Earthquake monitoring system and method based on capacitance sensing and electrostatic driving technology
Through the combination of capacitive sensing and electrostatic driving technology, an earthquake monitoring system was designed, which solved the shortcomings of traditional seismometers in sensitivity and anti-interference capabilities, and achieved high-precision and high-sensitivity real-time measurement of ground vibration information.
Patent Information
- Application Number
- CN202510626293.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-15
- Publication Date
- 2025-08-15
- Estimated Expiration
- 2045-05-15
AI Technical Summary
Traditional seismometers have limitations in sensitivity, response speed and anti-interference ability, making it difficult to achieve high-precision and high-reliability seismic signal detection.
Using capacitive sensing and electrostatic drive technology, combined with high-precision position detection and real-time electrostatic drive control, an earthquake monitoring system is designed, including a base, a regulating platform, a front-end electronic system, a protective shell, a sensitive device and a computer. The seismic signal is detected through capacitive sensors and the position of the mass in the electrode cage is controlled using electrostatic drive.
Real-time measurement of ground vibration information with high sensitivity and high accuracy is achieved, reducing the risk of performance degradation caused by wear and aging, enhancing the dynamic response range, and able to capture weak vibrations.
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Figure CN120491154A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of ground vibration monitoring, and in particular to an earthquake monitoring system and a monitoring method based on capacitive sensing and electrostatic drive technology. Background Art
[0002] A seismograph is an instrument used to detect and record seismic activity and is widely used in fields such as earthquake monitoring, geological exploration, and engineering geology. Traditional seismographs typically rely on mechanical or electromagnetic sensors, which have limitations in sensitivity, response speed, and interference resistance. In recent years, with the rapid development of microelectronics and sensing technologies, seismographs based on capacitive sensors have gained increasing attention. Capacitive sensors detect external vibrations by detecting changes in capacitance and offer advantages such as high sensitivity, low noise, and good linearity. Furthermore, capacitive sensors have a simple structure, small size, and low power consumption, making them suitable for integrated and miniaturized designs. The introduction of electrostatic drive control technology in seismograph design further enhances system performance. Electrostatic drive control uses electrostatic force to precisely control and adjust the sensor, effectively improving the seismograph's dynamic range and frequency response. This technology combines the advantages of capacitive sensors, resulting in a seismograph with higher accuracy and reliability in detecting small earthquake fluctuations. This paper proposes a seismograph structural design based on capacitive sensing and electrostatic drive control, aiming to overcome the shortcomings of existing technologies and provide a highly sensitive, accurate, and reliable earthquake monitoring solution. By optimizing the sensor structure and control circuit design, the seismograph can achieve stable detection and analysis of seismic signals in complex environments. Summary of the Invention
[0003] In response to the technical problems existing in the above-mentioned background technology, the present invention proposes an earthquake monitoring system and method based on capacitive sensing and electrostatic drive technology. The system and method have a reasonable design and realize real-time measurement of ground vibration information through high-precision and high-sensitivity position detection and real-time electrostatic drive control.
[0004] To solve the above technical problems, the present invention provides an earthquake monitoring system based on capacitive sensing and electrostatic drive technology, which includes a base, an adjustment platform, a front-end electronic system, a protective housing, a sensitive device and a host computer;
[0005] The base is fixed on the ground; the protective shell is fixed to the base and covers the base;
[0006] The adjustment platform is located inside the protective shell and is matched with the upper part of the base;
[0007] The sensitive device is matched and arranged on the upper part of the adjustment platform, and includes a test mass and an electrode cage; the test mass is fixed to the protective housing by a metal filament, and the metal filament is connected to the front-end electronic system; the electrode cage is matched and fixed to the adjustment platform and has electrodes matched and arranged inside;
[0008] The front-end electronics system is mounted on the side wall of the protective housing, and is connected to and communicates with the host computer via a host computer interface, is connected to an external power supply via a power supply interface, and is connected to the electrode and the metal filament via a circuit interface.
[0009] The seismic monitoring system based on capacitive sensing and electrostatic drive technology, wherein: the electrode cage includes an electrode cage shell; the electrode cage shell is matched and fixed to the upper part of the adjustment platform, which is made of metal material and is insulated on the outside; the electrode is matched and fixed on the inside of the electrode cage shell and maintains insulation between the electrode cage shell.
[0010] The seismic monitoring system based on capacitive sensing and electrostatic drive technology, wherein: the electrode cage also includes a limit block; the limit block is matched and fixed on the inner side of the electrode cage shell and is made of insulating material, which is used to limit the initial position of the test mass and prevent the test mass from touching the electrode and causing a short circuit during the control process; the height of the limit block is designed to be more than 1.5 times the height of the electrode.
[0011] The earthquake monitoring system based on capacitive sensing and electrostatic drive technology, wherein: the electrode cage shell is provided with a through hole for facilitating the connection between the electrode and the front-end electronic system.
[0012] The earthquake monitoring system based on capacitive sensing and electrostatic drive technology, wherein: the front-end electronic system also includes a circuit board matched with the inner side of the protective shell; the circuit board includes a sensing system, a control system and a data acquisition system; the sensing system adopts a capacitive sensing structure to detect the position of the test mass in the electrode cage; the control system is used to control the test mass to be in the center position of the electrode cage, and it adopts a PID control method with a preload voltage, applies the same preload voltage to each electrode to be controlled, and applies opposite control voltages to the opposite electrodes, and uses the difference in electrostatic force to achieve control of the test mass; the data acquisition system is used to realize signal acquisition of the sensing system and the control system.
[0013] The earthquake monitoring system based on capacitive sensing and electrostatic drive technology, wherein: the front-end electronic system also includes a circuit protection shell; the circuit protection shell covers the outside of the circuit board and is fixed to the inner wall of the protective shell to protect the circuit board.
[0014] The earthquake monitoring system based on capacitive sensing and electrostatic drive technology, wherein: the host computer is connected to the data acquisition system through the host computer interface; the host computer is equipped with a data processing system, and the data processing system is used to save the collected data and realize the conversion of the collected signal into the ground vibration level.
[0015] The seismic monitoring system based on capacitive sensing and electrostatic drive technology, wherein: the adjustment platform is used to adjust the initial position relationship between the test mass and the electrode cage, and can achieve precise adjustment in six degrees of freedom, namely, translation along three axes and rotation around three axes in a spatial rectangular coordinate system.
[0016] A seismic monitoring method based on capacitive sensing and electrostatic drive technology, based on the above-mentioned seismic monitoring system based on capacitive sensing and electrostatic drive technology, specifically comprises the following steps:
[0017] 1) Start the seismograph system, perform testing and calibration, and use the sensing system to detect the current position of the test mass. If the deviation is too large, adjust the adjustment platform to control the test mass to be close to the center of the electrode cage shell;
[0018] 2) Due to ground vibration, the relative position of the electrode cage shell and the test mass changes. The control system controls the test mass to be located at the center of the electrode cage shell. When the data collected by the sensor system fluctuates slightly around the equilibrium position, the data acquisition system collects the control voltage value applied to the electrode.
[0019] 3) In the data processing system, the control voltage value obtained in the above step 2) is processed to further obtain the translational acceleration and rotational angular acceleration of the ground vibration.
[0020] The earthquake monitoring method based on capacitive sensing and electrostatic drive technology, wherein: the method for solving the translational acceleration and rotational angular acceleration of the ground vibration is:
[0021] Assume that the detection voltages of the two channels of the X-axis of the spatial rectangular coordinate system are V X1 , V X2 The detection voltages of the two electrodes on the Y axis of the spatial rectangular coordinate system are V Y1 , V Y2 ; Then the translational acceleration of ground vibration is expressed as:
[0022]
[0023] The angular acceleration is expressed as:
[0024]
[0025] Among them, ε ris the relative dielectric constant, ε0 is the dielectric constant in vacuum, A is the area of a single electrode, V r is the DC bias voltage applied to the electrode, m is the mass of the test mass, d0 is the nominal gap of the sensitive structure, l is the distance from the center point of the test mass to the center point of the electrode on the plane, and J is the moment of inertia of the test mass.
[0026] By adopting the above technical solution, the present invention has the following beneficial effects:
[0027] This invention is well-conceived, combining capacitive sensing and electrostatic drive control technologies to achieve real-time measurement of ground vibration information through high-precision, high-sensitivity position detection and real-time electrostatic drive control. Compared to the connected measurement structure of traditional mechanical seismic monitors, this invention uses capacitive sensing, a non-contact measurement method. This reduces the risk of performance degradation due to wear, aging, or other physical damage, while also achieving a wider dynamic response range through high-precision displacement sensing using capacitance, enabling the capture of weak vibrations. BRIEF DESCRIPTION OF THE DRAWINGS
[0028] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the specific embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.
[0029] Figure 1 A schematic diagram of the structure of a device according to an embodiment of the present invention;
[0030] Figure 2 This is a schematic diagram of the assembly of the sensitive device of the present invention;
[0031] Figure 3 The figure is a flow chart of the use of the present invention.
[0032] Notes:
[0033] 01-base, 02-adjustment platform, 03-front-end electronics system, 031-host computer interface, 032-circuit board, 033-circuit interface, 034-power interface, 035-circuit protection shell, 04-coaxial cable, 05-protective shell, 06-metal filament, 07-sensitive device, 071-test mass, 072-limit block, 073-electrode, 074-electrode cage shell, 08-host computer. DETAILED DESCRIPTION
[0034] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.
[0035] The present invention will be further explained below with reference to specific embodiments.
[0036] In order to address the limitations of traditional mechanical or electromagnetic seismometers in terms of sensitivity, response speed and anti-interference ability, this paper combines capacitive sensing and electrostatic drive control technology to achieve real-time measurement of ground vibration information through high-precision, high-sensitivity position detection and real-time electrostatic drive control.
[0037] like Figure 1 As shown, this embodiment provides an earthquake monitoring system based on capacitive sensing and electrostatic drive technology, including a base 01, an adjustment platform 02, a front-end electronics system 03, a coaxial cable 04, a protective shell 05, a metal filament 06, a sensitive device 07 and a host computer 08.
[0038] The base 01 is fixed to the ground by screws.
[0039] The protective shell 05 serves to insulate and shield interference, and is fixed to the base 01 and covers the base 01 .
[0040] The adjustment platform 02 is located inside the protective housing 05 and is matched to the upper center of the base 01. It can achieve precise adjustment in six degrees of freedom, namely, translation along three axes and rotation around three axes in a rectangular coordinate system. In this embodiment, the adjustment platform 02 can achieve six degrees of freedom adjustment: translation along the X, Y, and Z axes and rotation around the X, Y, and Z axes. The main function of the adjustment platform 02 is to adjust the initial positional relationship between the test mass 071 of the sensitive device 07 and the electrode cage, ensuring that the test mass 071 is as close to the center of the electrode 073 of the sensitive device 07 as possible.
[0041] The sensitive device 07 is mounted in the center of the upper portion of the adjustment platform 02 and comprises a test mass 071 and an electrode cage. The electrode cage comprises a stopper 072, an electrode 073, and an electrode cage housing 074. The electrode cage housing 074 is constructed of metal, insulated from the outside, and secured to the adjustment platform 02 by screws. A through-hole is provided in the center of the electrode cage housing 074 for connecting the electrode 073 to the front-end electronics system 03. The electrode 073 is a rectangular metal structure, secured to the inside of the electrode cage housing 074 and insulated from the cage. The test mass 071 is a metallic cube, secured to the top center of the protective housing 05 by a flexible metal filament 06. This filament 06 connects to the circuit interface 033 in the front-end electronics system 03 to provide excitation for the detection circuit. The stopper 072 is made of insulating material and has a cubic structure. It is fixed inside the electrode cage housing 074 and is used to limit the initial position of the test mass 071. The height of the stopper 072 must be greater than the height of the electrode 073. At the same time, it prevents the test mass 071 from contacting the electrode 073 during the control process and causing a short circuit. To achieve a better limiting effect, in this embodiment, the stopper 072 is installed at the center of the two electrodes 073 on each plane, with a total of six stoppers. The height of the stopper 072 is designed to be at least 1.5 times the height of the electrode 073 (in this embodiment, 2 times). To facilitate connection with the front-end electronics system 03, a connecting structure is attached to the electrode 073. It passes through the through hole of the electrode cage housing 074 and maintains an electrical connection with the electrode 073. It also leads to an interface that connects to the front-end electronics system 03 via the coaxial cable 04. When the ground shakes, the relative position of the test mass 071 and the electrode 073 will change due to the effect of the metal filament 06. With the help of the sensitive structure, the seismic signal can be converted into a displacement signal.
[0042] like Figure 2 , is an assembly diagram of the sensitive device 07 in this embodiment. The electrode 073 is processed into a metal rectangular parallelepiped structure. The electrode 073 is closely attached to the six surfaces of the electrode cage shell 074. Two electrodes 073 are attached to each surface, for a total of twelve electrodes 073. The electrodes 073 are symmetrically distributed on the opposite surfaces of the electrode cage shell 074. The distribution of the electrodes 073 in this embodiment is as follows: Figure 2As shown, four electrodes 073 are distributed along each axis, with each pair of opposing electrodes 073 forming a path. Electrodes 073 are distinguished by positive and negative, with electrodes 073 in the positive direction of the coordinate axis being designated as positive electrodes, and electrodes 073 in the negative direction of the coordinate axis being designated as negative electrodes. Horizontally, electrodes 073 are distributed left and right on one pair of planes and up and down on another pair of planes. The axis of the left and right distribution planes of electrodes 073 is designated as the X-axis, and the axis of the up and down distribution planes is designated as the Y-axis. Vertically, two pairs of electrodes 073 are distributed parallel to the Y-axis, with the vertical direction designated as the Z-axis. There are twelve electrodes: the two pairs of electrodes 073 along the X-axis are used to detect translational motion of the test mass 071 along the X-axis and rotational motion around the Z-axis; the two pairs of electrodes 073 along the Y-axis are used to detect translational motion of the test mass 071 along the Y-axis and rotational motion around the X-axis; and the two pairs of electrodes 073 along the Z-axis are used to detect translational motion of the test mass 071 along the Z-axis and rotational motion around the Y-axis. For example, there are two paths distributed along the X-axis, denoted as X1 and X2. The two electrodes 073 in the positive direction of the X-axis are denoted as X1+ and X2+, and the two electrodes 073 in the negative direction of the X-axis are denoted as X1- and X2-. The electrode 073 is electrically insulated from the electrode cage shell 074.
[0043] The front-end electronics system 03 is mounted on the side wall of the protective housing 05 and includes a host computer interface 031, a circuit board 032, a circuit interface 033, a power supply interface 034, and a circuit protective shell 035. The host computer interface 031 is mounted on the outer side wall of the protective housing 05 and is connected to the host computer 08 for communication with the host computer 08. The circuit board 032 is mounted on the inner side wall of the protective housing 05 and includes three parts: a sensing system, a control system, and a data acquisition system. The sensing system uses a capacitive sensing structure to detect the position of the test mass 071 in the electrode cage. The control system is used to control the test mass 071 to be located at the center of the electrode cage. The control system uses a PID control method with a preload voltage, applying the same preload voltage to each electrode 073 to be controlled, and applying opposite control voltages to the opposite electrodes 073, thereby controlling the test mass 071 using the difference in electrostatic force. The data acquisition system is used to acquire signals from the sensing system and the control system. The circuit interface 033 is mounted on the outside of the circuit protection shell 035 and is primarily used for electrical connection to the sensitive device 07. There are thirteen circuit interfaces 033 in total, twelve of which are connected to the electrodes 073 of the sensitive device 07 via coaxial cables 04. One circuit interface 033 is connected to the metal filament 06 to provide an excitation signal. The power interface 034 is used to connect to a power source to power the system. The circuit protection shell 035 covers the outside of the circuit board 032 and is fixed to the inner wall of the protective shell 05 to protect the circuit board 032.
[0044] The host computer 08 is equipped with a data processing system, which mainly includes a data storage module and a data processing module. The host computer 08 is connected to the data acquisition system of the circuit board 032 of the front-end electronics system 03 through the host computer interface 031 (using a USB interface) to save the collected data and realize the conversion of the collected signal into the ground vibration level.
[0045] like Figure 3 As shown, the earthquake monitoring method based on capacitive sensing and electrostatic drive technology of the present invention specifically includes the following steps:
[0046] S100, start the seismograph system, perform detection and calibration, and detect the current position of the test mass 071 through the sensor system. If the deviation is too large, adjust the adjustment platform 02 to control the test mass 071 to be close to the center of the electrode cage housing 074;
[0047] S200: Due to ground vibration, the relative positions of the electrode cage housing 074 and the test mass 071 change. The control system controls the test mass to be located at the center of the electrode cage housing 074. When the sensor system collects data that fluctuates slightly around the equilibrium position, the data acquisition system collects the control voltage values of the X1, X2, Y1, and Y2 channels of the electrode 073.
[0048] S300, in the data processing system, the data obtained by the control is processed to further obtain the translational acceleration and rotational angular acceleration of the ground vibration. The specific solution method is: suppose the detection voltages of the two channels of the X axis are V X1 , V X2 ; The detection voltages of the two electrodes on the Y axis are V Y1 , V Y2 ; Then the translational acceleration of ground vibration can be expressed as:
[0049]
[0050] The angular acceleration can be expressed as:
[0051]
[0052] Among them, ε r is the relative dielectric constant, ε0 is the dielectric constant in vacuum, A is the area of a single electrode, V r is the DC bias voltage applied to the electrode, m is the mass of the test mass, d0 is the nominal gap of the sensitive structure, l is the distance from the center point of the test mass to the center point of the electrode on the plane, and j is the moment of inertia of the test mass.
[0053] Due to the presence of air within the system, during the electrostatic drive control of the test mass, the test mass is subject to additional air damping while receiving the electrostatic force, which can lead to certain errors in the test results. To adapt to applications requiring high precision, another optimization example of the present invention is to optimize the above structure by replacing the protective shell with a high-strength vacuum protective cover. Before the test begins, a vacuum pump is used to draw a vacuum to maintain the vacuum environment inside the structure, which can significantly reduce the impact of air damping.
[0054] The present invention has a reasonable concept and realizes real-time measurement of ground vibration information through high-precision and high-sensitivity position detection and real-time electrostatic drive control.
[0055] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.
Claims
1. An earthquake monitoring system based on capacitive sensing and electrostatic drive technology, characterized by: The ground vibration monitoring system comprises a base (01), an adjustment platform (02), a front-end electronics system (03), a protective housing (05), a sensitive device (07) and a host computer (08); The base (01) is fixed on the ground; the protective shell (05) is fixed to the base (01) and covers the base (01); The adjustment platform (02) is located inside the protective shell (05) and is matched with the upper part of the base (01); The sensitive device (07) is matched and arranged on the upper part of the adjustment platform (02), and includes a test mass (071) and an electrode cage; the test mass (071) is fixed to the protective shell (05) through a metal filament (06), and the metal filament (06) is connected to the front-end electronic system (03); the electrode cage is matched and fixed on the adjustment platform (02) and has an electrode (073) matched inside; The front-end electronics system (03) is matched and mounted on the side wall of the protective housing (05), is connected and communicated with the host computer (08) via a host computer interface (031), is connected to an external power supply via a power supply interface (034), and is connected to the electrode (073) and the metal filament (06) via a circuit interface (033).
2. The earthquake monitoring system based on capacitive sensing and electrostatic drive technology according to claim 1, characterized in that: The electrode cage includes an electrode cage shell (074); The electrode cage shell (074) is matched and fixed to the upper part of the adjustment platform (02), and is made of metal material and is insulated on the outside; The electrode (073) is matched and fixed to the inner side of the electrode cage shell (074) and is insulated from the electrode cage shell (074).
3. The earthquake monitoring system based on capacitive sensing and electrostatic drive technology according to claim 2, characterized in that: The electrode cage further comprises a limit block (072); The limit block (072) is matched and fixed to the inner side of the electrode cage shell (074) and is made of insulating material. It is used to limit the initial position of the test mass (071) and prevent the test mass (071) from touching the electrode (073) during the control process to cause a short circuit. The height of the limiting block (072) is designed to be more than 1.5 times the height of the electrode (073).
4. The earthquake monitoring system based on capacitive sensing and electrostatic drive technology according to claim 2, characterized in that: The electrode cage housing (074) is provided with a through hole for facilitating the connection between the electrode (073) and the front-end electronics system (03).
5. The earthquake monitoring system based on capacitive sensing and electrostatic drive technology according to claim 1, wherein: The front-end electronics system (03) further comprises a circuit board (032) matchedly arranged on the inner side of the protective shell (05); the circuit board (032) comprises a sensing system, a control system and a data acquisition system; the sensing system adopts a capacitive sensing structure for detecting the position of the test mass (071) in the electrode cage; the control system is used to control the test mass (071) to be located at the center of the electrode cage, and adopts a PID control method with a preload voltage, applies the same preload voltage to each electrode (073) to be controlled, applies opposite control voltages to the opposite electrodes (073), and utilizes the difference in electrostatic force to realize the control of the test mass (071); the data acquisition system is used to realize signal acquisition of the sensing system and the control system.
6. The earthquake monitoring system based on capacitive sensing and electrostatic drive technology according to claim 1, characterized in that: The front-end electronics system (03) further includes a circuit protection shell (035); the circuit protection shell (035) covers the outside of the circuit board (032) and is fixed to the inner wall of the protective shell (05) for protecting the circuit board (032).
7. The earthquake monitoring system based on capacitive sensing and electrostatic drive technology according to claim 1, characterized in that: The host computer (08) is connected to the data acquisition system via the host computer interface (031); the host computer (08) is equipped with a data processing system, which is used to save the collected data and realize the conversion of the collected signal into the ground vibration level.
8. The earthquake monitoring system based on capacitive sensing and electrostatic drive technology according to claim 1, wherein: The adjustment platform (02) is used to adjust the initial position relationship between the test mass (071) and the electrode cage, and can achieve precise adjustment in six degrees of freedom, namely translation along three axes and rotation around three axes in a spatial rectangular coordinate system.
9. A seismic monitoring method based on capacitive sensing and electrostatic drive technology, based on the seismic monitoring system based on capacitive sensing and electrostatic drive technology according to any one of claims 1 to 8, characterized in that: The specific steps include: 1) Start the seismograph system, perform detection and calibration, detect the current position of the test mass (071) through the sensing system, and if the deviation is too large, control the test mass (071) to be close to the center position of the electrode cage shell (074) by adjusting the adjustment platform (02); 2) Due to ground vibration, the relative position of the electrode cage housing (074) and the test mass (071) changes. The control system controls the test mass (071) to be located at the center of the electrode cage housing (074). When the data collected by the sensor system fluctuates slightly around the equilibrium position, the control voltage value applied to the electrode (073) is collected by the data acquisition system. 3) In the data processing system, the control voltage value obtained in the above step 2) is processed to further obtain the translational acceleration and rotational angular acceleration of the ground vibration.
10. The earthquake monitoring method based on capacitive sensing and electrostatic drive technology according to claim 9, characterized in that: The solution method for the translational acceleration and rotational angular acceleration of the ground vibration is: Assume that the detection voltages of the two channels of the X-axis of the spatial rectangular coordinate system are V X1 , V X2 The detection voltages of the two electrodes on the Y axis of the spatial rectangular coordinate system are V Y1 , V Y2 ; Then the translational acceleration of ground vibration is expressed as: The angular acceleration is expressed as: Among them, ε r is the relative dielectric constant, ε0 is the dielectric constant in vacuum, A is the area of a single electrode, V r is the DC bias voltage applied to the electrode, m is the mass of the test mass, d0 is the nominal gap of the sensitive structure, l is the distance from the center point of the test mass to the center point of the electrode on the plane, and J is the moment of inertia of the test mass.
Citation Information
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