A method for guiding seismic design of equipment-support systems

Abstract

The present invention provides a method for guiding the seismic design of a device-support system, comprising the following steps: simplifying the device and its support into a first spring-mass system with two degrees of freedom, and simplifying the device without the support into a second spring-mass system with a single degree of freedom; for the first spring-mass system, calculating the deviation Δ1 between the natural frequency of the system formed by the device and the support and the natural frequency of the device, as well as the deviation Δ2 between the natural frequency of the system formed by the device and the support and the natural frequency of the support; and calculating the influence coefficient R of the support on the displacement response of the device. x And the influence coefficient R of the support on the acceleration response of the equipment a ; According to the Δ1, Δ2, R x and R a Guiding the seismic design of equipment-support systems, this paper quantifies the impact of supports on equipment response, reveals the root cause of the support impact, and defines its impact extent, providing guidance for the seismic design of equipment-support systems.

Description

[0001] This application is a divisional application of the invention patent application with application date of July 4, 2018, application number 2018107227885, and invention name “A method for guiding seismic design of equipment-support system based on spring-mass model”. Technical Field

[0002] The present invention relates to the technical field of seismic design, and in particular to a method for guiding seismic design of an equipment-support system based on a spring-mass model. Background Art

[0003] For the seismic evaluation of equipment, analytical methods, test methods, similarity methods, earthquake empirical data methods, or a combination of the above methods can be used for reasoning and argumentation. However, no matter which seismic evaluation method is used, earthquake simulation is an indispensable part of it, and the accuracy of earthquake simulation is directly related to the rationality of the seismic evaluation of the equipment. For equipment that is not directly installed on the floor but uses a supporting structure, when only the equipment is studied (for example, equipment installed on a base or pipeline), the seismic evaluation of the equipment generally uses the following method to determine the earthquake input:

[0004] (1) If the natural frequency of the equipment is lower than the cutoff frequency of the seismic wave, the response spectrum of the floor above the equipment is selected as the seismic input to envelop the influence of the supporting structure (for example, the equipment base) on the seismic response of the equipment.

[0005] (2) If the natural frequency of the equipment is greater than the cutoff frequency of the seismic wave, when the static method is used to calculate the seismic response of the equipment, the equivalent static force of the seismic load is determined by the following method:

[0006] (a) Use the envelope acceleration given in the applicable equipment specifications;

[0007] (b) Zero-period acceleration (ZPA) of the equipment's upper floor response spectrum;

[0008] (c) For multi-degree-of-freedom components, when the component model is simple, 1.5 times the maximum value of the spectrum value corresponding to the frequency band greater than or equal to the fundamental frequency of the equipment on the upper floor response spectrum of the equipment can be used.

[0009] For equipment with supporting structures, the seismic load transmission path is first through the building, then through the supporting structure, and finally through the equipment. Therefore, for equipment seismic evaluation, the combined effects of the building, supports, and equipment need to be considered. According to GB50267-1997, "Code for Seismic Design of Nuclear Power Plants," in the seismic design of nuclear power plants, the main structure can be considered the primary system, while other supported structures, systems, and components can be considered subsystems. When categorizing the building, supports (including the foundation), and equipment into primary and subsystems, it is appropriate to consider the building as the primary system and the supports and equipment as subsystems. This is based on the following considerations: first, supports and equipment are local structures relative to the building; second, the vibration characteristics of supports and equipment, especially those of supporting structures directly connected to the building, differ significantly from those of the building; and third, the floor response spectrum of a building primarily reflects the vibration characteristics of the building as a whole, not the vibration characteristics of the supporting structure (e.g., the foundation). Therefore, supports and equipment are considered subsystems relative to the building. Generally speaking, the sum of the masses of equipment and supports is much smaller than the mass of the plant building, which satisfies the decoupling condition that the mass ratio of the subsystem to the main system is less than 0.01. Therefore, the equipment and supports can be seismically assessed independently of the plant building, and the seismic loads transmitted by the plant building can be reflected through the floor response spectrum of the plant building.

[0010] When purchasing equipment at nuclear power plants, seismic requirements are typically submitted to the equipment manufacturer through technical specifications and procurement specifications. For equipment whose seismic loads are given in the form of a floor response spectrum, if the equipment is installed on supports rather than floors, the seismic response at the connections between the supports and the equipment and the floor will inevitably differ, as the support structure itself will deform under earthquakes. Therefore, NB / T 20036.2-2011, "Qualification of Nuclear Power Plant Dynamic Mechanical Equipment - Part 2: Seismic Qualification," stipulates in the "Seismic Simulation" section that "the input earthquake should be determined for the foundation, floor, or system where the equipment is installed." This means that when performing seismic qualification for equipment with supporting structures, the seismic input for the equipment must be determined for the supporting structure.

[0011] However, for equipment installed on a supporting structure, if the seismic assessment is conducted without considering the equipment and the supporting structure as a whole, but only the equipment as the analysis object, existing methods cannot quantify the impact of the support on the equipment response, let alone define the extent of the impact. Summary of the Invention

[0012] The present invention provides a method for guiding the seismic design of equipment-support systems based on a spring-mass model. By establishing a supported model and an unsupported model of the equipment, the method quantifies the influence of the support on the equipment response, thereby being used to guide the seismic design of the equipment-support system.

[0013] To achieve the above object, the present invention adopts a technical solution: a method for guiding the seismic design of an equipment-support system based on a spring-mass model, comprising the following steps:

[0014] (1) simplifying the device and its support into a first spring-mass system with two degrees of freedom; simplifying the device without the support into a second spring-mass system with a single degree of freedom;

[0015] (2) Obtaining the vibration equation of the first spring-mass system, using the regular matrix Ψ as the coordinate transformation matrix, obtaining the two natural frequencies of the device-support system in the first spring-mass system, and the response corresponding to each mode, using the SRSS method for modal combination, and obtaining the displacement response and acceleration response of the device in the first spring-mass system;

[0016] (3) obtaining a vibration equation of the second spring-mass system, and when a ground earthquake acceleration response spectrum is known, performing a dynamic analysis using a response spectrum earthquake load to obtain a displacement response and an acceleration response of the device in the second spring-mass system;

[0017] (4) for the first spring-mass system, obtaining a deviation Δ1 between the natural frequency of the system consisting of the device and the support and the natural frequency of the device, and a deviation Δ2 between the natural frequency of the system consisting of the device and the support and the natural frequency of the support;

[0018] (5) The ratio of the displacement response of the device in the first spring-mass system to the displacement response of the device in the second spring-mass system is used to quantify the influence of the support on the displacement response of the device, and the influence coefficient R of the support on the displacement response of the device is obtained. x ;

[0019] (6) Quantify the influence of the support on the displacement response of the device by the ratio of the acceleration response of the device in the first spring-mass system to the acceleration response of the device in the second spring-mass system; obtain the influence coefficient R of the support on the acceleration response of the device a ;

[0020] (7) According to the Δ1, Δ2, R x and R a Provide guidance for seismic design of equipment-support systems.

[0021] Furthermore, the vibration equation of the first spring-mass system is:

[0022]

[0023] in,

[0024]

[0025] m1 is the mass of the device, k1 is the stiffness of the device, and x1 is the displacement of the device relative to the ground in the first spring-mass system;

[0026] m2 is the mass of the support, k2 is the stiffness of the support, and x2 is the displacement of the support relative to the ground in the first spring-mass system;

[0027] x g is the displacement of the ground under earthquake action;

[0028] The vibration equation of the second spring-mass system is:

[0029]

[0030] Or written as

[0031]

[0032] in,

[0033] x3 is the displacement of the device relative to the ground in the second spring-mass system.

[0034] Furthermore, the displacement and acceleration responses of the device in the first spring-mass system are:

[0035]

[0036]

[0037] in,

[0038] n1 is the support / equipment mass ratio, that is

[0039] ω1 is the natural frequency of the equipment,

[0040] ω s1 and ω s2 are the two natural frequencies of the device-support system in the first spring-mass system;

[0041] S a1 For ω s1 The corresponding acceleration response spectrum value, S a2 For ω s2 Corresponding acceleration response spectrum value;

[0042] The displacement response of the device in the second spring-mass system is:

[0043]

[0044] Among them, the acceleration response of the device is Sa , S a is the earthquake acceleration response spectrum value corresponding to frequency ω1.

[0045] Further,

[0046]

[0047]

[0048] in,

[0049] ω2 is the natural frequency of the support,

[0050] n3 is the support / device frequency ratio, that is,

[0051] The variation patterns of Δ1 and Δ2 with the support / equipment frequency ratio under different support / equipment mass ratios were investigated.

[0052] Furthermore, within the following ranges of the support / equipment mass ratio n1 and the support / equipment frequency ratio n3: 1≤n1≤100, 0.1≤n3≤10, the variation patterns of the deviations Δ1 and Δ2 are explored.

[0053] Furthermore, the influence coefficient R of the support on the displacement response of the equipment x for:

[0054]

[0055] Investigate the displacement response influence coefficient R under different support / equipment mass ratios and support / equipment frequency ratios x The law of change.

[0056] Furthermore, the influence coefficient R of displacement response under different support / equipment mass ratios and support / equipment frequency ratios is studied respectively when the natural frequency of the equipment is higher than the seismic wave cutoff frequency and lower than the seismic wave cutoff frequency. x The law of change.

[0057] Furthermore, the influence coefficient R of the support on the acceleration response of the equipment a for:

[0058]

[0059] Investigate the acceleration response influence coefficient R under different support / equipment mass ratios and support / equipment frequency ratios a The law of change.

[0060] Furthermore, the acceleration response influence coefficient R is studied under different support / equipment mass ratios and support / equipment frequency ratios when the natural frequency of the equipment is higher than the seismic wave cutoff frequency and lower than the seismic wave cutoff frequency. a The law of change.

[0061] Furthermore, in step (7), the equipment-support system should avoid situations where the support / equipment frequency ratio is equal to 1 and the support / equipment frequency ratio is less than 1 during seismic design.

[0062] After adopting the above technical solution, the present invention has the following advantages compared with the existing technology: the present invention quantifies the influence of support on equipment response by establishing supported and unsupported equipment models, essentially reveals the root cause of the support influence, defines its influence degree, and determines its influencing factors, thereby providing guidance for the seismic design of the equipment-support system. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Attachment Figure 1 It is a simplified apparatus and support two-degree-of-freedom spring-mass system in the present invention;

[0064] Attachment Figure 2 It is a simplified single-degree-of-freedom spring-mass system of the device in the present invention;

[0065] Attachment Figure 3 is a curve showing the variation of the deviation Δ1 with the support / device frequency ratio n3 under different support / device mass ratios in the present invention;

[0066] Attachment Figure 4 is a curve showing the variation of the deviation Δ2 with the support / device frequency ratio n3 under different support / device mass ratios in the present invention;

[0067] Attachment Figure 5 is the spectral shape of the earthquake input response spectrum 1 in the present invention;

[0068] Attachment Figure 6 is the spectral shape of the earthquake input response spectrum 2 in the present invention;

[0069] Attachment Figure 7 The flexible device in the present invention has an earthquake input of 1 R x Curves changing with n1 and n3;

[0070] Attachment Figure 8 The flexible device earthquake input 2 R x Curves changing with n1 and n3;

[0071] Attachment Figure 9 R is the seismic input of the rigid equipment in the present invention. x Curves changing with n1 and n3;

[0072] Attachment Figure 10 R is the seismic input of the rigid equipment in the present invention. x Local variation curve with n3;

[0073] Attachment Figure 11 The rigid equipment earthquake input 2 R in the present invention x Curves changing with n1 and n3;

[0074] Attachment Figure 12 The rigid equipment earthquake input 2 R in the present invention x Local variation curve with n3;

[0075] Attachment Figure 13 In the present invention, x1 The changing pattern of n1 and n3;

[0076] Attachment Figure 14 In the present invention, x2 The changing pattern of n1 and n3;

[0077] Attachment Figure 15 The flexible device in the present invention has an earthquake input of 1 R a Curve changing with n3;

[0078] Attachment Figure 16 The flexible device earthquake input 2 R a Curve changing with n3;

[0079] Attachment Figure 17 R is the seismic input of the rigid equipment in the present invention. a Curve with the change of n3;

[0080] Attachment Figure 18 The rigid equipment earthquake input 2 R in the present invention a Curve changing with n3;

[0081] Attachment Figure 19 R is the value of different earthquake inputs for the softer device in the present invention. a contrast;

[0082] Attachment Figure 20 R is the value of different earthquake inputs for the rigid equipment in the present invention. a contrast;

[0083] Attachment Figure 21 In the present invention, a1 The changing pattern of n1 and n3;

[0084] Attachment Figure 22 In the present invention, a2 The changing pattern of n1 and n3. DETAILED DESCRIPTION

[0085] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0086] A method for guiding the seismic design of a device-support system based on a spring-mass model comprises the following steps:

[0087] (1) Establishing a spring-mass model with supporting equipment

[0088] The device and its support are simplified as a spring-mass system with two degrees of freedom, e.g. Figure 1 As shown. m1, k1, x1 are the mass, stiffness and displacement of the equipment relative to the ground, m2, k2, x2 are the mass, stiffness and displacement of the support relative to the ground, x g is the displacement of the ground under the action of an earthquake.

[0089] The equation of motion of the system in the horizontal direction is

[0090]

[0091] in,

[0092] By solving the characteristic equation of the system described in equation (1), let The natural frequency ω of the system can be obtained s

[0093]

[0094] Let ω s1 and ω s2 are the two solutions of Equation (2), i.e. the two natural frequencies of the equipment-support system. Therefore, ω s1 ≠ω s2 , so the two-degree-of-freedom system composed of the equipment and support has no repeated roots. From the vibration equation (1), it can be seen that the system has elastic coupling in the original coordinate system. If the regular array matrix Ψ is used as the coordinate transformation matrix, the original vibration equation (1) can be decoupled. Therefore, x = Ψ η Substituting into formula (1) we can get

[0095]

[0096] η is the canonical coordinate,

[0097] For known mass matrix and stiffness matrix, the corresponding regular array matrix Ψ can be solved as

[0098]

[0099] in,

[0100] After decoupling, the solution of Equation (4) can be obtained by solving the vibration of the two single-degree-of-freedom systems:

[0101]

[0102]

[0103] For Figure 1 In the system shown in Figure 5, the parts in brackets of equations (5) and (6) are constants. For simplicity, let For engineering design problems, such as the seismic design of nuclear power plant buildings (structures), equipment and components, the concern is not the motion law of the system under a given excitation, but how to select certain system parameters to limit the maximum value of the system response to a certain range. In this case, the following assumption is made for Figure 1 For the system shown in the figure, the ground earthquake acceleration response spectrum is known. By performing dynamic analysis on the response spectrum earthquake load, we can obtain

[0104]

[0105]

[0106] Among them, S a1 For ω s1 The corresponding acceleration response spectrum value, S a2 For ω s2 The corresponding acceleration response spectrum value. The response corresponding to each mode is

[0107] r i =η i ψ i ,i=1,2 (9)

[0108] Among them, r i is the modal response, i is the modal order, ψ i is the column vector of the regular array matrix Ψ.

[0109] Since the response spectrum only provides the maximum amplitude information of the earthquake load and cannot provide phase information, appropriate processing methods need to be adopted when combining modes to ensure the conservatism of the final result. The present invention adopts the SRSS method for mode combination. Finally, the displacement and acceleration responses of the mass point m1, that is, the equipment, are

[0110]

[0111]

[0112] (2) Establishing a spring-mass model for unsupported equipment

[0113] If we ignore the support of the equipment and only consider the equipment, we can simplify the equipment into Figure 2 The single-degree-of-freedom spring-mass system shown.

[0114] Figure 2 The vibration equation for the single-degree-of-freedom spring-mass system shown is

[0115]

[0116] Or written as

[0117]

[0118] For the system described by Equation (13), assuming that its ground earthquake acceleration response spectrum is known, the mass point m1 can be obtained by dynamic analysis through the response spectrum earthquake load, that is, the displacement response of the equipment is

[0119]

[0120] Among them, S a is the earthquake acceleration response spectrum value corresponding to frequency ω1.

[0121] (3) Exploring the impact of support on frequency

[0122] For a single degree of freedom system containing only the device, it can be seen from Equation (13) that the natural frequency of the system is the natural frequency of the device itself. When the device and the support are coupled to form a system, the vibration characteristics of the system, such as the natural frequency, will deviate from the vibration characteristics of the device and the support to a certain extent. This deviation is defined as

[0123]

[0124]

[0125] Among them, ω1 is the natural frequency of the equipment, ω2 is the natural frequency of the support, ω s1 ,ω s2 are the two roots of formula (2), and ω s1 >ω s2 According to formula (2), within the following ranges of support / equipment mass ratio n1 and support / equipment frequency ratio n3: 1≤n1≤100, 0.1≤n3≤10, the deviations Δ1 and Δ2 are quantified to obtain: Figure 3 and 4 The changing rules shown.

[0126] from Figure 3 and 4It can be seen that when n1 ≥ 100 or 10 ≤ n1 ≤ 100, and n3 is outside the range of (0.8, 1.25), the deviations Δ1 and Δ2 are negligible. For the equipment, the natural frequencies with and without supports are similar; for the support, the natural frequencies with and without the equipment are similar. For the equipment-support system, the vibration characteristics of two components (equipment and support) will not be significantly altered by the presence of the other component (support or equipment). Therefore, in this case, the equipment and support in the system can be decoupled. The above analysis verifies the rationale of using a two-degree-of-freedom model to simulate the relationship between equipment and support.

[0127] (4) Exploring the impact of support on response

[0128] The influence of the support on the displacement response of the equipment is quantified by the ratio of the equipment displacement response of the two-degree-of-freedom system considering the support (Equation (10)) to the equipment displacement response of the single-degree-of-freedom system without considering the support (Equation (14)). The influence coefficient R of the support on the displacement response of the equipment can be inferred. x for

[0129]

[0130] Similarly, the acceleration response of the device of the two-degree-of-freedom system considering the support (Eq. (11)) is compared with the acceleration response of the device of the single-degree-of-freedom system without considering the support S a The influence of the support on the acceleration response of the equipment can be quantified by the ratio of a for

[0131]

[0132] According to equations (17) and (18), the displacement response influence coefficient R x and acceleration response influence coefficient R a and the support / equipment mass ratio, support / equipment frequency ratio, and the frequency (ω1, ω s1 、ω s2 ) is related to the corresponding acceleration spectrum value. Considering that the nuclear industry generally considers equipment with a natural frequency above the seismic wave cutoff frequency to be rigid equipment, and equipment below the seismic wave cutoff frequency to be flexible equipment, this embodiment uses flexible equipment below the cutoff frequency and rigid equipment above the cutoff frequency as examples.

[0133] In order to investigate the effect of the response spectrum on the displacement response coefficient R x and acceleration response influence coefficient R a Here we consider two different spectral shapes (such as Figure 5 、 6These two spectral shapes differ somewhat in form and specific values ​​during the rising and falling phases, representing the influence of the spectral shape.

[0134] Table 1

[0135]

[0136]

[0137] (6) Investigate the influence of support on equipment displacement response

[0138] Taking the flexible device with a natural frequency of 10 Hz as an example and the rigid device with a natural frequency of 50 Hz as an example, the two acceleration response spectra listed in Table 1 are used as earthquake inputs. The displacement response influence coefficient R under different support / device mass ratios (n1) and support / device frequency ratios (n3) is calculated by formula (17): x changes in Figure 7-12 shown.

[0139] from Figures 7-12 It can be found that the displacement response influence coefficient R under the two earthquake inputs is x Except for some differences in the specific values, the change patterns are basically the same, that is, the trend shown in the figure is independent of the specific earthquake response spectrum, and thus has a certain degree of representativeness. The relevant reasons can be explained as follows. Equation (17) can be organized into the following form

[0140]

[0141] in, is a function of n1 and n3, and its trend is as follows Figure 13 and 14 shown.

[0142] Because r x2 R x1 、 There is an order of magnitude advantage, so on the whole it obeys r x2 The decreasing trend is partially shown in r x1 The trend of the crest.

[0143] Whether for flexible or rigid equipment, the displacement response influence coefficient R x The variation pattern of R is consistent, that is, except when the support / device frequency ratio n3 is close to 1, R x In addition to forming a local maximum, in other areas R xAs n3 increases, R decreases gradually and approaches 1 as n3 approaches infinity. This is because the presence of the support always amplifies the displacement response of the device, and as the stiffness of the support approaches infinity, the influence of the support on the displacement response of the device approaches zero, and the effect of the device installed on the support is similar to that of the device installed directly on the floor. In addition, except for the case where n3 = 1, R x In addition to increasing with the increase of support / equipment mass ratio n1, in other areas n1 has an influence on R x The influence of n3 is very small, which means that near n3 = 1, due to the strong coupling relationship between the support and the equipment, the larger the support mass, the greater the displacement response influence coefficient; in other areas, due to the weak coupling between the support and the equipment, the support / equipment mass ratio has a greater influence on the displacement response coefficient R x The impact is weak.

[0144] (7) The impact of support on equipment acceleration response

[0145] Taking the flexible device with a natural frequency of 10 Hz and the rigid device with a natural frequency of 50 Hz as an example, the two acceleration response spectra listed in Table 1 are used as earthquake inputs. The acceleration response influence coefficient R under different support / device mass ratios (n1) and support / device frequency ratios (n3) is calculated by formula (18): a changes in Figure 15-18 shown.

[0146] contrast Figures 15-16 and Figures 17-18 It can be found that the acceleration response influence coefficient R a and displacement response influence coefficient R x Different from the former, it also has a certain relationship with the natural frequency of the equipment. As the natural frequency of the equipment increases, R a The number of peaks changes from one to two. Calculations show that this transition occurs near 16 Hz. One of the peaks is located near n3 = 1 and remains fixed, while the position of the other peak gradually moves from n3 = 1 toward the direction of decreasing n3. The generation of the former is mainly related to the coupling relationship formed between the equipment and the support, while the generation of the latter is mainly related to the spectral shape of the seismic input. As the natural frequency of the equipment increases, the peak gradually moves toward the direction of decreasing the support / equipment frequency ratio, while basically maintaining the maximum value of the seismic input response spectrum corresponding to the support frequency.

[0147] For softer devices, R a A peak is formed near n3=1. When n3<1, R a As n3 decreases, it gradually approaches zero; when n3>1, R a As n3 increases, it gradually approaches 1. For relatively rigid equipment, Ra Two peaks are formed in the area of ​​n3<1 and near n3=1. When away from these two peaks, R a Rapidly decreases, and when n3>1, R a As n3 increases, it gradually approaches 1. When n3<1, R a As n3 decreases, it gradually approaches zero or forms a peak, which is determined by the earthquake input response spectrum; when n3>1, R a As n3 increases, it gradually approaches 1. This is because when the support stiffness increases to a certain extent and its deformation can be ignored, the effect of the equipment installed on the support is similar to that of the equipment being installed directly on the floor. At this time, the influence of the support on the acceleration of the equipment can be ignored. Therefore, R a It approaches 1.

[0148] Although, the natural frequency of the equipment is different, which may cause the acceleration response coefficient R a The changing rules are different. However, when the natural frequency of the equipment is the same, the acceleration response influence coefficient R under two different earthquake inputs is a The change law of is basically the same, that is, the acceleration response influence coefficient R a The changing pattern of does not depend on the specific form of the earthquake input response spectrum.

[0149] Acceleration response influence coefficient R a Another characteristic is that, in addition to the fact that the variation patterns are basically the same under different earthquake inputs, the values ​​are also close or consistent. Therefore, the following uses a device with a natural frequency of 10Hz and a device with a natural frequency of 50Hz as examples (representing a relatively soft device and a relatively rigid device, respectively) to compare the acceleration response influence coefficient R under different earthquake inputs. a (See Figure 19 、 20 ).

[0150] For softer devices, Figure 19 It can be found that as the support / equipment mass ratio n1 increases, the coincidence of the two curves increases, indicating that as the mass ratio increases, the specific earthquake input affects the acceleration response coefficient R a The influence of the acceleration response coefficient R a The maximum value of gradually increases and tends to a certain value for different earthquake inputs. This phenomenon can be explained as follows. Equation (18) can be organized into the following form

[0151]

[0152] in, is a function of n1 and n3, and its trend is as follows Figure 21 and 22 shown.

[0153] The peak related to coupling, according to formula (2), the larger n1 is, and The closer it is to 1, the and The closer it is to 1, the more R a All the terms in become independent of the earthquake response spectrum. Figure 21 and 22 It can be seen that the larger n1 is, the larger r a1 and r a2 The larger the value, the lower the impact of the earthquake response spectrum, making R a For different earthquake inputs, they tend to a certain value. Therefore, within a certain range of support / equipment mass ratio and support / equipment frequency ratio, R a Determine an envelope value. The practical significance of this envelope value is that it can provide a conservative estimate of the seismic load for seismic analysis or identification of equipment and supports.

[0154] from Figure 20 It can be seen that the acceleration response influence coefficient R a In addition to the above characteristics of the softer device, the more rigid device has another peak value (the peak value located in the region of n3<1) which is basically unchanged for the same earthquake input and different support / equipment mass ratios, thus proving from another perspective that the peak value is related to the earthquake input.

[0155] Based on the above information about R a The analysis of the peaks is that the peaks formed by coupling are slightly affected by the earthquake input response spectrum and are mainly determined by the support / equipment mass ratio. The peaks related to the earthquake input response spectrum are slightly affected by the support / equipment mass ratio and are mainly determined by the earthquake input response spectrum. Therefore, when the support / equipment mass ratio or the earthquake input response spectrum envelope is known, R can be inferred. a The envelope value of the support can be used to understand the maximum possible amplification effect of the support on the acceleration response of the equipment.

[0156] (8) Guiding earthquake-resistant design

[0157] By comparing and analyzing the response characteristics of equipment with and without support, the following guidance can be provided for the seismic design of the equipment-support system:

[0158] (1) Avoid situations where the support / equipment frequency ratio is close to or equal to 1 to avoid excessive amplification of the acceleration response and displacement response related to the coupling.

[0159] (2) Avoid situations where the support / equipment frequency ratio is less than 1 to prevent the displacement response from being over-amplified. This also helps to avoid the acceleration response of the stiffer equipment from being over-amplified relative to the earthquake input response spectrum.

[0160] (3) The influence coefficient of the support on the acceleration response of the equipment has an envelope value, which makes it possible to use the equivalent acceleration envelope value in the equivalent static method.

[0161] Therefore, when designing the support for the equipment, care should be taken to avoid coupling caused by the frequency of the equipment and the supporting structure being close to each other. For equipment installed on flexible structures (for example, valves installed on pipelines), the frequency of the valve support structure can be increased by adding supports and hangers, thereby reducing the response of the equipment.

[0162] The above embodiments are intended only to illustrate the technical concepts and features of the present invention. Their purpose is to enable those skilled in the art to understand the contents of the present invention and implement them accordingly. They are not intended to limit the scope of protection of the present invention. Any equivalent changes or modifications made in accordance with the spirit of the present invention are intended to be covered by the scope of protection of the present invention.

Claims

1. A method for guiding the seismic design of equipment-support systems, characterized in that: The steps include: Simplifying the device and its support into a first spring-mass system with two degrees of freedom; obtaining a vibration equation for the first spring-mass system, and obtaining two natural frequencies of the device-support system in the first spring-mass system, as well as the response corresponding to each mode, performing modal combination, and obtaining a displacement response and an acceleration response of the device in the first spring-mass system; Simplifying the device in the absence of the support into a second spring-mass system with a single degree of freedom; obtaining a vibration equation of the second spring-mass system, and obtaining a displacement response and an acceleration response of the device in the second spring-mass system; The influence of the support on the displacement response of the device is quantified by the ratio of the displacement response of the device in the first spring-mass system to the displacement response of the device in the second spring-mass system, and the influence coefficient R of the support on the displacement response of the device is obtained. x ; quantifying the effect of the support on the displacement response of the device by a ratio of the acceleration response of the device in the first spring-mass system to the acceleration response of the device in the second spring-mass system; Get the influence coefficient R of the support on the acceleration response of the equipment a ; According to the R x and R a Provide guidance on seismic design of equipment-support systems; For the first spring-mass system, determining a deviation Δ1 between the natural frequency of the device and support system and the natural frequency of the device, and a deviation Δ2 between the natural frequency of the device and support system and the natural frequency of the support; and guiding the seismic design of the device-support system based on Δ1 and Δ2; in, ω s1 and ω s2 are the two natural frequencies of the device-support system in the first spring-mass system; ω1 is the natural frequency of the equipment, m1 is the mass of the equipment, k1 is the stiffness of the equipment; ω2 is the natural frequency of the support, m2 is the mass of the support, k2 is the stiffness of the support; n3 is the support / device frequency ratio, that is, The variation patterns of Δ1 and Δ2 with the support / equipment frequency ratio under different support / equipment mass ratios were investigated.

2. A method for guiding seismic design of equipment-support systems according to claim 1, characterized in that: The two natural frequencies of the device-support system in the first spring-mass system are obtained based on the vibration equation of the first spring-mass system and using the regular array matrix as the coordinate transformation matrix.

3. A method for guiding seismic design of equipment-support systems according to claim 2, characterized in that: The vibration equation of the first spring-mass system is: in, m1 is the mass of the device, k1 is the stiffness of the device, and x1 is the displacement of the device relative to the ground in the first spring-mass system; m2 is the mass of the support, k2 is the stiffness of the support, and x2 is the displacement of the support relative to the ground in the first spring-mass system; x g is the displacement of the ground under the action of an earthquake.

4. A method for guiding seismic design of equipment-support systems according to claim 3, characterized in that: The response corresponding to each mode is obtained by the following steps: Solve the vibration equations of the first spring-mass system: make The natural frequency ω of the system can be obtained s ; Let ω s1 and ω s2 are the two solutions of the above equation, i.e. the two natural frequencies of the equipment-support system; Since in the above formula 0, so ω s1 ≠ω s2 , so the two-degree-of-freedom system composed of equipment and support has no repeated roots; The vibration equation of the first spring-mass system shows that the system has elastic coupling in the original coordinate system. If the regular array matrix Ψ is used as the coordinate transformation matrix, the vibration equation of the first spring-mass system can be decoupled. Therefore, substituting x = Ψη into the vibration equation of the first spring-mass system yields: Among them, η is the canonical coordinate, For known mass matrix and stiffness matrix, the corresponding regular array matrix Ψ can be solved as: in, After decoupling, the solution of the regular array matrix Ψ can be obtained by solving the vibration of the two single-degree-of-freedom systems make Given the ground earthquake acceleration response spectrum, dynamic analysis is performed through the response spectrum earthquake load to obtain Among them, S a1 For ω s1 The corresponding acceleration response spectrum value, S a2 For ω s2 Corresponding acceleration response spectrum value; The responses corresponding to each mode are: r i =the i ψ i ,i=1.2 Among them, r i is the modal response, i is the modal order, ψ i is the column vector of the regular array matrix Ψ.

5. A method for guiding seismic design of equipment-support systems according to claim 3, characterized in that: The vibration equation of the second spring-mass system is: Or written as in, x3 is the displacement of the device relative to the ground in the second spring-mass system.

6. A method for guiding seismic design of equipment-support systems according to claim 5, characterized in that: The displacement and acceleration responses of the device in the first spring-mass system are: in, n1 is the support / equipment mass ratio, that is ω1 is the natural frequency of the equipment, ω s1 and ω s2 are the two natural frequencies of the device-support system in the first spring-mass system; S a1 For ω s1 The corresponding acceleration response spectrum value, S a2 For ω s2 Corresponding acceleration response spectrum value; The displacement response of the device in the second spring-mass system is: Among them, the acceleration response of the device is S a , S a is the earthquake acceleration response spectrum value corresponding to frequency ω1.

7. A method for guiding seismic design of equipment-support systems according to claim 6, characterized in that: The influence coefficient R of the support on the displacement response of the equipment x for: Investigate the displacement response influence coefficient R under different support / equipment mass ratios and support / equipment frequency ratios x The law of change.

8. A method for guiding seismic design of equipment-support systems according to claim 6, characterized in that: The influence coefficient R of the support on the acceleration response of the equipment a for: Investigate the acceleration response influence coefficient R under different support / equipment mass ratios and support / equipment frequency ratios a The law of change.

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