A method and system for acquiring acceleration equivalent spectrum

Abstract

The present invention discloses a method and system for acquiring an acceleration equivalent spectrum, the method comprising the following steps: step one: according to a single-degree-of-freedom spring oscillator system, obtaining the absolute acceleration response of the spring oscillator under a preset basic acceleration excitation, and calculating the impact response spectrum of the basic acceleration excitation to the absolute acceleration response of the spring oscillator; step two: according to the response of the virtual spring oscillator in step one, obtaining the steady-state amplification coefficient Q of the spring oscillator system; step three: according to the steady-state amplification coefficient in step two, obtaining the transient amplification coefficient of the virtual spring oscillator; step four: according to the impact response spectrum in step one and the transient amplification coefficient in step three, obtaining the equivalent spectrum of the basic excitation acceleration. The present invention takes into account the influence of transient effects, is closer to the actual engineering situation, and helps to improve the rationality of determining acceleration test conditions.

Description

Technical Field

[0001] The present invention belongs to the technical field of equivalent spectrum corresponding to transient mechanical environment of spacecraft, launch vehicle and components thereof in a launch phase, and in particular to a method and system for acquiring acceleration equivalent spectrum. Background Art

[0002] At present, the low-frequency acceleration test conditions for spacecraft, launch vehicles and their components are mainly formulated based on the satellite-rocket coupling analysis results to obtain the time domain response value of acceleration, and then the acceleration spectrum is obtained by shock response spectrum transformation. The acceleration spectrum is enveloped to formulate the acceleration vibration test conditions. The shock response spectrum is based on a certain form of external excitation (usually basic acceleration excitation), giving a curve of the relationship between the maximum response and the natural frequency (such as Figure 1 As shown in Figure 2.1 ...

[0003] From the perspective of mathematical transformation, the shock response spectrum is a special mathematical transformation, which is often used in aerospace engineering to replace the traditional Fourier transform (FFT). Since the system response of the launch vehicle is rapidly attenuated by damping during ignition, shutdown, interstage separation, satellite-rocket separation, and spacecraft landing, it is a typical transient response. If you want to transform the time domain results obtained from the transient response analysis into the frequency domain, the Fourier transform cannot obtain reasonable amplitude characteristics. At this time, the engineering often uses the shock response spectrum transformation technology to obtain the equivalent spectrum. The low-frequency mechanical environment (generally within 100Hz) experienced by satellites and launch vehicles during the launch phase is actually dominated by non-stationary transient environments, and the corresponding ground tests usually use frequency domain methods (such as sine sweep tests). In this way, it is necessary to convert the transient environment into frequency domain quantities, and the shock response spectrum transformation is often used in engineering to achieve this process.

[0004] However, research has found that in satellite and launch vehicle engineering, the equivalent spectrum of the low-frequency mechanical environment (such as the satellite-rocket interface or the internal acceleration response of the satellite) is often obtained by dividing the impact response spectrum by the steady-state magnification factor Q. The result of this processing method is greatly affected by the value of the steady-state magnification factor. As the value of the steady-state magnification factor increases, the amplitude of the equivalent spectrum gradually decreases (infinitely close to 0) and the frequency distribution characteristics change. Therefore, the above commonly used engineering processing methods have unreasonable factors, and it is necessary to explore new methods for determining the equivalent spectrum of the satellite-rocket mechanical environment. Summary of the invention

[0005] The technical problem solved by the present invention is: to overcome the deficiencies of the prior art, to provide a method and system for acquiring an acceleration equivalent spectrum, to take into account the influence of transient effects, to be closer to actual engineering conditions, and to help improve the rationality of determining acceleration test conditions.

[0006] The object of the present invention is achieved by the following technical solution: A method for obtaining an acceleration equivalent spectrum, the method comprising the following steps: Step 1: According to a single-degree-of-freedom spring oscillator system, obtain a preset basic acceleration excitation Absolute acceleration response of a spring oscillator under action The basic acceleration excitation is calculated using the following formula: The absolute acceleration response of the spring oscillator Shock response spectrum Step 2: Based on the response of the virtual spring oscillator in step 1 The steady-state magnification coefficient Q of the spring oscillator system is calculated using the following formula; Step 3: According to the steady-state magnification coefficient Q in step 2, the transient magnification coefficient Q' of the virtual spring oscillator is obtained; Step 4: According to the impact response spectrum in step 1 And the transient amplification factor Q' in step 3, the basic excitation acceleration is obtained The equivalent spectrum of .

[0007] In the above method for obtaining the acceleration equivalent spectrum, in step 1, the shock response spectrum It is obtained by the following formula:

[0008]

[0009] Where t is time, ω n is the natural circular frequency corresponding to the spring oscillator, It means taking the maximum value within time t, and || is the symbol for taking the absolute value.

[0010] In the above method for acquiring the acceleration equivalent spectrum, in step 2, the steady-state amplification factor Q of the spring oscillator system is obtained by the following formula:

[0011]

[0012]

[0013] Where ω is the excitation frequency, j is the imaginary unit, To preset the basic acceleration excitation, is the absolute acceleration response of the spring oscillator, is the Fourier transform amplitude of the absolute acceleration response of the spring oscillator, The Fourier transform amplitude of the basic acceleration excitation, the function Fourier() represents the Fourier transform, H(ω;ω n ) is the transfer function between response and excitation.

[0014] In the above method for acquiring the acceleration equivalent spectrum, in step 3, the transient amplification factor Q' of the virtual spring oscillator is obtained by the following formula:

[0015]

[0016] ω n is the natural circular frequency corresponding to the spring oscillator.

[0017] In the above method for obtaining the acceleration equivalent spectrum, in step 4, the equivalent spectrum of the basic excitation acceleration It is obtained by the following formula:

[0018]

[0019] A system for acquiring acceleration equivalent spectrum, comprising: a first module, for obtaining a single-degree-of-freedom spring oscillator system under a preset basic acceleration excitation Absolute acceleration response of a spring oscillator under action The basic acceleration excitation is calculated using the following formula: The absolute acceleration response of the spring oscillator Shock response spectrum The second module is used to generate a virtual spring oscillator according to the response of the virtual spring oscillator in the first module. The steady-state magnification coefficient Q of the spring oscillator system is calculated by the following formula; the third module is used to obtain the transient magnification coefficient Q' of the virtual spring oscillator according to the steady-state magnification coefficient Q in the second module; the fourth module is used to obtain the transient magnification coefficient Q' of the virtual spring oscillator according to the impact response spectrum in the first module And the transient amplification factor Q' in the third module, the basic excitation acceleration is obtained The equivalent spectrum of .

[0020] In the above acceleration equivalent spectrum acquisition system, the shock response spectrum It is obtained by the following formula:

[0021]

[0022] Where t is time, ω n is the natural circular frequency corresponding to the spring oscillator, It means taking the maximum value within time t, and || is the symbol for taking the absolute value.

[0023] In the above acceleration equivalent spectrum acquisition system, the steady-state amplification factor Q of the spring oscillator system is obtained by the following formula:

[0024]

[0025]

[0026] Where ω is the excitation frequency, j is the imaginary unit, To preset the basic acceleration excitation, is the absolute acceleration response of the spring oscillator, is the Fourier transform amplitude of the absolute acceleration response of the spring oscillator, The Fourier transform amplitude of the basic acceleration excitation, the function Fourier() represents the Fourier transform, H(ω;ω n ) is the transfer function between response and excitation.

[0027] In the above acceleration equivalent spectrum acquisition system, the transient amplification coefficient Q' of the virtual spring oscillator is obtained by the following formula:

[0028]

[0029] ω n is the natural circular frequency corresponding to the spring oscillator.

[0030] In the above acceleration equivalent spectrum acquisition system, the equivalent spectrum of the basic excitation acceleration It is obtained by the following formula:

[0031]

[0032] Compared with the prior art, the present invention has the following beneficial effects:

[0033] (1) Currently in satellite and launch vehicle engineering, the equivalent spectrum of low-frequency mechanical environment (such as the satellite-rocket interface or the acceleration response inside the satellite) is often obtained by dividing the impact response spectrum by the steady-state magnification factor Q. The result of this processing method is greatly affected by the value of the steady-state magnification factor; as the value of the steady-state magnification factor increases, the amplitude of the equivalent spectrum gradually decreases (infinitely close to 0) and the frequency distribution characteristics change. The present invention proposes that when the acceleration response of the virtual spring oscillator is in a transient state, the impact response spectrum is divided by the transient magnification factor of the oscillator acceleration response amplitude relative to the basic acceleration to obtain the equivalent spectrum of the transient basic excitation acceleration. This new method can take into account the influence of transient effects, is closer to the actual engineering situation, and helps to improve the rationality of the determination of acceleration test conditions.

[0034] (2) The present invention provides a quantitative calculation method for the transient amplification factor from the basic acceleration sinusoidal excitation to the virtual spring oscillator response spectrum. The approximate expression of the transient amplification factor is derived based on the sinusoidal excitation assumption and is usually only used for qualitative analysis of the factors affecting the coefficient, making it difficult to calculate quantitatively. Moreover, the expression contains multiple unknown parameters, making its quantitative calculation even more difficult. The present invention provides a specific selection method for the relevant parameters to ensure that a reasonable quantitative result of the transient amplification factor is obtained. Through theoretical derivation, the difference and connection between the transient amplification factor and the traditional steady-state coefficient are established, providing an intuitive evaluation method for the study of the transfer characteristics of transient excitation. Its physical meaning is clear, and the parameters to be determined are very clear, which is convenient for promotion and application. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Various other advantages and benefits will become apparent to those of ordinary skill in the art by reading the detailed description of the preferred embodiments below. The accompanying drawings are only for the purpose of illustrating the preferred embodiments and are not to be considered as limiting the present invention. Moreover, the same reference symbols are used throughout the accompanying drawings to represent the same components. In the accompanying drawings:

[0036] Figure 1 is a schematic diagram of the shock response spectrum of the prior art;

[0037] Figure 2 is a schematic diagram of the ratio of the transient amplification factor provided by an embodiment of the present invention to the traditional steady-state amplification factor;

[0038] Figure 3 It is a flow chart of a method for acquiring an acceleration equivalent spectrum provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0039] Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided in order to enable a more thorough understanding of the present disclosure and to be able to fully convey the scope of the present disclosure to those skilled in the art. It should be noted that, in the absence of conflict, the embodiments of the present invention and the features described in the embodiments can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0040] Figure 3 FIG. 1 is a flow chart of a method for obtaining an acceleration equivalent spectrum provided by an embodiment of the present invention. Figure 3 As shown, the method comprises the following steps:

[0041] Step 1: Based on the single-degree-of-freedom spring oscillator system, calculate the acceleration excitation under a given base Absolute acceleration response of a spring oscillator under action The incentive is calculated using the following formula arrive Shock response spectrum

[0042]

[0043] Where t is time, ω n is the natural circular frequency corresponding to the spring oscillator, and the superscript “¨” means the second-order derivative with respect to time. It means taking the maximum value within time t, and || is the symbol for taking the absolute value.

[0044] Step 2: Response of the virtual spring oscillator calculated in step 1 The steady-state amplification factor Q of the spring oscillator system is calculated using the following formula:

[0045]

[0046]

[0047] Where ω is the excitation frequency, Re() is the real part function, j is the imaginary unit, e() is the natural exponent, max() is the maximum value function, and || is the absolute value symbol.

[0048] Step 3: According to the steady-state magnification factor Q obtained in step 3, calculate the transient magnification factor Q' of the virtual spring oscillator:

[0049]

[0050] Step 4: The shock response spectrum calculated in step 1 The basic excitation acceleration is calculated by the following formula: The equivalent spectrum of:

[0051]

[0052] (1) Calculate the impact response spectrum of the virtual spring oscillator

[0053] For a single degree of freedom system, the vibration equation under base excitation is:

[0054]

[0055] in,

[0056] m, c, and k represent the mass, damping, and stiffness of the virtual spring oscillator, respectively;

[0057] y(t) and x(t) represent the absolute displacements of the spring oscillator and the foundation, respectively.

[0058] Assume the system natural circular frequency

[0059] Damping ratio

[0060] Relative displacement z(t)=y(t)-x(t),

[0061] Then there is

[0062]

[0063] If the basic acceleration excitation is given Then, by solving the differential equation of (2), we can find z(t) and The expression of z(t) is as follows:

[0064]

[0065] in,

[0066] z 0 and is the initial relative displacement and initial relative velocity,

[0067] Damping circle frequency

[0068] Then we can find the absolute acceleration of the spring oscillator:

[0069]

[0070] The above formula is a natural circular frequency ω n The acceleration response time history curve below.

[0071] For different n , we can draw an acceleration response time history curve. On this basis, we can find the maximum acceleration (absolute value) at different times as the corresponding ω n The response spectrum value of To the response Shock response spectrum transformation

[0072]

[0073] For acceleration excitation The corresponding shock response spectrum. The shock response spectrum is a curve of the maximum response of a single-degree-of-freedom system under a given load and the change of the natural frequency. For any shock load function, the response spectrum of different excitations can be obtained according to the above method. Changing the damping ratio ζ or the steady-state magnification factor A series of response spectrum curves will be obtained. For satellites and launch vehicles, Q is usually taken as 10 or 20 in engineering.

[0074] From the above analysis, it can be seen that the key to calculating the shock response spectrum is to solve the given ω n The corresponding equation (2) can be used to obtain the acceleration time history For the derivation of the above formulas (1)-(5), please refer to the document "Practical Vibration Engineering (1)-Vibration Theory and Analysis" (Aviation Industry Press, 1996)

[0075] Assuming base acceleration excitation If the linear change between adjacent moments (i.e., the trapezoidal rule) is applied, equation (3) becomes:

[0076]

[0077] in,

[0078] Δt i =t i+1 -t i ,

[0079]

[0080] Substituting the right side of the above equation into equation (3), we can deduce the relative displacement z(t)(t i ≤t≤t i+1 ) expression:

[0081]

[0082] in,

[0083]

[0084]

[0085] Taking the derivative of (7), we can get

[0086] Therefore, it is known that z(t i )and It can be obtained by z(t) and The expression (t i ≤t≤t i+1 ) to obtain z(t i+1 )and Then, we use formula (4) to obtain

[0087] For the derivation of the above formulas (6)-(9), please refer to the literature "Mechanical vibrations in spacecraft design" (Springer-Verlag Berlin Heidelberg, 2004).

[0088] (2) Calculate the steady-state amplification factor of the virtual spring oscillator response relative to the base excitation

[0089] In order to determine the spectral characteristics of the mechanical environment of the satellite and rocket, the engineering community often uses the impact response spectrum analysis method to convert the maximum response of the virtual single-degree-of-freedom spring oscillator into the equivalent spectrum of the basic acceleration, which is used as the basis for the formulation of the mechanical environment conditions. For example, in the satellite-rocket coupling analysis, the transient response analysis method is first used to obtain the time domain response of the acceleration of any node on the satellite-rocket structure, and then the response is used as the basic excitation of several virtual single-degree-of-freedom spring oscillators with different natural frequencies to solve the maximum response of these oscillators (i.e., the impact response spectrum), and then the response spectrum is divided by the steady-state amplification factor as the acceleration spectrum of the node, which is used to formulate the vibration test conditions of the satellite or its components. The steady-state amplification factor is the ratio of the acceleration response spectrum to the amplitude of the basic excitation acceleration under the steady-state assumption. The derivation is as follows:

[0090] The frequency domain transfer function of equation (1) under steady-state excitation is:

[0091]

[0092] in,

[0093] ω is the excitation frequency,

[0094]

[0095]

[0096]

[0097]

[0098] in,

[0099] κ=γ 2 .

[0100] In order to find the maximum value, take the first-order derivative of the right-hand side of the above formula with respect to κ and set it to 0, then we have:

[0101]

[0102] Using Taylor series expansion, omitting ζ 4 And higher-order terms, we have:

[0103]

[0104] Substitute (17) into (15), omitting ζ 4 And higher-order terms, we can get:

[0105]

[0106] Because Q is usually greater than 10, and when |H(ω)| takes the maximum value, κ≈1, ω≈ω n , so the steady-state amplification factor is approximately obtained:

[0107]

[0108] (3) Calculate the transient amplification factor of the virtual spring oscillator response relative to the base excitation

[0109] Actual excitation is often transient and may not reach a steady state. There are few relevant literatures on whether a simplified expression similar to the steady-state amplification factor can be given under transient excitation, and whether this can provide an intuitive evaluation method for the transfer characteristics of transient excitation. The present invention provides an approximate formula for the transient amplification factor from the basic acceleration sinusoidal excitation to the virtual spring oscillator response spectrum.

[0110] set up Initial relative displacement z 0 and relative speed is 0, then from (4) we can get:

[0111]

[0112]

[0113] in,

[0114]

[0115]

[0116] Substituting (21) and (22) into equation (4), we can take ω = ω n ,ω d ≈ω n , we can get:

[0117]

[0118] Since Q is usually greater than 10 (corresponding to ζ not exceeding 0.05), sinω is omitted. n The contribution of the t-term coefficient to the amplitude is:

[0119]

[0120] The right-hand side of the above equation consists of two parts, one part changes with the cosine, and the other part is related to exponential decay. The amplitude of the cosine change part is taken as the maximum value 1, and this is used to calculate The envelope of the absolute value changing with time (using Expressed), and then the transient amplification factor is obtained:

[0121]

[0122] It can be seen from formula (25) that before the acceleration response of the virtual spring oscillator reaches a steady state (i.e., in a transient state), the transient amplification factor Q' of the oscillator's acceleration response amplitude relative to the basic acceleration is not equal to Q, and its value is smaller than Q. The ratio of the transient amplification factor Q' to Q changes nonlinearly with Q; the larger the value of Q, the smaller the ratio; when Q is infinite, the ratio tends to 0. Its characteristic curve is shown in Figure 2 .

[0123] Among them, Q does not use the commonly used 20 in engineering, but is determined by the corresponding structural damping, that is, where is the damping ratio of the test object (the actual measured value or the designed value), and the physical meaning is clear; how to determine the time t has always been a difficult point. The present invention selects the corresponding ω n The moment when the peak of the impact response spectrum of the virtual spring oscillator appears.

[0124] (4) Obtaining the equivalent spectrum of transient acceleration based on the transient amplification factor

[0125] Defining transient acceleration The equivalent spectrum of:

[0126]

[0127] When the acceleration response of the virtual spring oscillator is in a transient state, the equivalent spectrum of the basic excitation acceleration is obtained by dividing the impulse response spectrum by the transient magnification factor of the oscillator acceleration response amplitude relative to the basic acceleration.

[0128] This embodiment also provides a system for acquiring an acceleration equivalent spectrum, including: a first module, for obtaining an acceleration equivalent spectrum under a preset basic acceleration excitation according to a single-degree-of-freedom spring oscillator system; Absolute acceleration response of a spring oscillator under action The basic acceleration excitation is calculated using the following formula: The absolute acceleration response of the spring oscillator Shock response spectrum The second module is used to generate a virtual spring oscillator according to the response of the virtual spring oscillator in the first module. The steady-state magnification coefficient Q of the spring oscillator system is calculated by the following formula; the third module is used to obtain the transient magnification coefficient Q' of the virtual spring oscillator according to the steady-state magnification coefficient Q in the second module; the fourth module is used to obtain the transient magnification coefficient Q' of the virtual spring oscillator according to the impact response spectrum in the first module And the transient amplification factor Q' in the third module, the basic excitation acceleration is obtained The equivalent spectrum of .

[0129] At present, in satellite and launch vehicle engineering, the equivalent spectrum of low-frequency mechanical environment (such as the satellite-rocket interface or the internal acceleration response of the satellite) is often obtained by dividing the impact response spectrum by the steady-state magnification factor Q. The result of this processing method is greatly affected by the value of the steady-state magnification factor; as the value of the steady-state magnification factor increases, the amplitude of the equivalent spectrum gradually decreases as a whole (infinitely close to 0), and the frequency distribution characteristics will change. The present invention proposes that when the acceleration response of the virtual spring oscillator is in a transient state, the impact response spectrum is divided by the transient magnification factor of the oscillator acceleration response amplitude relative to the basic acceleration to obtain the equivalent spectrum of the transient basic excitation acceleration. This new method can take into account the influence of transient effects, is closer to the actual engineering situation, and helps to improve the rationality of the determination of acceleration test conditions.

[0130] The present invention provides a quantitative calculation method for the transient amplification factor from the basic acceleration sinusoidal excitation to the virtual spring oscillator response spectrum. The approximate expression of the transient amplification factor is derived based on the sinusoidal excitation assumption, and is usually only used for qualitative analysis of the factors affecting the coefficient, and is difficult to calculate quantitatively; and the expression contains multiple unknown parameters, making its quantitative calculation more difficult. The present invention provides a specific selection method for the relevant parameters to ensure that a reasonable transient amplification factor quantification result is obtained. Through theoretical derivation, the difference and connection between the transient amplification factor and the traditional steady-state coefficient are established, providing an intuitive evaluation method for the study of the transfer characteristics of transient excitation. Its physical meaning is clear, and the parameters to be determined are very clear, which is convenient for promotion and application.

[0131] Although the present invention has been disclosed as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solution of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

Claims

1. A method for obtaining an acceleration equivalent spectrum, characterized in that: The method comprises the following steps: Step 1: According to the single-degree-of-freedom spring oscillator system, the absolute acceleration response of the spring oscillator under the preset basic acceleration excitation is obtained, and the impact response spectrum from the basic acceleration excitation to the absolute acceleration response of the spring oscillator is calculated; Step 2: According to the response of the virtual spring oscillator in step 1, the steady-state amplification coefficient Q of the spring oscillator system is obtained; Step 3: Obtain the transient amplification factor of the virtual spring oscillator according to the steady-state amplification factor in step 2; Step 4: According to the impulse response spectrum in step 1 and the transient amplification factor in step 3, the equivalent spectrum of the basic excitation acceleration is obtained; In step 1, the shock response spectrum It is obtained by the following formula: Where t is time, ω n is the natural circular frequency corresponding to the spring oscillator, It means taking the maximum value within time t, and || is the symbol for taking the absolute value. is the absolute acceleration response; in step 2, the steady-state amplification factor Q of the spring oscillator system is obtained by the following formula: Where ω is the excitation frequency, j is the imaginary unit, To preset the basic acceleration excitation, is the absolute acceleration response of the spring oscillator, is the Fourier transform amplitude of the absolute acceleration response of the spring oscillator, is the Fourier transform amplitude of the basic acceleration excitation, the function Fourier() represents the Fourier transform, H(ω;ω n ) is the transfer function between response and excitation.

2. The method for obtaining the acceleration equivalent spectrum according to claim 1, characterized in that: In step 3, the transient amplification factor Q' of the virtual spring oscillator is obtained by the following formula: ω n is the natural circular frequency corresponding to the spring oscillator.

3. The method for obtaining the acceleration equivalent spectrum according to claim 1, characterized in that: In step 4, the equivalent spectrum of the base excitation acceleration It is obtained by the following formula:

4. A system for acquiring acceleration equivalent spectrum, characterized in that include: The first module is used to obtain the absolute acceleration response of the spring oscillator under the preset basic acceleration excitation according to the single-degree-of-freedom spring oscillator system, and calculate the impact response spectrum from the basic acceleration excitation to the absolute acceleration response of the spring oscillator; The second module is used to obtain a steady-state amplification factor of the spring oscillator system according to the response of the virtual spring oscillator in the first module; The third module is used to obtain the transient amplification factor of the virtual spring oscillator according to the steady-state amplification factor in the second module; The fourth module is used to obtain an equivalent spectrum of the basic excitation acceleration according to the impulse response spectrum in the first module and the transient amplification factor in the third module; Shock Response Spectrum It is obtained by the following formula: Where t is time, ω n is the natural circular frequency corresponding to the spring oscillator, Indicates the maximum value within time t, || is the absolute value symbol; the steady-state amplification factor Q of the spring oscillator system is obtained by the following formula: Where ω is the excitation frequency, j is the imaginary unit, To preset the basic acceleration excitation, is the absolute acceleration response of the spring oscillator, is the Fourier transform amplitude of the absolute acceleration response of the spring oscillator, The Fourier transform amplitude of the basic acceleration excitation, the function Fourier() represents the Fourier transform, H(ω;ω n ) is the transfer function between response and excitation.

5. The acceleration equivalent spectrum acquisition system according to claim 4, characterized in that: The transient amplification factor Q' of the virtual spring oscillator is obtained by the following formula: ω n is the natural circular frequency corresponding to the spring oscillator.

6. The acceleration equivalent spectrum acquisition system according to claim 4, characterized in that: Equivalent spectrum of base excitation acceleration It is obtained by the following formula:

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