Conservative determination method of seismic load input for seismic qualification of structures with supporting equipment

Abstract

The present application relates to a conservative determination method of seismic load input suitable for seismic identification of equipment with support device, comprising the following steps: determining seismic input by using the method in the prior art, and investigating the maximum stress intensity of the equipment under the corresponding seismic input; simplifying the equipment and its support into a spring mass model, investigating the stress intensity of the equipment-support system under the response spectrum of the installation floor, and comparing with the maximum stress intensity obtained by the above other methods. Investigating whether the method of determining seismic input used in the seismic identification of the equipment in the prior art can envelope the real seismic load experienced by the equipment installed on the support, so as to determine a conservative treatment method of the seismic input of the equipment.

Description

[0001] This application is a divisional application of the invention patent application filed on July 4, 2018, with application number 2018107227870 and invention title "A conservative method for determining seismic load input for seismic assessment of supported equipment". Technical Field

[0002] This invention relates to the field of seismic design technology, and more specifically to a conservative method for determining seismic load inputs applicable to seismic assessment of structures with supporting equipment. Background Technology

[0003] Equipment installed in the plant is connected to the plant in two ways: directly on the plant floor or via a support structure to the plant floor or walls. For the seismic assessment of equipment, the source of seismic load is the floor response spectrum obtained from the plant's seismic analysis. For equipment directly installed on the plant floor, the response spectrum of the corresponding floor can be directly used as the seismic input. For equipment mounted via a support structure to the plant floor or walls, the most reliable method is to calculate the seismic response at the support and use this as the seismic input. However, this method is generally only applied to certain critical equipment in nuclear power plants. For pumps, valves, and other equipment widely used in nuclear power plants, the following methods are primarily used.

[0004] For metal-supported structures, they are generally considered together with the equipment during seismic assessment (either designed by the equipment manufacturer or designed by the designer and submitted to the equipment manufacturer) to ensure that the seismic input of the equipment matches the actual situation. For concrete-supported structures (usually designed by the designer), the equipment technical specifications provided by the designer to the equipment manufacturer only provide the floor response spectrum of the building where the equipment is located, and do not provide relevant information on concrete-supported structures. Therefore, the equipment manufacturer only focuses on the equipment as the research object, and generally uses the following methods to determine the seismic input for the equipment's seismic assessment:

[0005] (1) If the natural frequency of the equipment is lower than the seismic wave cutoff frequency, the response spectrum of the upper floor of the equipment is selected as the seismic input in order to enclose the influence of the support structure on the seismic response of the equipment.

[0006] (2) If the natural frequency of the equipment is greater than the cutoff frequency of the seismic wave, the equivalent static load of the seismic load can be determined by the following method when calculating the seismic response of the equipment using the static method:

[0007] (a) Use the envelope acceleration given in the applicable equipment technical specifications;

[0008] (b) Zero-period acceleration (ZPA) of the response spectrum of the equipment on the previous floor;

[0009] (c) For multi-degree-of-freedom components, when the component model is simple, the maximum value of the spectral value corresponding to the frequency band greater than or equal to the fundamental frequency of the device on the response spectrum of the previous floor can be 1.5 times.

[0010] For the seismic input determined by the above method, since there is no linear relationship between the response spectrum at the equipment support and the response spectrum of the floor above the equipment, it remains to be investigated whether this is a conservative approach to handling the seismic input of the equipment. Summary of the Invention

[0011] This invention provides a conservative method for determining seismic load input for seismic assessment of equipment with supports. Based on a spring-mass model, it compares the influence of the support structure on the equipment response and combines existing methods for determining seismic input in seismic assessment of equipment to determine a conservative method for processing seismic input to equipment.

[0012] To achieve the above objectives, the technical solution adopted by the present invention is: a conservative method for determining the seismic load input for seismic assessment of supported equipment, comprising the following steps:

[0013] (1) Select the response spectrum of the upper floor of the equipment as the seismic input and examine the maximum stress intensity of the equipment under the action of the upper floor response spectrum;

[0014] (2) Using the envelope acceleration given in the applicable equipment technical specifications, examine the maximum stress intensity of the equipment when the envelope acceleration is used as the seismic input;

[0015] (3) Using the zero-period acceleration of the response spectrum of the previous floor of the equipment, we examine the maximum stress intensity of the equipment when the zero-period acceleration is used as the earthquake input.

[0016] (4) The maximum value of the spectrum corresponding to the frequency band greater than or equal to the fundamental frequency of the equipment on the previous floor response spectrum is taken as the determined acceleration, and the maximum stress intensity of the equipment when the determined acceleration is used as the earthquake input is investigated.

[0017] (5) Simplify the equipment and its support into a first spring-mass system with two degrees of freedom; simplify the equipment without the support into a second spring-mass system with one degree of freedom; examine the stress intensity of the equipment-support system under the action of the floor response spectrum based on the first spring-mass system and the second spring-mass system, which is the true stress intensity of the equipment, and obtain the maximum stress intensity in the true stress intensity.

[0018] (6) Compare the maximum stress intensity obtained in steps (1) to (4) with the maximum stress intensity obtained in step (5). If the maximum stress intensity of any one of steps (1) to (4) can encompass the maximum stress intensity obtained in step (5), then using the seismic input in the corresponding step as the seismic input for the supported equipment is conservative.

[0019] Furthermore, in step (1), the influence coefficient of the equipment acceleration response caused by increasing the floor response spectrum is calculated, and in step (5), the influence coefficient of the equipment acceleration response caused by considering the support is calculated. The two influence coefficients are compared to determine whether increasing the floor response spectrum can encompass the influence coefficient caused by considering the support.

[0020] Furthermore, for supported equipment, the ratio of stress values ​​is equal to the ratio of accelerations, that is:

[0021] σ1 / σ3=a1 / a3

[0022] In other words, the effect of the support on the equipment stress is comparable to the effect of the support on the equipment acceleration response;

[0023] in,

[0024] σ1 and a1 represent the stress and acceleration of the supported equipment, respectively.

[0025] σ3 and a3 represent the stress and acceleration of the equipment when it is unsupported, respectively.

[0026] Furthermore, in step (5),

[0027] The vibration equation of the first spring-mass system is:

[0028]

[0029] in,

[0030]

[0031] m1 is the mass of the equipment, k1 is the stiffness of the equipment, and x1 is the displacement of the equipment relative to the ground in the first spring-mass system.

[0032] 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.

[0033] x g This represents the ground displacement under earthquake action;

[0034] The vibration equation of the second spring-mass system is:

[0035]

[0036] Or written as

[0037]

[0038] in,

[0039] x3 represents the displacement of the device relative to the ground in the second spring-mass system.

[0040] Furthermore, the acceleration response of the device in the first spring-mass system is:

[0041]

[0042] in,

[0043] n1 is the support / equipment mass ratio, i.e.

[0044] ω1 is the inherent frequency of the device.

[0045] ω s1 and ω s2 These are the two natural frequencies of the equipment-support system in the first spring-mass system;

[0046] S a1 For ω s1 The corresponding acceleration response spectrum value, S a2 For ω s2 The corresponding acceleration response spectrum value;

[0047] The displacement response of the device in the second spring-mass system is:

[0048]

[0049] The acceleration response of the device is S. a S a This represents the seismic acceleration response spectrum value corresponding to frequency ω1.

[0050] Furthermore, the influence coefficient R of the support on the displacement response of the equipment. x for:

[0051]

[0052] Investigating the influence coefficient R of displacement response under different support / equipment mass ratios and support / equipment frequency ratios. x The changing pattern.

[0053] After adopting the above technical solution, the present invention has the following advantages compared with the prior art: The present invention is applicable to a conservative method for determining the seismic load input in the seismic assessment of supported equipment. Based on the spring-mass model, a supported model and an unsupported model of the equipment are established. By comparing the influence of the supported structure on the equipment and the influence of the method for determining the seismic input used in the seismic assessment of equipment in the prior art on the equipment, it is examined whether the method for determining the seismic input used in the seismic assessment of equipment in the prior art can encompass the actual seismic load experienced by the equipment installed on the support, thereby determining a conservative method for processing the seismic input of the equipment. Attached Figure Description

[0054] Appendix Figure 1 This invention presents a simplified device and support system consisting of a two-degree-of-freedom spring-mass system.

[0055] Appendix Figure 2 This is a simplified single-degree-of-freedom spring-mass system for the device in this invention;

[0056] Appendix Figure 3 This is a curve showing the change in the influence coefficient of the floor response spectrum from -15.2m to 0.2m on the acceleration response of equipment at different frequencies in this invention.

[0057] Appendix Figure 4 This is the curve showing the variation of the influence coefficient on the acceleration response of a 14Hz device in this invention;

[0058] Appendix Figure 5 This is the curve showing the variation of the influence coefficient of the support on the acceleration response of a 50Hz device in this invention;

[0059] Appendix Figure 6 This is the device model in the present invention;

[0060] Appendix Figure 7 This is the equipment-support system model in this invention;

[0061] Appendix Figure 8 This is a stress intensity cloud diagram of the equipment-support system under the action of the floor response spectrum in this invention (equipment fundamental frequency 14Hz);

[0062] Appendix Figure 9 This is a cloud diagram of the stress intensity of the equipment under the action of the response spectrum of the upper floor in this invention (equipment fundamental frequency 14Hz);

[0063] Appendix Figure 10 This is a stress intensity cloud diagram of the equipment-support system under the action of the floor response spectrum in this invention (equipment fundamental frequency 50Hz);

[0064] Appendix Figure 11 This is a cloud diagram of the stress intensity of the equipment under the action of the response spectrum of the upper floor in this invention (equipment fundamental frequency 50Hz);

[0065] Appendix Figure 12 The stress intensity cloud diagram of the equipment when the envelope acceleration (1.2g) given in the applicable equipment technical specifications is used as the seismic input in this invention;

[0066] Appendix Figure 13 This is a cloud map of the equipment stress intensity when the zero-period acceleration of the response spectrum of the previous floor is used as the seismic input in this invention.

[0067] Appendix Figure 14 In this invention, the maximum value of the spectral value corresponding to the frequency band greater than or equal to the fundamental frequency of the equipment on the previous floor response spectrum is used as the determined acceleration for the equipment stress intensity cloud map when used as seismic input. Detailed Implementation

[0068] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0069] A conservative method for determining the seismic load input in seismic assessment of supported equipment includes the following steps:

[0070] (I) Supporting Impact Analysis

[0071] 1. Establish a spring-mass model with supporting equipment.

[0072] The device and its support are simplified into a spring-mass system with two degrees of freedom, such as... Figure 1 As shown. m1, k1, and x1 represent the mass, stiffness, and displacement relative to the ground of the equipment; m2, k2, and x2 represent the mass, stiffness, and displacement relative to the ground of the support; x g This represents the displacement of the ground under earthquake action.

[0073] The equation of motion of the system in the horizontal direction is:

[0074]

[0075] in,

[0076] By solving the characteristic equation of the system described in equation (1), let... The natural frequency ω of the system can be obtained. s

[0077]

[0078] Let ω s1 and ω s2 These are the two solutions to equation (2), namely the two natural frequencies of the equipment-support system. Because in equation (2) Therefore, ωs1 ≠ω s2 Therefore, the two-degree-of-freedom system consisting of the equipment and the support has no repeated roots. From the vibration equation (1), it can be seen that the system exhibits elastic coupling in the original coordinate system. If the canonical matrix Ψ is used as the coordinate transformation matrix, the original vibration equation (1) can be decoupled. Therefore, substituting x=Ψη into equation (1) yields...

[0079]

[0080] η is a regular coordinate.

[0081] Given the mass matrix and stiffness matrix, the corresponding canonical matrix Ψ can be solved as follows:

[0082]

[0083] in,

[0084] After decoupling, the solution to equation (4) can be obtained by solving the vibration of the two single-degree-of-freedom systems.

[0085]

[0086]

[0087] For example Figure 1 In the system shown, the parts within parentheses in equations (5) and (6) are constants. For simplification, let... For engineering design problems, such as the seismic design of nuclear power plant buildings, equipment, and components, the concern is not the motion law of the system under a given excitation, but rather how to select certain system parameters to limit the maximum value of the system response within a certain range. In this case, the following assumptions are made for... Figure 1 The system shown has a known ground seismic acceleration response spectrum. Dynamic analysis using the seismic load based on the response spectrum can yield the following results.

[0088]

[0089]

[0090] Among them, S a1 For ω s1 The corresponding acceleration response spectrum value, S a2 For ω s2 The corresponding acceleration response spectrum values. The response corresponding to each mode is:

[0091] r i =η i ψ i ,i=1,2 (9)

[0092] Where, r i Let i be the modal response, i be the modal order, and ψ be the modal response. i Ψ is the column vector of the regular matrix Ψ.

[0093] Since the response spectrum only provides information on the maximum amplitude of the seismic load and not the phase information, appropriate processing methods are needed during modal combination to ensure the conservatism of the final result. This invention uses the SRSS method for modal combination. Finally, the acceleration response of mass m1, i.e., the equipment, is...

[0094]

[0095] 2. Establish a spring-mass model for unsupported equipment.

[0096] If we disregard the equipment support and only consider the equipment itself, the equipment can be simplified as follows: Figure 2 The spring-mass system shown is a single-degree-of-freedom system.

[0097] Figure 2 The vibration equation of the single-degree-of-freedom spring-mass system shown is:

[0098]

[0099] Or written as

[0100]

[0101] For the system described by equation (12), assuming that its ground seismic acceleration response spectrum is known, the mass m1 can be obtained through dynamic analysis of the seismic load and the response spectrum, i.e., the displacement response of the equipment is:

[0102]

[0103] Among them, S a This represents the seismic acceleration response spectrum value corresponding to frequency ω1.

[0104] 3. Examine the impact of support on the response.

[0105] The device acceleration response of a two-degree-of-freedom system considering support (Equation (10)) and the device acceleration response S of a single-degree-of-freedom system without support are compared. a The ratio is used to quantify the influence of the support on the equipment's acceleration response, and the influence coefficient R of the support on the equipment's acceleration response can be deduced. a for

[0106]

[0107] In the seismic assessment of equipment, the equipment must meet certain structural strength requirements under seismic conditions. Structural strength is generally represented by stress. The following examines the influence of supports on the equipment stress. Since the stress of the equipment cannot be directly solved from the spring-mass model, dimensional analysis is used here to analyze the degree of influence of supports on the equipment stress from a dimensional perspective. Quantities related to stress σ include force F, cross-sectional area A, mass m, and acceleration a. The dimensional power matrix of these variables is shown in Table 1.

[0108] Table 1

[0109] σ F A m a M 1 1 0 1 0 L -1 1 2 0 1 t -2 -2 0 0 -2

[0110] Since the power exponents of variables A, m, and a satisfy the necessary and sufficient condition, that is...

[0111]

[0112] Therefore, we choose A, m, and a as independent variables. This results in two dimensionless quantities.

[0113]

[0114] Therefore, the stress ratio between supported and unsupported equipment satisfies the following relationship.

[0115]

[0116] Where σ1 and a1 are the stress and acceleration of the equipment when it is supported, and σ3 and a3 are the stress and acceleration of the equipment when it is unsupported. Since the equipment is the same, the mass of the equipment and the cross-sectional area at the same position of the equipment are the same, which are m1 and A, respectively. According to equation (17), the following relationship exists.

[0117] σ1 / σ3=a1 / a3 (18)

[0118] Therefore, the ratio of stress to acceleration of the equipment is equivalent to that of the support, meaning that the influence of the support on the stress of the equipment is equivalent to the influence of the support on the acceleration response of the equipment.

[0119] (II) Comparison of the impact of support on equipment with the existing methods for determining seismic input in seismic assessment of equipment.

[0120] Taking a power plant pump room as an example, this study verifies whether the influence of the response spectrum of the upper floor on the equipment response can encompass the influence of the support on the equipment response. Table 2 shows the acceleration response spectra of the pump room at the -15.2m floor and the floor 0.2m above it.

[0121] Table 2

[0122] Frequency (Hz) Acceleration at -15.2m (g) Frequency (Hz) Acceleration at 0.2 m (g) 0.35 0.08 0.34 0.08 0.71 0.153 0.63 0.138 2.28 0.5 2.28 0.51 6.75 0.64 6.75 0.71 8.67 0.96 8.67 1.19 11.1 0.96 11.1 1.19 14.3 0.4 16.9 0.38 22.6 0.23 23.6 0.29 38.9 0.19 34.4 0.23 50 0.19 50 0.23

[0123] Based on a spring-mass model of unsupported equipment, the amplification effect of increasing the floor response spectrum on the acceleration response of the equipment is examined. For the acceleration response spectra of the two floors shown in Table 2, the amplification effect of increasing the spectrum from -15.2m to 0.2m on the acceleration response of equipment at different frequencies is as follows: Figure 3 As shown in the figure, except for devices with a natural frequency around 14Hz, where the influence coefficient reaches 1.86, the influence coefficient for devices in other frequency bands is within 1.3.

[0124] In contrast, based on equation (14) of the spring-mass model with supported equipment, the acceleration response influence coefficients of equipment with natural frequencies of 14Hz (representing more flexible equipment) and 50Hz (representing more rigid equipment) are calculated to be within the ranges of 1-10 and 1.1-4 (which are more likely to occur in the field), respectively. The trends of these two parameters are as follows: Figures 4-5 As shown. Figures 4-5 The influence coefficients of these two frequency devices due to the presence or absence of support are as follows: Figure 3 Compared to the impact coefficient caused by increasing the floor response spectrum, it is clear that within the range of support / equipment mass ratios and frequency ratios likely to occur on-site, increasing the floor response spectrum may fail to encompass the impact coefficient caused by considering whether or not support is taken into account. Therefore, it is unrealistic to use the method of increasing the floor response spectrum to compensate for the practice of expecting to encompass the impact of support on equipment in the results without considering support in the analysis.

[0125] To further clarify this issue, the present invention also employs the finite element method to simulate the influence coefficients caused by considering whether or not supports are in place, and the influence coefficients caused by increasing the floor response spectrum. The equipment is simulated using shell elements, such as... Figure 6 As shown, the system consists of equipment and support. Figure 7 As shown, the support structure is simulated using solid elements. The equipment model constrains the translational degrees of freedom in three directions for all nodes around the bottom ring. The equipment-support system model constrains the translational degrees of freedom in three directions for all nodes on the bottom surface of the support. The two floor response spectra shown in Table 2 are input into the equipment model to calculate the impact of increasing the floor response spectrum on the equipment response without considering the support. The floor response spectrum at -15.2m shown in Table 2 is input into the equipment-support system model to calculate the impact of the support on the equipment response. By adjusting the density and Young's modulus, the support / equipment mass ratio and frequency ratio are positioned within the range shown in Table 2. Figures 4-5 Within the scope of consideration

[0126] Considering that the nuclear industry generally classifies equipment with a natural frequency higher than the seismic cutoff frequency as rigid equipment, and equipment with a natural frequency lower than the seismic cutoff frequency as flexible equipment, this embodiment will use flexible equipment with a natural frequency lower than the cutoff frequency and rigid equipment with a natural frequency higher than the cutoff frequency as examples. Flexible equipment is exemplified by a device with a natural frequency of 14Hz, and rigid equipment is exemplified by a device with a natural frequency of 50Hz.

[0127] The following are two specific implementation methods: First, the equipment's fundamental frequency is 14Hz, the support's fundamental frequency is 40.6Hz, the support / equipment frequency ratio is 2.9, the equipment mass is 1570.56kg, the support mass is 4426.5kg, and the support / equipment mass ratio is 2.82; Second, the equipment's fundamental frequency is 50Hz, the support's fundamental frequency is 145Hz, the support / equipment frequency ratio is 2.9, the equipment mass is 1570.56kg, the support mass is 4426.5kg, and the support / equipment mass ratio is 2.82. For both scenarios, under the influence of the response spectrum of the installation floor (-15.2m floor), the stress intensity cloud diagrams of the equipment-support system are as follows: Figure 8 , 10 As shown (i.e., the actual condition of the equipment); under the influence of the response spectrum of the floor above (0.2m floor), the stress intensity cloud diagrams of the equipment are as follows: Figure 9 , 11 As shown (i.e., an approximation of the actual condition of the equipment).

[0128] from Figures 8-11 It can be observed that the location of the maximum stress intensity is basically the same, and the stress distribution is also basically the same. Therefore, only the maximum value of the stress intensity needs to be compared here. The comparison shows that for devices with different fundamental frequencies (fundamental frequencies of 14Hz and 50Hz), even if the response spectrum of the upper floor is directly used as the seismic input of the device, the maximum stress intensity values ​​(6.61MPa and 4.36MPa, respectively) cannot encompass the maximum stress intensity values ​​under the actual conditions (11.2MPa and 6.69MPa, respectively). Therefore, by directly applying the response spectrum of the upper floor to the device without considering the device support, it is possible to obtain non-conservative results, thus proving that the processing method of selecting the response spectrum of the upper floor of the device as the seismic input (i.e., the method (1) in the background art) is inappropriate.

[0129] The rationality of the three processing methods in method (2) in the background art is discussed as follows: the three processing methods are: using the envelope acceleration given in the applicable equipment technical specifications as the seismic input; using the zero-period acceleration of the response spectrum of the previous floor of the equipment as the seismic input; and using 1.5 times the maximum value of the spectrum corresponding to the frequency band greater than or equal to the equipment fundamental frequency on the response spectrum of the previous floor of the equipment as the determined acceleration as the seismic input.

[0130] The technical specifications of domestically produced equipment generally do not provide envelope acceleration. However, in seismic assessments of equipment conducted by French manufacturers, for example, the seismic assessment method of the SEC pump motor at the Daya Bay Nuclear Power Plant by the French company SOFINEL specifies an envelope acceleration of 1.2g. This invention will calculate the seismic response of rigid equipment with a fundamental frequency of 50Hz using the three methods in method (2), and the calculation results are as follows. Figures 12-14 As shown.

[0131] Will Figures 12-14 The maximum stress intensity value in and Figure 10 Compared to the maximum stress intensity values, the values ​​are 21.7 MPa, 4.16 MPa, 6.24 MPa, and 6.69 MPa, respectively. Compared to the latter (the actual situation), the results obtained by the first three (approximate cases) using the envelope acceleration method are all smaller than those obtained by the other two methods, except for the first one which uses the envelope acceleration method. This result indicates that the approximate method based on the response spectrum of the upper floor (with equivalent acceleration values ​​taken according to method (2b) or (2c)) and without considering supports in the model is insufficient to encompass the actual situation of the equipment and cannot make an assessment of the actual situation, thus losing the rationality of the assessment results. However, the equivalent static method using the reasonable envelope acceleration given in the equipment's technical specifications can encompass the actual situation of the equipment.

[0132] The above analysis shows that for seismic assessment of supported equipment, since the supports have a wide-ranging impact on the equipment, the supports should be included in the seismic assessment scope as much as possible to reasonably simulate the seismic input to the equipment. If practical conditions do not permit this, it is not recommended to use the response spectrum of the upper floor. Instead, a reasonable envelope acceleration should be proposed in the equipment's technical specifications, taking into account the equipment installation conditions.

[0133] The above embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. All equivalent changes or modifications made in accordance with the spirit and essence of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A conservative method for determining seismic load input suitable for seismic assessment of structures with supporting equipment, characterized in that, Includes the following steps: The equipment and its support are simplified into a first spring-mass system with two degrees of freedom; the equipment without the support is simplified into a second spring-mass system with one degree of freedom. The stress intensity of the equipment-support system under the action of the floor response spectrum is examined based on the first spring-mass system and the second spring-mass system. This is the true stress intensity of the equipment, and the maximum stress intensity in the true stress intensity is obtained. The response spectrum of the floor above the equipment was selected as the seismic input, and the maximum stress intensity of the equipment under the action of the response spectrum of the floor above was investigated. The maximum stress intensity of the equipment under the action of the response spectrum of the upper floor is compared with the maximum stress intensity in the actual stress intensity. If the former can enclose the latter, then using the seismic input in the corresponding step as the seismic input of the supported equipment is conservative. For supported equipment, the ratio of stress values ​​is equal to the ratio of accelerations, that is: σ1 / σ3=a1 / a3 In other words, the effect of the support on the equipment stress is comparable to the effect of the support on the equipment acceleration response; in, σ1 and a1 represent the stress and acceleration of the supported equipment, respectively. σ3 and a3 represent the stress and acceleration of the equipment when it is unsupported, respectively. The vibration equation of the first spring-mass system is: in, m1 is the mass of the equipment, k1 is the stiffness of the equipment, and x1 is the displacement of the equipment 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 This represents the ground displacement under earthquake action; The vibration equation of the second spring-mass system is: Or written as in, x3 represents the displacement of the device relative to the ground in the second spring-mass system; The acceleration response of the device in the first spring-mass system is: in, n1 is the support / equipment mass ratio, i.e. ω1 is the inherent frequency of the device. ω s1 and ω s2 These are the two natural frequencies of the equipment-support system in the first spring-mass system; S a1 For ω s1 The corresponding acceleration response spectrum value, S a2 For ω s2 The corresponding acceleration response spectrum value; The displacement response of the device in the second spring-mass system is: The acceleration response of the device is S. a S a This represents the seismic acceleration response spectrum value corresponding to frequency ω1.

2. The conservative determination method according to claim 1, characterized in that, Methods for determining seismic input and examining the maximum stress intensity of equipment also include: using the envelope acceleration given in the applicable equipment technical specifications and examining the maximum stress intensity of the equipment when that envelope acceleration is used as the seismic input.

3. The conservative determination method according to claim 1, characterized in that, Another method for determining the seismic input and examining the maximum stress intensity of equipment is to use the zero-period acceleration of the response spectrum of the previous floor of the equipment and examine the maximum stress intensity of the equipment when this zero-period acceleration is used as the seismic input.

4. The conservative determination method according to claim 1, characterized in that, Another method for determining the seismic input and examining the maximum stress intensity of the equipment is to use 1.5 times the maximum value of the spectral value corresponding to the frequency band greater than or equal to the equipment's fundamental frequency on the response spectrum of the previous floor as the determined acceleration, and examine the maximum stress intensity of the equipment when this determined acceleration is used as the seismic input.

5. The conservative determination method according to claim 1, characterized in that, The two natural frequencies ω of the device-support system in the first spring-mass system s1 and ω s2 It was calculated using the following method: 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 These are the two solutions to the above equation, namely the two natural frequencies of the equipment-support system.

6. The conservative determination method according to claim 1, characterized in that, With ω s1 The corresponding acceleration response spectrum value S a1 and with ω s2 The corresponding acceleration response spectrum value S a2 It was calculated using the following method: Substituting x = Ψη into the vibration equation of the first spring-mass system: achievable η is a regular coordinate. The corresponding regular matrix Ψ is obtained by solving for... in, After decoupling, the vibrations of the two single-degree-of-freedom systems are solved to obtain the results. The part inside the parentheses in the above equation is a constant, let Dynamic analysis using response spectrum seismic loads can yield the following results. Among them, S a1 For ω s1 The corresponding acceleration response spectrum value, S a2 For ω s2 The corresponding acceleration response spectrum value.

7. The conservative determination method according to claim 1, characterized in that, The influence coefficient R of the support on the displacement response of the equipment x for: Investigating the influence coefficient R of displacement response under different support / equipment mass ratios and support / equipment frequency ratios. x The changing pattern.

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