CN108846240A - A method of it is used to instruct equipment-support system Aseismic Design based on spring mass model - Google Patents
A method of it is used to instruct equipment-support system Aseismic Design based on spring mass model Download PDFInfo
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Abstract
The present invention relates to Aseismic Design technical fields, and in particular to a method of it is used to instruct equipment-support system Aseismic Design based on spring mass model, include the following steps：Equipment and its support are reduced to tool there are two the first spring-quality system of freedom degree, there will be no second spring-quality systems that the equipment when support is reduced to single-degree-of-freedom；For first spring-quality system, its intrinsic frequency of system of equipment and support composition and the bias Δ of equipment intrinsic frequency are acquired1And the bias Δ of its intrinsic frequency and support intrinsic frequency2；Support is acquired to the influence coefficients R of the dynamic respond of equipmentxAnd support is to the influence coefficients R of the acceleration responsive of equipmenta；According to the Δ1、Δ2、RxAnd RaEquipment-support system Aseismic Design is instructed, the influence that the present invention responds equipment by quantifying support discloses the root that support influences, defines its influence degree, can provide guidance for equipment-support system Aseismic Design.
Description
Technical field
The present invention relates to Aseismic Design technical fields, and in particular to a kind of setting for guidance based on spring mass model
The method of standby-support system Aseismic Design.
Background technique
For the Seismic of equipment, analysis method, test method, analogue method, earthquake empirical data method can be used,
Demonstration can be made inferences using the combination of the above method.But no matter which kind of asesmic appraisal method being used, the simulation of earthquake is all
It is a wherein essential link, and the accuracy of earthquake simulation is directly related to the reasonability of equipment Seismic.It is right
In the equipment for being not directly mounted to floor but using support construction, in the case where only using equipment as research object (for example,
The equipment for being installed on pedestal or pipeline), the Seismic of equipment generally determines Seismic input with the following method：
(1) if the intrinsic frequency of equipment is lower than seismic wave cutoff frequency, the upper floor response spectra of selected equipment is as ground
Shake input, the influence to envelope support construction (for example, equipment base) to seismic response of equipment.
(2) if the intrinsic frequency of equipment is greater than seismic wave cutoff frequency, when calculating seismic response of equipment using static method, ground
The equivalent static(al) of shake load has following determining method：
(a) using the envelope acceleration gone out given in applicable equipment technical Specification；
(b) floor response spectra acceleration null cycle (ZPA) in equipment；
(c) for multiple degrees of freedom component, when partial model is simple, it can use in equipment and be greater than on a floor response spectra
1.5 times of the maximum value of spectrum corresponding to frequency range equal to equipment fundamental frequency.
There is the equipment of support construction, seismic (seismal transmission path is workshop first, followed by support construction, is finally
Equipment.Therefore, for equipment Seismic, need to consider workshop, support and the common effect of equipment three.According to
GB50267-1997《Code for seismic design of unclear power plants》, in the Aseismic Design of nuclear power plant, main structure can be used as main body system,
Structure, system and the component that it is supported can be used as subsystem.Master is divided for workshop, support (including pedestal) and equipment three
System and subsystem, preferably using workshop as main body system, support and equipment are as subsystem.This is based on considered below, first, branch
Support and equipment are partial structurtes relative to workshop, second, the vibration characteristics of support and equipment, is especially connected directly with workshop
The vibration characteristics of support construction and the vibration characteristics of workshop greatly differ from each other, third, the major embodiment in the floor response spectra of workshop
Be workshop entirety vibration characteristics, there is no the vibration characteristics for embodying support construction (for example, pedestal), so will support and set
The standby subsystem being considered as relative to workshop.In general, equipment and the quality sum of support are much smaller than the quality of workshop, that is, meet
Subsystem and Decoupling Conditions of the main body system mass ratio less than 0.01, therefore, equipment and support can carry out antidetonation independently of workshop
Identification, while the seismic (seismal that workshop transmits being embodied by the floor response spectra of workshop.
It is raw to equipment generally by equipment technical Specification, equipment purchase technical specification when nuclear power plant purchases equipment
It produces producer and shockproof requirements is proposed to equipment.For the equipment that seismic (seismal is provided in the form of floor response spectra, if equipment is not pacified
It loaded on floor, and is mounted in support, since support construction is from that can generate certain deformation under earthquake, supports
Difference certainly will be had with equipment junction and support and the seismic response of floor junction.Thus, NB/T 20036.2-2011
《The active mechanical equipment qualification part 2 of nuclear power plant：Seismic》It claims in " earthquake simulation " section to Seismic input,
" input earthquake should be determined for the basis of installation equipment, floor or system ".That is, making the equipment antidetonation mirror with support construction
Periodically, it is desirable that the Seismic input of equipment is determined for support construction.
But the equipment for being installed on support construction, if in Seismic with equipment and support construction to be whole,
And when being only analysis object with equipment, existing method can not quantify to support the influence to equipment response, can not more define shadow
The degree of sound.
Summary of the invention
The present invention provide it is a kind of based on spring mass model for instructing equipment-support system Aseismic Design method,
Its influence for having bolster model by establishing equipment and equipment being responded without bolster model, quantization support, so as to for instructing
Equipment-support system Aseismic Design.
In order to achieve the above objectives, the technical solution adopted by the present invention is that：It is a kind of to be used to instruct based on spring mass model
Equipment-support system Aseismic Design method, includes the following steps：
(1) equipment and its support are reduced to the first spring-quality system for having there are two freedom degree；There will be no described
Equipment when support is reduced to second spring-quality system of single-degree-of-freedom；
(2) vibration equation for acquiring first spring-quality system, using canonical formation matrix Ψ as coordinate transform
Matrix, acquires two intrinsic frequencies of equipment-support system in first spring-quality system, and with each mode pair
The response answered carries out modality combinations using SRSS method, acquire in first spring-quality system dynamic respond of equipment and
Acceleration responsive；
(3) vibration equation for acquiring the second spring-quality system, in known surface seismic acceleration responsive time spectrum,
Kinematic analysis, which is carried out, by response spectra seismic (seismal obtains the dynamic respond of equipment and acceleration in the second spring-quality system
Degree response；
(4) it is directed to first spring-quality system, acquires its intrinsic frequency of system and equipment of equipment and support composition
The bias Δ of intrinsic frequency1And equipment and support constitute its intrinsic frequency of system and support intrinsic frequency bias
Δ2；
(5) it will be set in the dynamic respond of equipment in first spring-quality system and the second spring-quality system
Influence of the ratio quantization support of standby dynamic respond to equipment dynamic respond, the influence being supported to the dynamic respond of equipment
Coefficients Rx；
It (6) will be in the acceleration responsive of equipment in first spring-quality system and the second spring-quality system
Influence of the ratio quantization support of the acceleration responsive of equipment to equipment dynamic respond；The acceleration responsive being supported to equipment
Influence coefficients Ra；
(7) according to the Δ1、Δ2、RxAnd RaInstruct equipment-support system Aseismic Design.
Further, the vibration equation of first spring-quality system is：
Wherein,
m1For the quality of equipment, k1For the rigidity of equipment, x1It is equipment in first spring-quality system relative to ground
The displacement in face；
m2For the quality of support, k2For the rigidity of support, x2It is support phase in first spring-quality system for ground
The displacement in face；
xgFor the displacement on ground under geological process；
The vibration equation of the second spring-quality system is：
Or it is separately written as
Wherein,
x3For displacement of the equipment relative to ground in the second spring-quality system.
Further, the displacement of equipment and acceleration responsive are respectively in first spring-quality system：
Wherein,
n1For support/equipment quality ratio, i.e.,
ω1For the intrinsic frequency of equipment,
ωs1And ωs2For two intrinsic frequencies of equipment-support system in first spring-quality system；
Sa1For with ωs1Corresponding acceleration responsive spectrum, Sa2For with ωs2Corresponding acceleration responsive spectrum；
The dynamic respond of equipment is in the second spring-quality system：
Wherein, wherein the acceleration responsive of equipment is Sa, SaFor with frequencies omega1Corresponding seismic acceleration responds spectrum.
Further,
Wherein,
ω2For the intrinsic frequency of support,
n3For support/device frequency ratio, i.e.,
Different support/equipment qualities are probed into than lower Δ1And Δ2With support/device frequency ratio changing rule.
Further, in support/equipment quality ratio n1With support/device frequency ratio n3Following range in 1≤n1≤100、
0.1≤n3≤ 10, probe into bias Δ1And Δ2Changing rule.
Further, the influence coefficients R to the dynamic respond of equipment is supportedxFor：
It probes under different supports/equipment quality ratio and support/device frequency ratio, dynamic respond influences coefficients RxVariation rule
Rule.
Further, the intrinsic frequency probed into respectively in equipment is higher than seismic wave cutoff frequency and lower than seismic wave cut-off
Under frequency both of these case, under different supports/equipment quality ratio and support/device frequency ratio, dynamic respond influences coefficients Rx's
Changing rule.
Further, the influence coefficients R to the acceleration responsive of equipment is supportedaFor：
It probes under different supports/equipment quality ratio and support/device frequency ratio, acceleration responsive influences coefficients RaVariation
Rule.
Further, the intrinsic frequency probed into respectively in equipment is higher than seismic wave cutoff frequency and lower than seismic wave cut-off
Under frequency both of these case, under different supports/equipment quality ratio and support/device frequency ratio, acceleration responsive influences coefficients Ra
Changing rule.
Further, in step (7), equipment-support system should avoid support/device frequency ratio in Aseismic Design and be equal to
The case where 1 the case where and support/device frequency ratio are less than 1.
After the above technical solution is adopted, the present invention has the following advantages that compared with prior art：The present invention is set by establishing
The influence for having bolster model and responding without bolster model, quantization support to equipment inherently discloses the root that support influences,
Its influence degree is defined, determines its influence factor, to provide guidance for equipment-support system Aseismic Design.
Detailed description of the invention
Attached drawing 1 is the equipment simplified in the present invention and support two-freedom spring-quality system；
Attached drawing 2 is the equipment single-degree-of-freedom spring-quality system simplified in the present invention；
Attached drawing 3 is support/equipment qualities different in the present invention than lower bias Δ1With support/device frequency ratio n3Variation
Curve；
Attached drawing 4 is support/equipment qualities different in the present invention than lower bias Δ2With support/device frequency ratio n3Variation
Curve；
Attached drawing 5 is the spectrum shape of Seismic input response spectra 1 in the present invention；
Attached drawing 6 is the spectrum shape of Seismic input response spectra 2 in the present invention；
Attached drawing 7 is the lower R of flexible apparatus Seismic input 1 in the present inventionxWith n1、n3Change curve；
Attached drawing 8 is the lower R of flexible apparatus Seismic input 2 in the present inventionxWith n1、n3Change curve；
Attached drawing 9 is the lower R of rigid device Seismic input 1 in the present inventionxWith n1、n3Change curve；
Attached drawing 10 is the lower R of rigid device Seismic input 1 in the present inventionxWith n3Localized variation curve；
Attached drawing 11 is the lower R of rigid device Seismic input 2 in the present inventionxWith n1、n3Change curve；
Attached drawing 12 is the lower R of rigid device Seismic input 2 in the present inventionxWith n3Localized variation curve；
Attached drawing 13 is r in the present inventionx1With n1、n3Changing rule；
Attached drawing 14 is r in the present inventionx2With n1、n3Changing rule；
Attached drawing 15 is the lower R of flexible apparatus Seismic input 1 in the present inventionaWith n3Change curve；
Attached drawing 16 is the lower R of flexible apparatus Seismic input 2 in the present inventionaWith n3Change curve；
Attached drawing 17 is the lower R of rigid device Seismic input 1 in the present inventionaWith n3Change curve；
Attached drawing 18 is the lower R of rigid device Seismic input 2 in the present inventionaWith n3Change curve；
R when attached drawing 19 is more soft equipment different earthquake input in the present inventionaComparison；
R when attached drawing 20 is more rigid equipment different earthquake input in the present inventionaComparison；
Attached drawing 21 is r in the present inventiona1With n1、n3Changing rule；
Attached drawing 22 is r in the present inventiona2With n1、n3Changing rule.
Specific embodiment
Below in conjunction with the accompanying drawings and embodiment the invention will be further described.
A method of it is used to instruct equipment-support system Aseismic Design based on spring mass model, including walks as follows
Suddenly：
(1) the spring mass model for having support equipment is established
Equipment and its support are reduced to tool, and there are two the spring-quality systems of freedom degree, as shown in Figure 1.m1、k1、x1For
Quality, rigidity and the displacement relative to ground of equipment, m2、k2、x2For the quality of support, rigidity and relative to the displacement on ground,
xgFor the displacement on ground under geological process.
The equation of motion in the system level direction is
Wherein,
By solving the characteristic equation of equation (1) described system, enable The natural frequency ω of the available systems
Enable ωs1And ωs2For two solutions of formula (2), i.e. two intrinsic frequencies of equipment-support system.Due in formula (2)Therefore, ωs1≠ωs2, therefore
The two degree freedom system that equipment, support form is without repeated root.By vibration equation (1) it is found that the system exists under original coordinate system
Elastic Coupling.According to canonical formation matrix Ψ as transformation matrix of coordinates, former vibration equation (1) can be decoupled.Therefore, by x
=Ψ η substitutes into formula (1) and can obtain
η is canoncial coordinates,
For known mass matrix and stiffness matrix, can solve corresponding canonical formation matrix Ψ is
Wherein,
After decoupling, the solution of formula (4) can be obtained by solving the vibration of two single-mode systems
For system as shown in Figure 1, the part in formula (5), (6) bracket is constant, for simplification, is enabledFor problems of engineering design, such as nuclear power plant's buildings or structures,
How equipment and the Aseismic Design of component etc., the not given characteristics of motion for motivating lower system of care, select system
Within the scope of the maximum value that system responds is limited in centainly by certain parameters.Under in response to this, it is assumed below for Fig. 1
Shown system, it is known that surface seismic acceleration responsive spectrum.Kinematic analysis is carried out by response spectra seismic (seismal, it can be in the hope of
Wherein, Sa1For with ωs1Corresponding acceleration responsive spectrum, Sa2For with ωs2Corresponding acceleration responsive spectrum.With
The corresponding response of each mode is
ri=ηiψi, i=1,2 (9)
Wherein, riFor modal response, i is rank number of mode, ψiFor the column vector of canonical formation matrix Ψ.
Since response spectra provides only the maximum amplitude information of seismic (seismal, phase information cannot be provided, therefore, in mode
It needs to take corresponding processing method when combination, to guarantee the conservative of final result.The present invention carries out mould using SRSS method
State combination, finally, particle m1, i.e. the displacement of equipment and acceleration responsive be respectively
(2) the spring mass model without support equipment is established
If not considering the support of equipment, equipment is only considered, equipment can be reduced to single-degree-of-freedom spring-as shown in Figure 2
Quality system.
The vibration equation of single-degree-of-freedom spring-quality system shown in Fig. 2 is
Or it is separately written as
For system described in formula (13), it is assumed that its surface seismic acceleration responsive spectrum be it is known, therefore, Ke Yitong
It crosses the progress kinematic analysis of response spectra seismic (seismal and acquires particle m1, i.e. the dynamic respond of equipment is
Wherein, SaFor with frequencies omega1Corresponding seismic acceleration responds spectrum.
(3) influence supported to frequency is probed into
For only include equipment single-mode system, from formula (13) as can be seen that system intrinsic frequency be equipment from
The intrinsic frequency of body.To form a system when equipment and support couple, the vibration characteristics of the system, such as intrinsic frequency, will with set
Certain deviation occurs for the standby and respective vibration characteristics of support, this bias is defined as
Wherein, ω1For the intrinsic frequency of equipment, ω2For the intrinsic frequency of support, ωs1, ωs2Respectively two of formula (2)
Root, and ωs1> ωs2.According to formula (2), in support/equipment quality ratio n1With support/device frequency ratio n3Following range in 1≤
n1≤100、0.1≤n3≤ 10, the amount of will deviate from Δ1、Δ2Quantization, can get changing rule as shown in Figures 3 and 4.
From Fig. 3 and 4 it is found that in n1>=100 or in 10≤n1≤ 100 and n3When except the range of (0.8,1.25),
Bias Δ1、Δ2It is negligible.For equipment, there is intrinsic frequency of the support with without support when close；For support
For, there is equipment close with intrinsic frequency when no equipment；For equipment-support system, two parts in system (are set
Standby and support) will not because of another part (support or equipment) presence and significantly change vibration characteristics, at this time
Equipment and support in system can not make copling calculation.The above analysis is demonstrated using two-freedom modeling equipment and support
The reasonability of relationship.
(4) influence supported to response is probed into
To consider the equipment dynamic respond (formula (10)) of the two degree freedom system of support and not consider the single-degree-of-freedom of support
The ratio of the equipment dynamic respond (formula (14)) of system quantifies to support the influence to equipment dynamic respond, and support can be deduced to setting
The influence coefficients R of standby dynamic respondxFor
Similarly, to consider the equipment Acceleration response (formula (11)) of the two degree freedom system of support and not consider support
The equipment Acceleration of single-mode system responds SaRatio quantify to support the influence to equipment Acceleration response, can deduce branch
Support the influence coefficients R to the acceleration responsive of equipmentaFor
According to formula (17), (18), dynamic respond influences coefficients RxCoefficients R is influenced with acceleration responsiveaWith support/equipment matter
Amount ratio, support/device frequency ratio and each frequency (ω1、ωs1、ωs2) corresponding acceleration table value is related.In view of nuclear industry
The equipment that intrinsic frequency is higher than seismic wave cutoff frequency is generally considered as rigid device by boundary, and is lower than setting for seismic wave cutoff frequency
Standby is flexible apparatus.Therefore, with the flexible apparatus lower than cutoff frequency and higher than the rigid device of cutoff frequency in the present embodiment
It is illustrated for respectively.
Response influence coefficients R is moved in order to investigate response spectra Correct formsxCoefficients R is influenced with acceleration responsiveaInfluence, this
In consider two different spectrum shapes (as shown in Figure 5,6), i.e. Seismic input 1 and Seismic input 2 (specific value is shown in Table 1).This
Two kinds of spectrum shapes in ascent stage, decline stage, in form with have different in specific value, can represent spectrum shape shadow
It rings.
Table 1
(6) influence supported to equipment dynamic respond is probed into
By taking intrinsic frequency is the equipment of 10Hz as an example, rigid device is flexible apparatus for the equipment of 50Hz with intrinsic frequency
Example is composed respectively as Seismic input with two acceleration responsives as listed in table 1, is calculated by formula (17) and different support/set
Standby mass ratio (n1) and support/device frequency ratio (n3) under, dynamic respond influences coefficients RxSituation of change, as shown in fig.7-12.
From Fig. 7~12 it can be found that two kinds of Seismic input bottom offset responses influence coefficients RxExcept specific value have it is certain poor
Not outer, changing rule is almost the same, i.e., the trend presented in figure is unrelated with specific earthquake response spectrum, to have certain
Representativeness.Related causes are interpretable as follows.Formula (17) can arrange as following form
Wherein,For n1、n3's
Function, trend is as shown in Figs. 13 and 14.
Due to rx2Compare rx1、There is the advantage of the order of magnitude, therefore, obey r on the wholex2That successively decreases becomes
R is presented in gesture, partx1The trend of wave crest.
No matter for flexible apparatus or rigid device, dynamic respond influences coefficients RxChanging rule it is consistent, that is, remove
In support/device frequency ratio n3Close at 1, RxIt is formed except a local maximum, in other region RxAll with n3Increasing
It gradually decreases greatly, and with n3Tend to be infinite and tends to 1.This is because the presence of support, so that the dynamic respond of equipment begins
It is amplified eventually, and as the rigidity of support tends to be infinite, the influence to the dynamic respond of equipment is supported to go to zero, equipment peace
Effect loaded on support is similar to equipment and is directly mounted on floor.In addition, in addition in n3Near=1, RxWith support/equipment
Mass ratio n1Increase and except increasing, in other region n1To RxInfluence it is little, explanation：In n3Near=1, due to support
Stronger coupled relationship is generated with equipment, causes the quality of support bigger, correspondingly, it is also bigger that dynamic respond influences coefficient；And
Weaker with equipment coupling due to supporting in other regions, support/equipment mass ratio influences coefficients R to dynamic respondxIt influences micro-
It is weak.
(7) influence responded to equipment Acceleration is supported
By taking intrinsic frequency is the equipment of 10Hz as an example, rigid device is flexible apparatus for the equipment of 50Hz with intrinsic frequency
Example is composed respectively as Seismic input with two acceleration responsives as listed in table 1, is calculated by formula (18) and different support/set
Standby mass ratio (n1) and support/device frequency ratio (n3) under, acceleration responsive influences coefficients RaSituation of change, such as Figure 15-18 institute
Show.
Comparison diagram 15~16 and Figure 17~18 are it can be found that acceleration responsive influences coefficients RaCoefficient is influenced with dynamic respond
RxDifference, the former also has certain relationship with the intrinsic frequency of equipment, with the raising of equipment intrinsic frequency, RaWave crest number
It is changed into two by one.It is found by calculating, this transformation occurs near 16Hz.One of wave crest is located at n3=1 is attached
Closely, position immobilizes, and the position of another wave crest is by n3=1 nearby gradually to n3Reduced direction is mobile.The former generation
The coupled relationship mainly formed between equipment and support is related, and the generation of the latter is mainly related with the spectrum shape of Seismic input, with
The raising of equipment intrinsic frequency, wave crest is gradually more mobile than reduced direction to support/device frequency, meanwhile, it is basic to keep branch
It is maximum to support the response spectrum of Seismic input corresponding to frequency.
For more soft equipment, RaIn n3=1 is formed about a wave crest, in n3<When 1, RaWith n3Reduction and gradually become
It is bordering on zero；In n3>When 1, RaWith n3Increase and gradually level off to 1.For more rigid equipment, RaIn n3<1 region and n3=
1 is formed about two wave crests, when far from the two wave crests, RaIt reduces rapidly, and in n3>When 1, RaWith n3Increase and by
Gradually it is bordering on 1.In n3<When 1, RaWith n3Reduction and gradually level off to zero or formed a wave crest be to be responded by Seismic input
What spectrum determined；In n3>When 1, RaWith n3Increase and gradually level off to 1, be due to when support stiffness increase to a certain extent,
When it, which is deformed, can be ignored, the effect that equipment is installed on support is similar to equipment and is directly mounted on floor, at this point, support
Influence for the acceleration of equipment can be ignored, therefore, RaJust level off to 1.
Although equipment intrinsic frequency is different, being likely to result in acceleration responsive influences coefficients RaChanging rule is different, but
It is that, when equipment intrinsic frequency is identical, two kinds of different earthquakes, which input lower acceleration responsive, influences coefficients RaChanging rule it is basic
Unanimously, i.e., acceleration responsive influences coefficients RaChanging rule also not dependent on specific Seismic input response spectra form.
Acceleration responsive influences coefficients RaThere are also another features, that is, in addition in the case where different earthquake inputs, it becomes
Law is almost the same outer, and numerical value is also close or consistent.It therefore, is below 10Hz equipment with intrinsic frequency and intrinsic frequency is
(more soft equipment and more rigid equipment are respectively represented) for 50Hz equipment, compare acceleration responsive shadow when different earthquake input respectively
Ring coefficients Ra(see Figure 19,20).
For more soft equipment, from Figure 19 it can be found that with support/equipment quality ratio n1Increase, the weight of two curves
Right raising, illustrates the increase with mass ratio, and specific Seismic input influences coefficients R to acceleration responsiveaInfluence in institute
Accounting in having an impact is gradually reduced.Especially with the increase of support/equipment quality ratio, acceleration responsive influences coefficients Ra's
Maximum value is gradually increased, and tends to certain value for different Seismic inputs.This phenomenon can be explained as follows.Formula (18) can
By arrange be it is following in the form of
Wherein,For n1、n3Function,
Its trend is as shown in figs. 21 and 22.
Wave crest relevant to coupling, according to formula (2) it is found that n1It is bigger,WithCloser to 1, thusWith?
Closer to 1, R is eventually led toaIn all items all become unrelated with earthquake response spectrum.Meanwhile from Figure 21 and 22 as can be seen that n1
It is bigger, ra1And ra2It is bigger, the influence of earthquake response spectrum is reduced from another point of view, so that RaDifferent Seismic inputs is tended to
Certain value.Therefore, in certain support/equipment quality ratio and support/device frequency than that in range, can be RaDetermine a packet
Network value.The realistic meaning of this envelope value is --- seismic (seismal can be provided for the aseismic analysis or identification of equipment and support
Conservative estimation.
As can be seen from Figure 20, coefficients R is influenced for acceleration responsiveaFor, more rigid equipment is in addition to having the above more soft equipment
Characteristic except, (n is located at for another peak value of more rigid equipment3<Peak value in 1 region), the value is for identical earthquake
For input, different supports/equipment quality ratio, it is basically unchanged, to prove the peak value and Seismic input from another angle
It is related.
In summary about RaThe analysis of wave crest, by coupling the wave crest formed, Seismic input response spectra influences its peak value
It is little, mainly determined by support/equipment quality ratio；Wave crest related with Seismic input response spectra, support/equipment quality compare it
Peak value influence is little, is mainly determined by Seismic input response spectra.Therefore in known support/equipment quality ratio or Seismic input response spectra
In the case where envelope, R can be deducedaEnvelope value, to understand support to the possible maximum enlarge-effect of equipment Acceleration response.
(8) Aseismic Design is instructed
It can be equipment-support system by there is the comparative analysis of support and the response characteristic without support situation to equipment
Aseismic Design following guidance is provided：
(1) the case where support/device frequency ratio is close or equal to 1 is avoided, to avoid there is acceleration relevant to coupling
Response, the excessive amplification of dynamic respond.
(2) the case where support/device frequency ratio is less than 1 is avoided, is excessively amplified to avoid dynamic respond, while is also advantageous
In the acceleration responsive appearance excessive amplification relevant to Seismic input response spectra for avoiding more rigid equipment.
(3) support on equipment Acceleration respond influence coefficient exist an envelope value, in Equivalent static method use etc.
Effect acceleration envelope value provides possibility.
Therefore in the supported design of equipment, it should be noted that avoid equipment the case where coupling close with support construction frequency；
For being installed on the equipment (for example, the valve for being installed on pipeline) of flexible structure, can be improved by increasing the methods of suspension and support
The frequency of valve support construction, to reduce the response of equipment.
The above embodiments merely illustrate the technical concept and features of the present invention, and its object is to allow person skilled in the art
Scholar cans understand the content of the present invention and implement it accordingly, and it is not intended to limit the scope of the present invention.It is all according to the present invention
Equivalent change or modification made by Spirit Essence, should be covered by the protection scope of the present invention.
Claims (10)
1. a kind of be used to instruct equipment-support system Aseismic Design method based on spring mass model, which is characterized in that
Include the following steps：
(1) equipment and its support are reduced to the first spring-quality system for having there are two freedom degree；There will be no the supports
When the equipment be reduced to second spring-quality system of single-degree-of-freedom；
(2) vibration equation for acquiring first spring-quality system, using canonical formation matrix as transformation matrix of coordinates,
Acquire two intrinsic frequencies of equipment-support system in first spring-quality system, and sound corresponding with each mode
It answers, modality combinations is carried out using SRSS method, acquire the dynamic respond and acceleration of equipment in first spring-quality system
Response；
(3) vibration equation for acquiring the second spring-quality system passes through in known surface seismic acceleration responsive time spectrum
Response spectra seismic (seismal carries out kinematic analysis and obtains dynamic respond and the acceleration sound of equipment in the second spring-quality system
It answers；
(4) it is directed to first spring-quality system, its intrinsic frequency of system and the equipment for acquiring equipment and support composition are intrinsic
The bias Δ of frequency1And the bias Δ of its intrinsic frequency of system and support intrinsic frequency of equipment and support composition2；
(5) by equipment in the dynamic respond of equipment in first spring-quality system and the second spring-quality system
Influence of the ratio quantization support of dynamic respond to equipment dynamic respond, the influence coefficient being supported to the dynamic respond of equipment
Rx；
(6) by equipment in the acceleration responsive of equipment in first spring-quality system and the second spring-quality system
Acceleration responsive influence of the ratio quantization support to equipment dynamic respond；The shadow being supported to the acceleration responsive of equipment
Ring coefficients Ra；
(7) according to the Δ1、Δ2、RxAnd RaInstruct equipment-support system Aseismic Design.
2. it is according to claim 1 it is a kind of based on spring mass model for instructing equipment-support system Aseismic Design
Method, which is characterized in that
The vibration equation of first spring-quality system is：
Wherein,
m1For the quality of equipment, k1For the rigidity of equipment, x1It is equipment in first spring-quality system relative to ground
Displacement；
m2For the quality of support, k2For the rigidity of support, x2It is support phase in first spring-quality system for ground
Displacement；
xgFor the displacement on ground under geological process；
The vibration equation of the second spring-quality system is：
Or it is separately written as
Wherein,
x3For displacement of the equipment relative to ground in the second spring-quality system.
3. it is according to claim 2 it is a kind of based on spring mass model for instructing equipment-support system Aseismic Design
Method, which is characterized in that the displacement of equipment and acceleration responsive are respectively in first spring-quality system：
Wherein,
n1For support/equipment quality ratio, i.e.,
ω1For the intrinsic frequency of equipment,
ωs1And ωs2For two intrinsic frequencies of equipment-support system in first spring-quality system；
Sa1For with ωs1Corresponding acceleration responsive spectrum, Sa2For with ωs2Corresponding acceleration responsive spectrum；
The dynamic respond of equipment is in the second spring-quality system：
Wherein, the acceleration responsive of equipment is Sa, SaFor with frequencies omega1Corresponding seismic acceleration responds spectrum.
4. it is according to claim 3 it is a kind of based on spring mass model for instructing equipment-support system Aseismic Design
Method, it is characterised in that：
Wherein,
ω2For the intrinsic frequency of support,
n3For support/device frequency ratio, i.e.,
Different support/equipment qualities are probed into than lower Δ1And Δ2With support/device frequency ratio changing rule.
5. it is according to claim 4 it is a kind of based on spring mass model for instructing equipment-support system Aseismic Design
Method, it is characterised in that：In support/equipment quality ratio n1With support/device frequency ratio n3Following range in 1≤n1≤
100、0.1≤n3≤ 10, probe into bias Δ1And Δ2Changing rule.
6. it is according to claim 3 it is a kind of based on spring mass model for instructing equipment-support system Aseismic Design
Method, which is characterized in that support the influence coefficients R to the dynamic respond of equipmentxFor：
It probes under different supports/equipment quality ratio and support/device frequency ratio, dynamic respond influences coefficients RxChanging rule.
7. it is according to claim 6 it is a kind of based on spring mass model for instructing equipment-support system Aseismic Design
Method, it is characterised in that：The intrinsic frequency probed into respectively in equipment is higher than seismic wave cutoff frequency and lower than seismic wave section
Only under frequency both of these case, under different supports/equipment quality ratio and support/device frequency ratio, dynamic respond influences coefficients Rx
Changing rule.
8. it is according to claim 3 it is a kind of based on spring mass model for instructing equipment-support system Aseismic Design
Method, which is characterized in that support the influence coefficients R to the acceleration responsive of equipmentaFor：
It probes under different supports/equipment quality ratio and support/device frequency ratio, acceleration responsive influences coefficients RaChanging rule.
9. it is according to claim 8 it is a kind of based on spring mass model for instructing equipment-support system Aseismic Design
Method, it is characterised in that：The intrinsic frequency probed into respectively in equipment is higher than seismic wave cutoff frequency and lower than seismic wave section
Only under frequency both of these case, under different supports/equipment quality ratio and support/device frequency ratio, acceleration responsive influences coefficient
RaChanging rule.
10. it is according to any one of claims 1 to 9 it is a kind of based on spring mass model for instructing equipment-support system
The method for Aseismic Design of uniting, which is characterized in that in step (7), equipment-support system should be avoided supporting in Aseismic Design/is set
The case where the case where standby frequency ratio is equal to 1 and support/device frequency ratio are less than 1.
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