074A (en) * | 2007-04-23 | 2008-11-06 | Toshiba Corp | Plant equipment vibration measuring system |
| CN101826118A (en) * | 2009-03-04 | 2010-09-08 | 中国核电工程有限公司 | Interactive manufacturing method of floor response spectrum for aseismatic calculation |
| CN104849750A (en) * | 2015-04-21 | 2015-08-19 | 大连理工大学 | Nuclear power floor spectrum artificial seismic wave fitting method based on objective wave waveform analysis |
| CN108038262A (en) * | 2017-11-14 | 2018-05-15 | 中国核电工程有限公司 | A kind of floor response spectrum simplified calculation method of consideration SSSI effects |
| CN108229056A (en) * | 2018-01-29 | 2018-06-29 | 江苏壹鼎崮机电科技有限公司 | The Aseismic Reliability design method of building aseismicity suspension and support |
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2018
- 2018-11-15 CN CN201811356382.6A patent/CN109508439B/en active Active
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|---|---|---|---|---|
| JPH0434330A (en) * | 1990-05-31 | 1992-02-05 | Toshiba Corp | Floor response spectrum evaluator |
| JP2008268074A (en) * | 2007-04-23 | 2008-11-06 | Toshiba Corp | Plant equipment vibration measuring system |
| CN101826118A (en) * | 2009-03-04 | 2010-09-08 | 中国核电工程有限公司 | Interactive manufacturing method of floor response spectrum for aseismatic calculation |
| CN104849750A (en) * | 2015-04-21 | 2015-08-19 | 大连理工大学 | Nuclear power floor spectrum artificial seismic wave fitting method based on objective wave waveform analysis |
| CN108038262A (en) * | 2017-11-14 | 2018-05-15 | 中国核电工程有限公司 | A kind of floor response spectrum simplified calculation method of consideration SSSI effects |
| CN108229056A (en) * | 2018-01-29 | 2018-06-29 | 江苏壹鼎崮机电科技有限公司 | The Aseismic Reliability design method of building aseismicity suspension and support |
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| "a novel time continous p-galerkin scheme with 2p-oeder accuracy for seismic dynamic analysis";Xu Junjie等;《16th World Conference on Earthquake Engineering》;全文 * |
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