Spatial thin film structure vibration analysis method under electrostatic discharge effect

Abstract

The invention relates to the technical field of thin film structure vibration analysis, and particularly provides a space thin film structure vibration analysis method under the action of electrostatic discharge. In order to solve the problems that electrostatic discharge is neglected as a vibration source, a potential-prestress coupling model is difficult to establish, transient force simulation is inaccurate and the like in the prior art, a geometric model comprising a thin film surface, an electrode surface and an electrostatic field area is established, and a triangular thin film unit and a tetrahedral electrostatic field unit are adopted to divide grids; constructing an electrostatic field-thin film structure nonlinear coupling kinetic equation, and through initial equilibrium state establishment, selecting channel step discharge and free vibration attenuation monitoring simulation discharge transient; changing the initial voltage of the electrode surface, the second load step time and the discharge channel position, and quantitatively analyzing the vibration law; the invention also discloses a key rule of weak influence of voltage amplitude dominated vibration energy and discharge position, and provides effective theoretical support for on-orbit vibration suppression of structures such as a space film antenna and a solar sail.

Description

Technical Field

[0001] The present invention relates to the technical field of membrane structure vibration analysis, and in particular to a method for analyzing the vibration of a spatial membrane structure under the action of electrostatic discharge. Background Art

[0002] With the gradual implementation of a series of major aerospace projects such as manned lunar exploration, space-based observation, and lunar research stations, there is an urgent need to develop large-scale space membrane structures such as spaceborne membrane antennas, membrane sunshades, and membrane solar sails to meet the needs of future aerospace technology development. However, when membrane structures are used on-orbit, vibrations caused by various space environments are unavoidable, seriously affecting the performance of spacecraft. Although the establishment of nonlinear dynamic models and equivalent methods for membrane structures have been widely studied by scholars at home and abroad, and the influence of factors such as temperature and membrane tension on the dynamic characteristics of membrane structures has been paid attention to, current research has only considered the impact of the on-orbit thermal environment on the vibration of membrane structures, and has not yet considered electrostatic discharge as a source of on-orbit vibration of membrane structures.

[0003] In early experimental research on thin-film antennas, it was discovered that electrostatic discharge can cause the thin-film structure to vibrate. On the one hand, there is a nonlinear coupling relationship between the on-track charging potential of the thin-film structure and the prestressed stress on the film's reflective surface. On the other hand, electrostatic discharge can cause transient forces on the film's reflective surface, both of which affect the dynamic characteristics of the thin-film antenna. Regarding the vibration analysis of spatial thin-film structures under electrostatic discharge, the existing technology has the following technical problems:

[0004] First, existing research has focused on the impact of factors such as temperature and film tension on the dynamic characteristics of film structures, but has not yet paid attention to the fact that electrostatic discharge is one of the vibration sources of spatial film structures.

[0005] Secondly, there is a nonlinear coupling relationship between the potential of the membrane structure and the prestress of the membrane structure. How to establish a nonlinear coupling dynamic model between the electrostatic field and the deformation field of the membrane structure is one of the current technical difficulties.

[0006] In addition, the electrostatic discharge process will cause the thin film structure to be affected by transient forces. How to accurately establish a transient dynamic analysis model of the thin film structure during the electrostatic discharge process is a current problem.

[0007] Therefore, it is urgent to propose a vibration analysis method for space membrane structures under the action of electrostatic discharge to provide theoretical support for the prevention and control of on-orbit vibration of space membrane structures. Summary of the Invention

[0008] To solve the problems existing in the background technology, the present invention provides a method for analyzing the vibration of a spatial membrane structure under electrostatic discharge, comprising the following steps:

[0009] S1. Establish a spatial film structure geometric model including the film surface, electrode surface, and electrostatic field region;

[0010] S2. Perform finite element meshing on the film surface and electrostatic field region and set solution parameters to establish a nonlinear coupled dynamic analysis model of the electrostatic field and spatial film structure;

[0011] S3. Simulate the stress of the spatial membrane structure during electrostatic discharge using transient voltage;

[0012] S4. Solve the nonlinear vibration transient analysis model of the spatial membrane structure and obtain the relationship curve between amplitude and time;

[0013] S5. Change the transient voltage amplitude, duration, or discharge voltage channel to analyze the vibration patterns of the spatial membrane structure.

[0014] Preferably, S1 specifically includes:

[0015] S11. Create a planar circular membrane structure with a center at (0,0,0) and a radius of 2.5 m.

[0016] S12. Create a circular electrode surface with a center at (0, 0, -0.05 m) and a radius of 2.5 m, and six electrode channels.

[0017] S13. Construct a cylindrical surface based on the boundary lines of the film structure and the electrode surface, and combine the film surface, electrode surface and cylindrical surface to generate a geometric model of the electrostatic field region.

[0018] Preferably, the S2 specifically includes:

[0019] S21. Use triangular planar membrane elements to divide the membrane surface. The element type is shell181, with a thickness of 25 μm, an elastic modulus of 2.17 GPa, a Poisson's ratio of 0.34, and a mass density of 1432 kg / m³.

[0020] S22. Use tetrahedral elements to divide the electrostatic field region. The element type is solid227, the elastic modulus is 0 GPa, the Poisson's ratio is 0, and the mass density is 0 kg / m³.

[0021] S23. Establish a nonlinear coupling dynamic analysis model:

[0022] ;

[0023] in, is the mass matrix of the membrane structure; is the damping matrix of the membrane structure; is the membrane structure stiffness matrix; is the equivalent stiffness matrix of the electrostatic field; 、 is the coupling matrix between the film field and the electrostatic field; is the external load force of the membrane structure; is the charge; is the node acceleration; is the node speed; is the node displacement; For electric potential.

[0024] Preferably, the S3 specifically includes:

[0025] S31. Set the first load step: time 0.01s, turn off the time integration effect, enable stress stiffening and geometric nonlinear effects, the film surface voltage is 0V, and the initial voltage of each channel on the electrode surface is ;

[0026] S32. Set the second load step: time , turn on the time integration effect, the voltage of the Nth channel on the electrode surface steps to 0V, and the voltages of the other channels remain unchanged;

[0027] S33. Set the third load step: time 20s, and maintain the load conditions of the second load step.

[0028] Preferably, the S4 specifically includes:

[0029] S41. Set the solution parameters: Solution type is transient dynamic analysis, mass damping coefficient is 0.05, stiffness damping coefficient is 0.05, transient integral constant is 0.05;

[0030] S42. Use the full method to solve transient dynamics, and L to solve multiple load steps using the SSOLVE command;

[0031] S43. Extract the displacement data of the center point of the thin film structure and draw the displacement-time curve using MATLAB.

[0032] Preferably, the S5 specifically includes:

[0033] S51. Change the initial voltage of the electrode surface Repeat S1-S4 for 100V, 300V, and 500V;

[0034] S52. Change the second load step time 0.002s, 0.05s, 0.1s, repeat S1-S4;

[0035] S53. Step the voltage of the first, third, and fifth channels of the electrode surface to 0 V respectively, and repeat S1-S4.

[0036] The beneficial effects achieved by the present invention are:

[0037] First, this invention incorporates electrostatic discharge as the core vibration source of space membrane structures into the analysis framework for the first time, breaking through the limitations of traditional research that only focuses on thermal environment or mechanical tension. By establishing an electrode-membrane spatial mapping relationship and a 6-channel discharge model, it successfully reveals the excitation mechanism of electrostatic discharge on membrane vibration, providing a new theoretical perspective for on-orbit vibration tracing, enabling spacecraft designers to formulate targeted vibration prevention strategies.

[0038] Second, the electrostatic field-structure coupling dynamic model proposed in the present invention effectively solves the modeling problem of nonlinear coupling between potential and prestress. The present invention uses the field-structure coupling matrix to accurately characterize the interaction mechanism between charge distribution and film deformation. The zero-mass electrostatic field unit setting avoids inertial force interference and significantly improves the accuracy of electrostatic transient force simulation, making the vibration prediction results highly consistent with the real physical phenomena, laying a solid foundation for reliability analysis.

[0039] Third, the proposed method's step-voltage trigger mechanism and phased load-step design overcome the technical bottleneck of transient force simulation for electrostatic discharge. By separating the static balance establishment, discharge transient, and vibration attenuation processes through three load steps, the method accurately replicates the transient characteristics of microsecond-level discharges while ensuring computational stability for complex nonlinear problems. It also enables controllable adjustment of discharge parameters, including voltage amplitude, duration, and position, providing a flexible technical approach for multi-scenario vibration analysis.

[0040] Fourth, the present invention utilizes parametric analysis to reveal the differential influence of the three elements of electrostatic discharge on vibration characteristics. Experiments demonstrate that voltage amplitude dominates vibration energy, while discharge location has little influence on the overall modal response. This method can be extended to various thin-film structures in space, such as thin-film solar sails and sunshades. The established universal analytical framework provides universal technical support for the design of spacecraft on-orbit stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is an overall flow chart of the vibration analysis method of a spatial membrane structure under the action of electrostatic discharge of the present invention.

[0042] Figure 2 It is a flow chart of the geometric model of a spatial thin film structure having a thin film surface, an electrode surface and an electrostatic field area according to the present invention.

[0043] Figure 3 It is a flow chart of the present invention for establishing a nonlinear coupling dynamic analysis model of an electrostatic field-space film structure.

[0044] Figure 4 This is a flow chart of the stress conditions of a spatial membrane structure during the electrostatic discharge process simulated by applying a transient voltage according to the present invention.

[0045] Figure 5It is a flow chart of the present invention for solving the nonlinear vibration transient analysis model of spatial membrane structure.

[0046] Figure 6 This is a flow chart of the present invention for obtaining the vibration law of a spatial membrane structure during electrostatic discharge.

[0047] Figure 7 It is a geometric model diagram of the thin film structure of the present invention.

[0048] Figure 8 This is a voltage channel distribution diagram of the present invention.

[0049] Figure 9 This is a diagram showing the vibration law of the film structure when the initial voltage value is changed according to the present invention.

[0050] Figure 10 This is a diagram showing the vibration regularity of the film structure when changing the electrostatic discharge time according to the present invention.

[0051] Figure 11 This is a diagram showing the vibration regularity of the film structure of the electrostatic discharge voltage channel according to the present invention. DETAILED DESCRIPTION

[0052] The technical solutions of the present invention will be described clearly and completely below in conjunction with the drawings in the present invention. In addition, the forms of the various structures described in the following embodiments are merely examples. The present invention is not limited to the various structures described in the following embodiments. All other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0053] The following is combined with Figures 1 to 11 , the present invention is further described.

[0054] Example 1, the method for analyzing the vibration of a space membrane structure under electrostatic discharge provided by Example 1 of the present invention is as follows Figure 1 As shown, the following steps are included:

[0055] S1: Establish the geometric model of the spatial membrane structure; Figure 2 As shown, this step is implemented through the following sub-steps:

[0056] First, a planar circular membrane structure with a center at the coordinate point (0,0,0) and a radius of 2.5 meters is established. This structure serves as the basic geometric model of the spatial membrane reflective surface. Second, a planar circular electrode surface with a center at (0,0,-0.05 meters) and a radius of 2.5 meters is established, and 6 evenly distributed voltage channels are set (see Figure 8 ), Figure 8There are six rings in the diagram, each representing a voltage channel. From the inside out, they are Channel 1, Channel 2, and Channel 6, simulating multiple triggering points for electrostatic discharge. Finally, a closed cylindrical surface is constructed based on the boundary lines of the film structure and the electrode surface. The film, electrode, and cylindrical surfaces are combined to create a three-dimensional geometric model of the electrostatic field region, ensuring that the spatial relationship between the electrostatic field range and the film structure conforms to the actual physical scenario.

[0057] This invention establishes a spatial mapping relationship between electrodes and thin films for the first time. Using a six-channel electrode design, it accurately simulates multi-point discharge scenarios in space, effectively addressing the difficulty of simulating multi-point triggering of electrostatic discharge. Furthermore, the modeling method of a cylindrically enclosed electrostatic field region successfully addresses the technical challenge of precisely defining electrostatic field boundary conditions.

[0058] S2: Establish a nonlinear coupled dynamics model; e.g. Figure 3 As shown, the specific implementation includes:

[0059] First, triangular planar membrane elements (Shell181) were used to partition the film surface, setting the thickness to 25 microns, the elastic modulus to 2.17 GPa, the Poisson's ratio to 0.34, and the mass density to 1432 kg / m³ to accurately characterize the material properties of the polyimide film. Second, tetrahedral elements (Solid227) were used to partition the electrostatic field region, setting the elastic modulus to 0 GPa, the Poisson's ratio to 0, and the mass density to 0 kg / m³ to reflect the massless nature of the electrostatic field. Finally, the nonlinear coupled dynamic equations were established as follows:

[0060] ;

[0061] in, is the mass matrix of the membrane structure; is the damping matrix of the membrane structure; is the membrane structure stiffness matrix; is the equivalent stiffness matrix of the electrostatic field; 、 is the coupling matrix between the film field and the electrostatic field; is the external load force of the membrane structure; is the charge; is the node acceleration; is the node speed; is the node displacement; For electric potential.

[0062] The zero-mass electrostatic field modeling method avoids inertial forces and significantly improves the accuracy of transient force simulations. This equation fully encompasses inertia, damping, stiffness, and coupling terms, providing a comprehensive mathematical foundation for transient dynamics analysis.

[0063] S3: Simulates the transient stress of electrostatic discharge; Figure 4 As shown, this is achieved through three load steps:

[0064] First, in the first load step (duration of 0.01 seconds), turn off the time integration effect, enable stress stiffening and geometric nonlinear effects, set the membrane surface voltage to 0 volts, and the initial voltage of each electrode channel to , establish the initial equilibrium state of the electrostatic field. Secondly, in the second load step (time ), turn on the time integration effect and set the electrode The channel voltage is stepped to 0V to simulate single-point discharge, and the voltages of the other channels are maintained Finally, in the third load step (duration 20 s), the post-discharge conditions are maintained to capture the decay process of the film's free vibrations.

[0065] The present invention uses a step voltage trigger mechanism to accurately simulate the transient nature of electrostatic discharge. The phased load step design successfully separates the static balance establishment, discharge transient, and vibration attenuation processes, significantly improving the calculation stability. In addition, through adjustable parameters 、 、 Achieve coverage of multiple discharge scenarios.

[0066] S4: solve the vibration response; Figure 5 As shown, the specific process is:

[0067] First, the transient dynamic analysis parameters were set to 0.05 for the mass damping coefficient, 0.05 for the stiffness damping coefficient, and 0.05 for the transient integral constant to ensure numerical convergence. Second, the full method was used in conjunction with the LSSOLVE command to solve multiple load steps, effectively handling nonlinear transient problems. Finally, the displacement data at the center of the membrane was extracted, and the displacement-time curve was plotted using MATLAB to quantify the vibration amplitude and attenuation characteristics.

[0068] The dual damping coefficient setting effectively suppresses numerical oscillation and significantly improves the smoothness of the vibration curve. In addition, the center point displacement monitoring directly reflects the overall vibration mode of the film. The relevant results can be found in Figures 9-11 .

[0069] S5: Parametric vibration law analysis; e.g. Figure 6 As shown in the figure, the rules are revealed by the variation of three groups of parameters: the three groups of parameters are initial voltage (0-1000V), discharge duration (0-0.1S) and discharge channel.

[0070] First, change the initial voltage (100 volts, 300 volts, 500 volts respectively): Figure 9As shown, the voltage increase leads to a significant increase in the vibration amplitude (when Volts, the amplitude reaches m), proving the dominant role of electrostatic force on vibration energy. Secondly, changing the discharge time (0.002 seconds, 0.05 seconds, and 0.1 seconds respectively): Figure 10 As shown, The increase mainly causes the vibration phase shift, and the amplitude change does not exceed 5%, revealing the mechanism of the influence of discharge duration on vibration frequency. Finally, changing the discharge channel (Channel 1, Channel 3, and Channel 5 respectively): Figure 11 As shown in Figure 2, the vibration waveforms at different discharge positions are basically the same. Figure 11 It is shown as a single line in , indicating that the membrane vibration is insensitive to the location of the discharge point, thus simplifying the design of the vibration control strategy.

[0071] This invention quantifies the differential impact of the three elements of electrostatic discharge (electrostatic discharge)—voltage, time, and location—on vibration, breaking through the traditional limitation of considering only the thermal environment. The parametric analysis results provide a clear theoretical basis for on-orbit vibration suppression, prioritizing control of charging voltage over discharge location.

[0072] Example 2: This example is a vibration analysis experiment of a 5m diameter space membrane structure, which is carried out according to the following steps:

[0073] 1) Experimental model construction: Taking the typical space membrane structure as the verification object, a circular membrane model with a diameter of 5m was established, such as Figure 7 As shown, the center of the film surface is located at the coordinate point , with a radius of 2.5 meters, a thickness of 25 microns, and material parameters of elastic modulus of 2.17 GPa and Poisson's ratio of 0.34, which precisely match the characteristics of polyimide film.

[0074] like Figure 8 As shown, the electrode surface is set 0.05 meters below the film, with the same radius as the film surface, and 6 voltage channels are evenly distributed on the edge of the electrode to simulate multi-point discharge scenarios.

[0075] The electrostatic field region is generated by the film boundary, electrode boundary and closed cylindrical surface to ensure that the electric field distribution conforms to the actual space environment.

[0076] 2) Experimental parameter setting.

[0077] Initial voltage experiment, initial voltage of electrode surface Set to 100 volts, 300 volts, and 500 volts respectively.

[0078] Discharge time experiment, discharge time of the second load step Set them to 0.002 seconds, 0.05 seconds, and 0.1 seconds respectively.

[0079] Discharge position experiment, trigger the 1st, 3rd and 5th voltage channels to discharge respectively (the rest of the channels maintain volt).

[0080] The dynamic solution parameters, mass damping coefficient and stiffness damping coefficient are both 0.05, and the transient integral constant is 0.05 to ensure numerical stability.

[0081] 3) The experimental results are as follows:

[0082] (1) Effect of voltage amplitude on vibration ( Figure 9 ).

[0083] when When the voltage is 10V, the maximum amplitude at the center of the film is rice.

[0084] when Volts, the amplitude increases to meters, an increase of 134%.

[0085] when Volts, the amplitude jumps to meters, an increase of 243% compared to 100 volts.

[0086] Conclusion: The vibration amplitude induced by electrostatic discharge is strongly positively correlated with the initial voltage, proving that electrostatic force is the core excitation source.

[0087] (2) Effect of discharge time on vibration ( Figure 10 ).

[0088] exist In the range of 0.1 seconds to 0.1 seconds, the amplitude variation is less than 5%, indicating that the discharge duration has little effect on the vibration energy.

[0089] but When the time increases from 0.002 seconds to 0.1 seconds, the vibration phase shifts by 1 / 4 cycle, revealing that the discharge duration mainly changes the vibration frequency characteristics.

[0090] The vibration energy is dominated by the voltage amplitude, and the discharge time only regulates the phase response, providing a basis for vibration frequency control.

[0091] (3) Effect of discharge position on vibration ( Figure 11 ).

[0092] During discharges in channels 1, 3, and 5, the membrane center displacement curves exhibited waveform overlap exceeding 95%, with maximum amplitude deviations less than 3%. The uniform distribution of vibration energy indicates that the overall modal response of the membrane is unaffected by the location of the partial discharge. The vibration characteristics are insensitive to the discharge location, simplifying the on-orbit vibration suppression strategy (no need to locate the discharge point).

[0093] In this embodiment, the geometric modeling parameters (coordinates, radius), material properties (elastic modulus, density), and element type (Shell181 / Solid227) are all publicly available. , coupled stiffness matrix ) is automatically generated by the finite element software without manual intervention. Load step time (0.01 seconds / The step voltage triggering mechanism is implemented through the ANSYS command flow, with a clear operation path. Results are extracted using the LSSOLVE command and MATLAB post-processing, allowing batch execution.

[0094] This invention quantifies the differential effects of the three elements of electrostatic discharge (voltage, time, and position) for the first time, solving the problem of not considering the electrostatic vibration source and the difficulty of transient force modeling. Accurately characterizing the potential-prestress relationship overcomes the challenges of nonlinear coupling modeling. Voltage amplitude is clearly identified as a key factor in vibration control, superior to adjusting discharge position or duration, guiding the prioritized implementation of voltage suppression strategies on-orbit. Vibration phase controllability provides new insights into active damping design, enabling the vibration frequency to be manipulated through discharge timing. This method is applicable to 5-meter-diameter thin-film antennas, and the same process can be directly extended to structures such as thin-film solar sails and thin-film sunshades.

[0095] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for analyzing the vibration of a spatial membrane structure under electrostatic discharge, characterized in that: The following steps are involved: S1. Establish a spatial film structure geometric model including the film surface, electrode surface, and electrostatic field region; S2. Perform finite element meshing on the film surface and electrostatic field region and set solution parameters to establish a nonlinear coupled dynamic analysis model of the electrostatic field and spatial film structure; S3. Simulate the stress of the spatial membrane structure during electrostatic discharge using transient voltage; S4. Solve the nonlinear vibration transient analysis model of the spatial membrane structure and obtain the relationship curve between amplitude and time; S5. Change the transient voltage amplitude, duration, or discharge voltage channel to analyze the vibration patterns of the spatial membrane structure.

2. The method according to claim 1, characterized in that Said S1 specifically includes: S11. Create a planar circular membrane structure with a center at (0,0,0) and a radius of 2.5 m. S12. Create a circular electrode surface with a center at (0, 0, -0.05 m) and a radius of 2.5 m, and six electrode channels. S13. Construct a cylindrical surface based on the boundary lines of the thin film structure and the electrode surface, and combine the thin film surface, electrode surface and cylindrical surface to generate a geometric model of the electrostatic field region.

3. The method according to claim 1, characterized in that The S2 specifically includes: S21. Use triangular planar membrane elements to divide the membrane surface. The element type is shell181, with a thickness of 25 μm, an elastic modulus of 2.17 GPa, a Poisson's ratio of 0.34, and a mass density of 1432 kg / m³. S22. Use tetrahedral elements to divide the electrostatic field region. The element type is solid227, the elastic modulus is 0 GPa, the Poisson's ratio is 0, and the mass density is 0 kg / m³. S23. Establish a nonlinear coupling dynamic analysis model: ； in, is the mass matrix of the membrane structure; is the damping matrix of the membrane structure; is the membrane structure stiffness matrix; is the electrostatic field equivalent stiffness matrix; 、 is the coupling matrix between the film field and the electrostatic field; is the external load force of the membrane structure; is the charge; is the node acceleration; is the node speed; is the node displacement; For electric potential.

4. The method according to claim 1, wherein The S3 specifically includes: S31. Set the first load step: time 0.01s, turn off the time integration effect, enable stress stiffening and geometric nonlinear effects, the film surface voltage is 0V, and the initial voltage of each channel on the electrode surface is ; S32. Set the second load step: time , turn on the time integration effect, the voltage of the Nth channel on the electrode surface steps to 0V, and the voltages of the other channels remain unchanged; S33. Set the third load step: time 20s, and maintain the load conditions of the second load step.

5. The method according to claim 1, wherein The S4 specifically includes: S41. Set the solution parameters: Solution type is transient dynamic analysis, mass damping coefficient is 0.05, stiffness damping coefficient is 0.05, transient integral constant is 0.05; S42. Use the full method to solve transient dynamics, and L to solve multiple load steps using the SSOLVE command; S43. Extract the displacement data of the center point of the thin film structure and draw the displacement-time curve using MATLAB.

6. The method according to claim 1, characterized in that The S5 specifically includes: S51. Change the initial voltage of the electrode surface Repeat S1-S4 for 100V, 300V, and 500V; S52. Change the second load step time 0.002s, 0.05s, 0.1s, repeat S1-S4; S53. Step the voltage of the first, third, and fifth channels of the electrode surface to 0 V respectively, and repeat S1-S4.

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