A solid-liquid rocket equipment longitudinal sine condition design method based on time series analysis

Abstract

The application discloses a kind of longitudinal sine condition design methods of solid-liquid rocket equipment based on time series analysis, comprising: obtaining the vibration response time domain curve of engine upper gyro pedestal or rack and cabin section joint when liquid engine ground test, and the vibration response time domain curve of solid engine rear skirt when solid engine ground test;The two vibration response time domain curves obtained are respectively pretreated, to obtain the first, second impact response spectrum equivalent sine data;The first, second impact response spectrum equivalent sine data are enveloped;According to longitudinal transfer characteristic, the acceptance level longitudinal sine vibration test level of other cabin sections of solid-liquid binding launch vehicle instrument equipment is obtained;Based on safety factor T, the identification level longitudinal sine vibration test level is obtained.The method can quickly give the longitudinal sine vibration test condition of each cabin section of solid-liquid binding launch vehicle single machine equipment in the early stage of launch vehicle demonstration, scheme, for single machine equipment selection and scheme design.

Description

Technical Field

[0001] This invention belongs to the field of launch vehicle technology, and particularly relates to a longitudinal sinusoidal condition design method for solid-liquid rocket equipment based on time series analysis. Background Technology

[0002] In the field of launch vehicles, the combination of solid and liquid propulsion systems leverages the advantages of solid propulsion (high thrust and good acceleration) and liquid propulsion (long operating time and easy thrust adjustment). After decades of development, solid-propellant launch vehicle technology has matured significantly both domestically and internationally. It has evolved from simply exploring the potential of launch vehicles to achieving serialization, modularization, universalization, and combination of launch vehicles. By bundling different numbers and types of solid boosters, a single rocket series can possess both a wide range of payload capacities and a fine gradient in payload capacity, flexibly meeting the diverse requirements of space launches.

[0003] Solid rocket motors offer superior acceleration, but generate more severe transient excitations compared to liquid rocket motors. Based on domestic and international experience with low-frequency sinusoidal vibration environments in launch vehicles, sinusoidal excitation is primarily caused by transient conditions during launch vehicle flight. With the addition of solid rocket motors, the increased external excitation sources lead to more complex vibration responses transmitted through the structure. Damage or failure of individual onboard equipment is closely related to the low-frequency sinusoidal vibration environment it experiences. The accuracy of test conditions directly impacts the product's design level and the effectiveness of ground testing, affecting the quality of individual equipment—a critical factor in the success or failure of rocket flight. Accurately designing sinusoidal vibration test conditions for instruments and equipment is crucial for rocket validation and instrument selection.

[0004] Because solid rocket motor ignition is irreversible, solid-liquid coupled launch vehicles typically ignite the liquid rocket motor first at liftoff, and then ignite the solid rocket motor after the liquid rocket motor has reached a steady state. This ignition sequence provides significant advantages for the design of longitudinal sinusoidal vibration conditions for solid-liquid coupled launch vehicles and effectively solves the coupling problem caused by the operation of multiple engines. Summary of the Invention

[0005] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a longitudinal sinusoidal condition design method for solid-liquid rocket equipment based on time-series analysis. This method can quickly provide longitudinal sinusoidal vibration test conditions for individual equipment on each section of a solid-liquid bundled launch vehicle in the early stages of launch vehicle demonstration and scheme design, so as to provide equipment selection and scheme design.

[0006] To address the aforementioned technical problems, this invention discloses a design method for longitudinal sinusoidal conditions of solid-liquid rocket equipment based on time-series analysis, comprising:

[0007] Step 1: Obtain the time-domain vibration response curve of the engine's normal bearing seat or the docking point between the engine frame and the compartment during the ground test of the liquid engine.

[0008] Step 2: Preprocess the vibration response time-domain curves of the engine's normal seat or the docking point between the engine frame and the compartment obtained in Step 1 during the ground test of the liquid engine to obtain the equivalent sinusoidal data of the first impact response spectrum.

[0009] Step 3: Obtain the time-domain curve of the vibration response at the rear skirt of the solid rocket motor during ground testing;

[0010] Step 4: Preprocess the time-domain curve of the vibration response at the rear skirt of the solid rocket motor obtained in Step 3 during the ground test to obtain the equivalent sinusoidal data of the second impact response spectrum.

[0011] Step 5: Envelope the first impact response spectrum equivalent sinusoidal data obtained in Step 2 and the second impact response spectrum equivalent sinusoidal data obtained in Step 4, and determine the envelope result as the acceptance level longitudinal sinusoidal vibration test level for instruments and equipment on the tail section of the solid-liquid bundled launch vehicle.

[0012] Step 6: Based on the longitudinal transmission characteristics, and using the longitudinal sinusoidal vibration test magnitude of the instruments and equipment on the tail section of the solid-liquid-bundled launch vehicle determined in Step 5, combined with the attenuation coefficient of the longitudinal transmission characteristics, obtain the longitudinal sinusoidal vibration test magnitude of the instruments and equipment on other sections of the solid-liquid-bundled launch vehicle.

[0013] Step 7: Multiply the acceptance-level longitudinal sinusoidal vibration test magnitude of the instruments and equipment on the tail section of the solid-liquid-bundled launch vehicle determined in Step 5 and the acceptance-level longitudinal sinusoidal vibration test magnitude of the instruments and equipment on other sections of the solid-liquid-bundled launch vehicle obtained in Step 6 by the safety factor T, and use the results as the evaluation-level longitudinal sinusoidal vibration test magnitude.

[0014] In the above-mentioned longitudinal sinusoidal condition design method for solid-liquid rocket equipment based on time-series analysis, the vibration response time-domain curve of the engine's normal seat or the docking point between the engine frame and the compartment during the ground test of the liquid engine, obtained in step 1, is preprocessed to obtain the equivalent sinusoidal data of the first impact response spectrum, including:

[0015] The vibration response time-domain curves of the engine's normal level seat or the docking point between the engine frame and the compartment obtained in step 1 during the ground test of the liquid engine were extracted for the start-up and shutdown periods and then subjected to f Hz bandpass filtering.

[0016] The impulse response spectrum of the data during the start-up and shutdown periods after bandpass filtering is calculated and then processed into an equivalent sine wave to obtain the equivalent sine wave data of the first impulse response spectrum during the start-up and shutdown periods.

[0017] In the above-mentioned longitudinal sinusoidal condition design method for solid-liquid rocket equipment based on time-series analysis, the time-domain curve of the vibration response at the rear skirt of the solid rocket motor obtained in step 3 during ground testing is preprocessed to obtain the equivalent sinusoidal data of the second impact response spectrum, including:

[0018] The vibration response time-domain curves at the rear skirt of the solid rocket motor obtained in step 3 during ground test were extracted for the start-up and shutdown periods and then subjected to fHz bandpass filtering.

[0019] The impulse response spectrum of the data during the start-up and shutdown periods after bandpass filtering is calculated and then processed into an equivalent sine wave to obtain the equivalent sine wave data of the second impulse response spectrum during the start-up and shutdown periods.

[0020] In the above-mentioned design method for longitudinal sinusoidal conditions of solid-liquid rocket equipment based on time series analysis, the value range of f is 2 to 100.

[0021] In the above-mentioned design method for longitudinal sinusoidal conditions of solid-liquid rocket equipment based on time series analysis, Q = 10 when performing equivalent sinusoidal processing.

[0022] In the above-mentioned design method for longitudinal sinusoidal conditions of solid-liquid rocket equipment based on time-series analysis, the scanning rate of the acceptance-level longitudinal sinusoidal vibration test is 4 oct / min.

[0023] In the above-mentioned design method for longitudinal sinusoidal conditions of solid-liquid rocket equipment based on time series analysis, the value range of T is 1.5 to 2.

[0024] In the above-mentioned design method for longitudinal sinusoidal conditions of solid-liquid rocket equipment based on time-series analysis, the scanning rate of the longitudinal sinusoidal vibration test of the qualification stage is 2 oct / min.

[0025] In the above-mentioned longitudinal sinusoidal condition design method for solid-liquid rocket equipment based on time-series analysis, the longitudinal transmission characteristic attenuation coefficients include: the attenuation coefficient λ1 from the first stage inter-stage section to the launch vehicle tail section, the attenuation coefficient λ2 from the first and second stage inter-stage section to the first stage inter-stage section, the attenuation coefficient λ3 from the second stage inter-stage section to the first and second stage inter-stage section, and the attenuation coefficient λ4 from the instrument compartment section to the second stage inter-stage section.

[0026] In the above-mentioned design method for longitudinal sinusoidal conditions of solid-liquid rocket equipment based on time series analysis, λ1=λ2=λ3=λ4=0.9.

[0027] The present invention has the following advantages:

[0028] This invention discloses a longitudinal sinusoidal condition design method for solid-liquid rocket equipment based on time-series analysis. It can quickly provide longitudinal sinusoidal vibration test conditions for individual equipment on each section of a solid-liquid bundled launch vehicle, solving the problem of the difficulty in designing longitudinal sinusoidal vibration conditions during the demonstration stage of solid-liquid bundled launch vehicle schemes. As a top-level design of model environmental conditions, it can be applied to model scheme demonstration and individual equipment development. Attached Figure Description

[0029] Figure 1 This is a flowchart illustrating the steps of a longitudinal sinusoidal condition design method for solid-liquid rocket equipment based on time-series analysis in an embodiment of the present invention.

[0030] Figure 2 This is a schematic diagram of the vibration response time domain curve at the constant level seat of a liquid engine during ground testing in an embodiment of the present invention.

[0031] Figure 3 A schematic diagram of equivalent sinusoidal data of the impact response spectrum at the engine's normal level seat during the start-up phase in an embodiment of the present invention during a ground test of a liquid engine;

[0032] Figure 4 A schematic diagram of equivalent sinusoidal data of the impact response spectrum during the shutdown period at the normal level seat of a liquid engine during a ground test of an embodiment of the present invention;

[0033] Figure 5 A schematic diagram of the time-domain vibration response curve at the rear skirt of a solid rocket motor during ground testing in an embodiment of the present invention;

[0034] Figure 6 A schematic diagram of equivalent sinusoidal data of the impact response spectrum at the engine rear skirt during the start-up phase of a solid rocket motor during ground testing in an embodiment of the present invention;

[0035] Figure 7 A schematic diagram of equivalent sinusoidal data of the impact response spectrum at the engine rear skirt during the shutdown period of a solid rocket motor during ground testing in an embodiment of the present invention;

[0036] Figure 8 A schematic diagram of the longitudinal sinusoidal vibration test magnitude of an instrument on the tail section of a solid-liquid rocket in an embodiment of the present invention. Detailed Implementation

[0037] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments disclosed in the present invention will be described in further detail below with reference to the accompanying drawings.

[0038] like Figure 1 In this embodiment, the longitudinal sinusoidal condition design method for solid-liquid rocket equipment based on time-series analysis includes:

[0039] Step 1: Obtain the time-domain curve of the vibration response at the junction of the engine's normal mounting seat or frame and the compartment during ground testing of the liquid engine.

[0040] In this embodiment, during ground testing of the liquid engine, vibration sensors can be placed at locations such as the engine's leveling seat or the docking point between the engine frame and the compartment. A sampling rate higher than 5120Hz is required to obtain the vibration response time-domain curves at the corresponding locations. The vibration response time-domain curve at the engine's leveling seat during ground testing is shown below. Figure 2 As shown.

[0041] Step 2: Obtain the time-domain curve of the vibration response at the junction of the engine's normal bearing seat or frame and the compartment during the ground test of the liquid engine.

[0042] In this embodiment, the preprocessing process is as follows:

[0043] 21) The vibration response time-domain curves of the engine's normal seat or the docking point between the engine frame and the compartment obtained in step 1 during the ground test of the liquid engine are extracted for the start-up period and the shutdown period, respectively, and then subjected to f Hz bandpass filtering.

[0044] For example, it can be intercepted Figure 2 The vibration response time-domain curve shown contains a segment of time-domain data exhibiting clear start-up characteristics (0–3s), representing the start-up period. This 0–3s segment of time-domain data is then subjected to an fHz bandpass filter. Figure 2 The time-domain data segment (199–202 s) in the vibration response time-domain curve shown represents the shutdown period, exhibiting a clear shutdown characteristic. The extracted 199–202 s time-domain data was subjected to an fHz bandpass filter. The value of f ranges from 2 to 100.

[0045] 22) Calculate the impulse response spectrum of the data during the start-up and shutdown periods after bandpass filtering, and perform equivalent sine processing to obtain the equivalent sine data of the first impulse response spectrum during the start-up and shutdown periods.

[0046] When calculating the impulse response spectrum, the improved digital filtering method in Appendix K of "GJB 2238A-2004 Telemetry Data Processing" can be used. The equivalent sine processing involves dividing the calculated impulse response spectrum by a constant Q at each frequency point. The equivalent sine data of the first impulse response spectrum during the startup and shutdown periods are shown below. Figure 3 , Figure 4 As shown. Where Q = 10.

[0047] Step 3: Obtain the time-domain curve of the vibration response at the rear skirt of the solid rocket motor during ground testing.

[0048] In this embodiment, during ground testing of the solid rocket motor, a vibration sensor can be placed at the rear skirt of the solid rocket motor, with a sampling rate required to be higher than 5120Hz, to obtain the time-domain vibration response curve at the corresponding location. The time-domain vibration response curve at the rear skirt of the solid rocket motor during ground testing is shown below. Figure 5 As shown.

[0049] Step 4: Preprocess the time-domain curve of the vibration response at the rear skirt of the solid rocket motor obtained in Step 3 during the ground test to obtain the equivalent sinusoidal data of the second impact response spectrum.

[0050] In this embodiment, the processing procedure of step 4 is similar to that of step 2, including:

[0051] 41) The vibration response time-domain curves at the rear skirt of the solid rocket motor obtained in step 3 during the ground test were extracted for the start-up and shutdown periods and then subjected to fHz bandpass filtering.

[0052] For example, it can be intercepted Figure 5 The vibration response time-domain curve shown contains a segment of time-domain data exhibiting clear start-up characteristics (time-domain data from 330 to 333 s), representing the start-up period. This 330–333 s segment of time-domain data is subjected to an fHz bandpass filter. Figure 5 The time-domain data segment with obvious shutdown characteristics in the vibration response time-domain curve shown (time-domain data from 445 to 448s) is the shutdown period. The extracted time-domain data from 445 to 448s is subjected to fHz bandpass filtering.

[0053] 42) Calculate the impulse response spectrum of the data during the start-up and shutdown periods after bandpass filtering, and perform equivalent sine processing to obtain the equivalent sine data of the second impulse response spectrum during the start-up and shutdown periods.

[0054] The equivalent sinusoidal data of the second impact response spectrum obtained during the startup and shutdown periods are as follows: Figure 6 , Figure 7 As shown.

[0055] Step 5: Envelope the first impact response spectrum equivalent sinusoidal data obtained in Step 2 and the second impact response spectrum equivalent sinusoidal data obtained in Step 4, and determine the envelope result as the acceptance level longitudinal sinusoidal vibration test level for the instruments and equipment on the tail section of the solid-liquid bundled launch vehicle.

[0056] In this embodiment, the equivalent sinusoidal data of the first impact response spectrum obtained in step 2 and the equivalent sinusoidal data of the second impact response spectrum obtained in step 4 are enveloped, and considering a certain engineering margin, the resulting envelope is determined to be at the acceptance level for longitudinal sinusoidal vibration tests of instruments and equipment on the tail section of a solid-liquid-binded launch vehicle. Figure 8As shown. Among them, the scanning rate of the acceptance-level longitudinal sinusoidal vibration test is 4 oct / min.

[0057] Preferred longitudinal sinusoidal vibration test conditions for instruments and equipment on the tail section of a solid-liquid-binding launch vehicle are shown in Table 1 below:

[0058]

[0059] Table 1. Acceptance-level longitudinal sinusoidal vibration test conditions for instruments and equipment on the tail section.

[0060] Step 6: Based on the longitudinal transmission characteristics, and using the longitudinal sinusoidal vibration test magnitude of the instruments and equipment on the tail section of the solid-liquid-bundled launch vehicle determined in Step 5, combined with the attenuation coefficient of the longitudinal transmission characteristics, obtain the longitudinal sinusoidal vibration test magnitude of the instruments and equipment on other sections of the solid-liquid-bundled launch vehicle.

[0061] In this embodiment, the longitudinal transfer characteristic attenuation coefficient includes: the attenuation coefficient λ1 from the first stage inter-stage section to the tail section of the launch vehicle, the attenuation coefficient λ2 from the first and second stage inter-stage section to the first stage inter-stage section, the attenuation coefficient λ3 from the second stage inter-stage section to the first and second stage inter-stage section, and the attenuation coefficient λ4 from the instrument compartment section to the second stage inter-stage section.

[0062] Preferably, based on the longitudinal transmission characteristics, and based on the longitudinal sinusoidal vibration test magnitude of the instruments and equipment on the tail section of the solid-liquid-bundled launch vehicle determined in step 5, combined with the longitudinal transmission characteristic attenuation coefficient, the acceptance level longitudinal sinusoidal vibration test magnitude of the instruments and equipment on other sections of the solid-liquid-bundled launch vehicle is obtained. Specifically, this means multiplying the acceptance level longitudinal sinusoidal vibration test magnitude of the instruments and equipment on the tail section of the solid-liquid-bundled launch vehicle determined in step 5 by the corresponding longitudinal transmission characteristic attenuation coefficient (λ1, λ2, λ3, λ4) to obtain the acceptance level longitudinal sinusoidal vibration test magnitude of the instruments and equipment on other sections of the solid-liquid-bundled launch vehicle.

[0063] Preferably, λ1=λ2=λ3=λ4=0.9.

[0064] For example, based on Table 1, the acceptance-level longitudinal sinusoidal vibration test conditions for instruments and equipment on other sections of the solid-liquid-binding launch vehicle are shown in Table 2 below:

[0065]

[0066] Table 2. Acceptance-level longitudinal sinusoidal vibration test conditions for instruments and equipment in other modules.

[0067] Step 7: Multiply the acceptance-level longitudinal sinusoidal vibration test magnitude of the instruments and equipment on the tail section of the solid-liquid-bundled launch vehicle determined in Step 5 and the acceptance-level longitudinal sinusoidal vibration test magnitude of the instruments and equipment on other sections of the solid-liquid-bundled launch vehicle obtained in Step 6 by the safety factor T, and use the results as the evaluation-level longitudinal sinusoidal vibration test magnitude.

[0068] In this embodiment, the value of T ranges from 1.5 to 2. For example, T = 1.5 is chosen, meaning that the acceptance-level test magnitudes in Tables 1 and 2 are multiplied by 1.5 to obtain the qualification-level test magnitude. The scanning rate for the qualification-level longitudinal sinusoidal vibration test is also specified as 2 oct / min. Thus, the qualification-level longitudinal sinusoidal vibration test conditions for instruments and equipment on other sections of the solid-liquid-binding launch vehicle are obtained, as shown in Table 3.

[0069]

[0070] Table 3. Test conditions for longitudinal sinusoidal vibration of instruments and equipment on other modules at the qualification level.

[0071] In summary, this invention discloses a longitudinal sinusoidal condition design method for solid-liquid rocket equipment based on time-series analysis. This method has been successfully applied to the development of a new generation of solid-liquid bundled launch vehicles, ensuring the sufficiency and accuracy of longitudinal sinusoidal vibration tests on individual rocket components. The new generation of solid-liquid bundled flight tests were a complete success, and the flight results demonstrate that the designed longitudinal sinusoidal vibration test can effectively reflect flight telemetry results. This invention's method has been applied to the development of subsequent models of the new rocket.

[0072] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

[0073] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A design method for longitudinal sinusoidal conditions of solid-liquid rocket equipment based on time series analysis, characterized in that, include: Step 1: Obtain the time-domain vibration response curve of the engine's normal bearing seat or the docking point between the engine frame and the compartment during the ground test of the liquid engine. Step 2: Preprocess the vibration response time-domain curves of the engine's normal seat or the docking point between the engine frame and the compartment obtained in Step 1 during the ground test of the liquid engine to obtain the equivalent sinusoidal data of the first impact response spectrum. Step 3: Obtain the time-domain curve of the vibration response at the rear skirt of the solid rocket motor during ground testing; Step 4: Preprocess the time-domain curve of the vibration response at the rear skirt of the solid rocket motor obtained in Step 3 during the ground test to obtain the equivalent sinusoidal data of the second impact response spectrum. Step 5: Envelope the first impact response spectrum equivalent sinusoidal data obtained in Step 2 and the second impact response spectrum equivalent sinusoidal data obtained in Step 4, and determine the envelope result as the acceptance level longitudinal sinusoidal vibration test level for instruments and equipment on the tail section of the solid-liquid bundled launch vehicle. Step 6: Based on the longitudinal transmission characteristics, and using the longitudinal sinusoidal vibration test magnitude of the instruments and equipment on the tail section of the solid-liquid-bundled launch vehicle determined in Step 5, combined with the attenuation coefficient of the longitudinal transmission characteristics, obtain the longitudinal sinusoidal vibration test magnitude of the instruments and equipment on other sections of the solid-liquid-bundled launch vehicle. Step 7: Multiply the acceptance-level longitudinal sinusoidal vibration test magnitude of the instruments and equipment on the tail section of the solid-liquid-bundled launch vehicle determined in Step 5 and the acceptance-level longitudinal sinusoidal vibration test magnitude of the instruments and equipment on other sections of the solid-liquid-bundled launch vehicle obtained in Step 6 by the safety factor T, and use the results as the evaluation-level longitudinal sinusoidal vibration test magnitude.

2. The method for designing longitudinal sinusoidal conditions for solid-liquid rocket equipment based on time-series analysis according to claim 1, characterized in that, The vibration response time-domain curves at the docking point between the engine's normal-level seat or frame and the compartment obtained in step 1 during the ground test of the liquid engine are preprocessed to obtain the equivalent sinusoidal data of the first impact response spectrum, including: The vibration response time-domain curves of the engine's normal level seat or the docking point between the engine frame and the compartment obtained in step 1 during the ground test of the liquid engine were extracted for the start-up and shutdown periods and then subjected to f Hz bandpass filtering. The impulse response spectrum of the data during the start-up and shutdown periods after bandpass filtering is calculated and then processed into an equivalent sine wave to obtain the equivalent sine wave data of the first impulse response spectrum during the start-up and shutdown periods.

3. The longitudinal sinusoidal condition design method for solid-liquid rocket equipment based on time-series analysis according to claim 2, characterized in that, The time-domain vibration response curves at the rear skirt of the solid rocket motor obtained in step 3 during ground testing are preprocessed to obtain equivalent sinusoidal data of the second impact response spectrum, including: The vibration response time-domain curves at the rear skirt of the solid rocket motor obtained in step 3 during ground testing were extracted for the start-up and shutdown periods and then subjected to f Hz bandpass filtering. The impulse response spectrum of the data during the start-up and shutdown periods after bandpass filtering is calculated and then processed into an equivalent sine wave to obtain the equivalent sine wave data of the second impulse response spectrum during the start-up and shutdown periods.

4. The longitudinal sinusoidal condition design method for solid-liquid rocket equipment based on time-series analysis according to claim 3, characterized in that, The value of f ranges from 2 to 100.

5. The method for designing longitudinal sinusoidal conditions for solid-liquid rocket equipment based on time-series analysis according to claim 3, characterized in that, When performing the equivalent sine treatment, Q = 10.

6. The longitudinal sinusoidal condition design method for solid-liquid rocket equipment based on time-series analysis according to claim 1, characterized in that, The scanning rate for the acceptance-level longitudinal sinusoidal vibration test is 4 oct / min.

7. The longitudinal sinusoidal condition design method for solid-liquid rocket equipment based on time-series analysis according to claim 1, characterized in that, The value of T ranges from 1.5 to 2.

8. The method for designing longitudinal sinusoidal conditions for solid-liquid rocket equipment based on time-series analysis according to claim 1, characterized in that, The scanning rate for the identification-grade longitudinal sinusoidal vibration test is 2 oct / min.

9. The method for designing longitudinal sinusoidal conditions for solid-liquid rocket equipment based on time-series analysis according to claim 1, characterized in that, The longitudinal transmission characteristic attenuation coefficients include: the attenuation coefficient λ1 from the first stage inter-stage section to the tail section of the launch vehicle, the attenuation coefficient λ2 from the first and second stage inter-stage section to the first stage inter-stage section, the attenuation coefficient λ3 from the second stage inter-stage section to the first and second stage inter-stage section, and the attenuation coefficient λ4 from the instrument compartment section to the second stage inter-stage section.

10. The method for designing longitudinal sinusoidal conditions for solid-liquid rocket equipment based on time-series analysis according to claim 9, characterized in that, λ1=λ2=λ3=λ4=0.9.

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