Friction nanometer vibration energy collection device based on high-speed railway bridge
By designing a triboelectric nano-vibration energy harvesting device on a high-speed railway bridge, the power supply problem of the bridge monitoring system is solved by utilizing the triboelectric effect generated by bridge vibration and the repulsive force of magnets, thus achieving efficient self-powered power supply and reliable monitoring.
Patent Information
- Application Number
- CN202610069434.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-01-20
- Publication Date
- 2026-02-17
AI Technical Summary
Existing bridge health monitoring systems rely on wired or battery power, which presents problems such as complex wiring, high maintenance costs, difficulty in deployment in remote areas, and easy monitoring failure due to power outages. In addition, existing energy harvesting devices have low power generation efficiency.
A triboelectric nano-vibration energy harvesting device based on a high-speed railway bridge is designed, including an energy harvesting mechanism and an auxiliary mechanism. The device utilizes the triboelectric effect generated by bridge vibration and the bistable phenomenon formed by magnetic repulsion to enhance power generation efficiency.
A self-powered bridge health monitoring system has been implemented, which improves power generation efficiency, solves the difficulties and inefficiencies of traditional power supply methods, and ensures the reliability of the monitoring system.
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Figure CN121546942A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of bridge technology, and in particular to a friction nano-vibration energy harvesting device based on high-speed railway bridges. Background Technology
[0002] Bridges, as key components of railway networks, account for more than 50% of the total length of the lines, and their safety and durability directly affect the reliability of railway operations. However, during long-term service, bridges are affected by environmental erosion, train loads, and other factors, causing their structural performance to gradually deteriorate. Traditional manual inspection and regular maintenance methods are insufficient to meet the needs of efficient operation and maintenance of modern railways.
[0003] Bridge health monitoring systems provide crucial data for bridge safety assessments by collecting real-time data on stress, displacement, and vibration. However, traditional monitoring systems rely on wired or battery power, which presents challenges such as complex wiring, high maintenance costs, difficulties in deployment in remote areas, and susceptibility to monitoring failure due to power outages. Therefore, developing self-powered monitoring systems has become a current research hotspot. Existing energy harvesting devices, however, rely solely on the displacement friction generated by railway vibrations to generate electricity, but the displacement is small, resulting in low power generation efficiency.
[0004] Therefore, it is necessary to provide a new triboelectric nano-vibration energy harvesting device based on high-speed railway bridges to solve the above-mentioned technical problems. Summary of the Invention
[0005] The main objective of this invention is to provide a frictional nano-vibration energy harvesting device based on high-speed railway bridges, which aims to solve the problem of low power generation efficiency caused by the small displacement of existing energy harvesting devices.
[0006] To achieve the above objectives, the present invention proposes a friction nano-vibration energy harvesting device based on a high-speed railway bridge, comprising: an energy harvesting mechanism and an auxiliary mechanism; The energy harvesting mechanism includes a base plate, a first friction assembly, and a second friction assembly; The first friction assembly includes a first mounting plate, copper foil tape, a wire, and a negative friction layer; the first mounting plate is mounted on the base plate, the copper foil tape is mounted on the first mounting plate, the negative friction layer is mounted on the copper foil tape, and the wire is connected to the copper foil tape. The second friction assembly includes a column, a counterweight, a positive friction layer, and a first magnet; the column is mounted on the base plate, the counterweight is slidably connected to the column, the negative friction layer is mounted on the first end of the counterweight and is in contact with the positive friction layer, and the first magnet is mounted on the second end of the counterweight; The auxiliary mechanism includes a mounting component and a second magnet; the second magnet is mounted on the mounting component, the second magnet is close to the first magnet, and the second magnet repels the first magnet.
[0007] Optionally, the second friction assembly further includes a base, a top plate, a first elastic element, and a second elastic element; The base is installed on the base plate, the bottom of the column is installed on the base, the top plate is installed on the top of the column, the first elastic element is installed between the base and the counterweight, and the second elastic element is installed between the top plate and the counterweight.
[0008] Optionally, the second friction assembly further includes a second mounting plate and an insulating layer, wherein the second mounting plate is mounted on the first end of the counterweight, the insulating layer is mounted on the second mounting plate, and the negative friction layer is mounted on the insulating layer.
[0009] Optionally, the first friction assembly further includes a support platform; the first mounting plate is mounted on the support platform; the support platform is slidably connected to the base plate, and the support platform is used to adjust the tightness between the negative friction layer and the positive friction layer.
[0010] Optionally, the energy harvesting mechanism further includes a slide rail; the slide rail has a groove, the side of the negative friction layer is located in the groove, and the side of the positive friction layer is slidably connected to the groove.
[0011] Optionally, two copper foil tapes are provided, arranged one above the other, with a gap between them.
[0012] Optionally, there are four energy harvesting mechanisms arranged around the auxiliary mechanism. Each auxiliary mechanism has four second magnets, which correspond one-to-one with the four first magnets on the four energy harvesting mechanisms, forming four sets of magnet areas.
[0013] Optionally, it also includes multiple partition plates; the multiple partition plates are respectively installed between the energy harvesting mechanism and the auxiliary mechanism, and the partition plates are used to isolate different magnet regions to prevent interference between different magnet regions.
[0014] Optionally, setting the vibration frequency of the energy harvesting mechanism includes the following steps: S1, obtain bridge vibration parameters; S2, use the REMD+MSST signal processing method to decompose the vibration parameters and extract the IMF signal representing the free vibration and / or forced vibration of the bridge to display the time-frequency diagram; S3, extract the free vibration frequency and / or forced vibration frequency based on the time-frequency diagram displayed; S4, set the vibration frequency of the energy harvesting mechanism according to the free vibration frequency and / or forced vibration frequency.
[0015] Optionally, the energy harvesting mechanism comprises four units; In step S3, the first-order free vibration frequency, the second-order free vibration frequency, the third-order free vibration frequency, and the forced vibration frequency are extracted from the time-frequency diagram displayed on the time-frequency display. In step S4, the vibration frequencies of the four energy harvesting mechanisms are set according to the first-order free vibration frequency, the second-order free vibration frequency, the third-order free vibration frequency, and the forced vibration frequency, respectively.
[0016] The technical solution of this invention has the following technical effects: The triboelectric nano-vibration energy harvesting device based on a high-speed railway bridge disclosed in this invention involves a counterweight that moves the positive friction layer and the first magnet up and down along the height of the column when the bridge vibrates. This causes friction between the positive and negative friction layers, resulting in the movement of electrons due to changes in electromotive force, which in turn generates current. The copper foil tape acts as an electrode to collect the amount of electrons transferred from the negative friction layer and transmits the power through a wire. Simultaneously, the device also utilizes the repulsive force between the first and second magnets to create a bistable phenomenon, which enhances the displacement between the positive and negative friction layers, thereby improving power generation efficiency. Attached Figure Description
[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.
[0018] Figure 1 This is a schematic diagram of the structure of an embodiment of the present invention; Figure 2 This is a schematic diagram of the energy harvesting mechanism in an embodiment of the present invention; Figure 3 This is a schematic diagram of the structure of the first friction assembly in an embodiment of the present invention; Figure 4 for Figure 3 Enlarged view of part A in the image; Figure 5 This is a schematic diagram of the structure of the second friction assembly in an embodiment of the present invention; Figure 6 for Figure 5Enlarged view of part B in the image; Figure 7 This is a schematic diagram of the installation group in an embodiment of the present invention; Figure 8 The following is a time-frequency diagram for time-frequency display in an embodiment of the present invention, wherein: (a) is a time-frequency diagram of free vibration frequency; and (b) is a time-frequency diagram of forced vibration frequency.
[0019] Explanation of icon numbers: 1. Energy harvesting mechanism; 101. Base plate; 102. First friction assembly; 1021. First mounting plate; 1022. Copper foil tape; 1023. Wire; 1024. Negative friction layer; 1025. Support platform; 103. Second friction assembly; 1031. Column; 1032. Counterweight; 1033. Positive friction layer; 1034. First magnet; 1035. Base; 1036. Top plate; 1037. First elastic element; 1038. Second elastic element; 1039. Second mounting plate; 10310. Insulation layer; 104. Slide rail; 2. Auxiliary mechanism; 201. Mounting assembly; 2011. Mounting base; 20111. Slide groove; 20112. Mounting hole; 2012. Fixing block; 2013. Pin; 202. Second magnet; 3. Divider plate.
[0020] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation
[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.
[0022] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present invention are only used to explain the relative positional relationship and movement of each component in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indication will also change accordingly.
[0023] Furthermore, in this invention, descriptions involving "first," "second," etc., are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.
[0024] In this invention, unless otherwise explicitly specified and limited, the terms "connection," "fixed," etc., should be interpreted broadly. For example, "fixed" can mean a fixed connection, a detachable connection, or an integral part; it can mean a mechanical connection or an electrical connection; it can mean a direct connection or an indirect connection through an intermediate medium; it can mean the internal communication of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.
[0025] Furthermore, the technical solutions of the various embodiments of the present invention can be combined with each other, but only if they are feasible for those skilled in the art. If the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.
[0026] Example: Please refer to Figures 1-7 This invention proposes a friction nano-vibration energy harvesting device based on a high-speed railway bridge, which is used to power the sensors and other components in the existing monitoring system. The device includes an energy harvesting mechanism 1 and an auxiliary mechanism 2. The energy harvesting mechanism 1 includes a base plate 101, a first friction assembly 102, and a second friction assembly 103; the base plate 101 is made of stainless steel and has anti-corrosion properties. The first friction assembly 102 includes a first mounting plate 1021, a copper foil tape 1022, a wire 1023, and a negative friction layer 1024; the first mounting plate 1021 is mounted on the base plate 101, the copper foil tape 1022 is mounted on the first mounting plate 1021, the negative friction layer 1024 is mounted on the copper foil tape 1022, and the wire 1023 is connected to the copper foil tape 1022; The second friction assembly 103 includes a column 1031, a counterweight 1032, a positive friction layer 1033, and a first magnet 1034; the column 1031 is mounted on the base plate 101, the counterweight 1032 is slidably connected to the column 1031, the negative friction layer 1024 is mounted on the first end of the counterweight 1032 and the negative friction layer 1024 is in contact with the positive friction layer 1033, and the first magnet 1034 is mounted on the second end of the counterweight 1032; The auxiliary mechanism 2 includes a mounting component 201 and a second magnet 202; the second magnet 202 is mounted on the mounting component 201, the second magnet 202 is close to the first magnet 1034, and the second magnet 202 and the first magnet 1034 repel each other.
[0027] In this embodiment, since the deflection is greatest at the mid-span of the bridge, the energy harvesting device is installed at the mid-span. When the bridge vibrates, the counterweight 1032 drives the positive friction layer 1033 and the first magnet 1034 to move up and down along the height direction of the column 1031, causing friction between the positive friction layer 1033 and the negative friction layer 1024. Due to the change in electromotive force, electrons move, thereby generating current. The copper foil tape 1022 acts as an electrode to collect the amount of electrons transferred from the negative friction layer 1024 and transmits the power through the wire 1023. At the same time, this device also connects the first magnet 1034 with the second... The repulsive force between the magnets 202 forms a bistable phenomenon, which can enhance the displacement between the positive friction layer 1033 and the negative friction layer 1024, thereby improving the power generation efficiency. It should also be noted that the repulsive force between the first magnet 1034 and the second magnet 202 can be controlled by adjusting the distance between them, thus forming a bistable phenomenon. At the same time, in order to enhance the smoothness of the counterweight 1032's up-and-down movement, industrial petroleum jelly or other lubricants can be applied between the counterweight 1032 and the column 1031 to reduce the frictional resistance between them.
[0028] Optionally, the second friction assembly 103 further includes a base 1035, a top plate 1036, a first elastic element 1037, and a second elastic element 1038; The base 1035 is installed on the base plate 101, the bottom of the column 1031 is installed on the base 1035, the top plate 1036 is installed on the top of the column 1031, the first elastic member 1037 is installed between the base 1035 and the counterweight 1032, and the second elastic member 1038 is installed between the top plate 1036 and the counterweight 1032.
[0029] In this embodiment, both the first elastic element 1037 and the second elastic element 1038 are springs. In other embodiments, the first elastic element 1037 and the second elastic element 1038 may also be other types of elastic elements. The top plate 1036 not only serves to abut against the second elastic element 1038, but also serves to limit the movement distance of the counterweight 1032, preventing the counterweight 1032 from moving too much upward and thus detaching from the column 1031. At the same time, the first elastic element 1037 and the second elastic element 1038 also serve as a buffer to prevent the counterweight 1032 from colliding with the base 1035 or the top plate 1036, which could lead to damage to the parts.
[0030] Optionally, the second friction assembly 103 further includes a second mounting plate 1039 and an insulating layer 10310. The second mounting plate 1039 is mounted on the first end of the counterweight 1032, the insulating layer 10310 is mounted on the second mounting plate 1039, and the negative friction layer 1024 is mounted on the insulating layer 10310.
[0031] In this embodiment, the second mounting plate 1039 serves to support the negative friction layer 1024, and the insulating layer 10310 is sandwiched between the second mounting plate 1039 and the negative friction layer 1024 to provide insulation. The second mounting plate 1039 is made of aluminum plate.
[0032] Optionally, the first friction assembly 102 further includes a support platform 1025; the first mounting plate 1021 is mounted on the support platform 1025; the support platform 1025 is slidably connected to the base plate 101, and the support platform 1025 is used to adjust the tightness between the negative friction layer 1024 and the positive friction layer 1033.
[0033] In this embodiment, a sliding groove is opened on the base plate 101, and a sliding part is provided at the bottom of the support platform 1025. The sliding part is slidably connected in the sliding groove. It should be noted that after the support platform 1025 is adjusted to the correct position, the support platform 1025 needs to be fixedly connected to the base plate 101. Epoxy resin or other strong adhesives can be used for fixing, or bolts can be used for fixing.
[0034] Optionally, the energy harvesting mechanism 1 further includes a slide rail 104; the slide rail 104 has a groove, the side of the negative friction layer 1024 is located in the groove, and the side of the positive friction layer 1033 is slidably connected to the groove.
[0035] In this embodiment, by setting the slide rail 104, the negative friction layer 1024 can be positioned, and the positive friction layer 1033 can be guided.
[0036] Optionally, two copper foil tapes 1022 are provided, arranged one above the other, with a gap between them.
[0037] In this embodiment, two copper foil tapes 1022 are arranged on the top and bottom to form a sliding independent layer mode, which has the characteristics of high power generation efficiency.
[0038] Optionally, there are four energy harvesting mechanisms 1 arranged around the auxiliary mechanism 2. The auxiliary mechanism 2 is provided with four second magnets 202. The four second magnets 202 are arranged in a one-to-one correspondence with the four first magnets 1034 on the four energy harvesting mechanisms 1, forming four sets of magnet areas.
[0039] Mounting assembly 201 includes mounting base 2011, which has four sides, on which a second magnet 202 is mounted. A groove 20111 is formed along the height direction on the side of mounting base 2011. A fixing block 2012 is slidably connected in the groove 20111. The second magnet 202 is mounted on the fixing block 2012. Multiple mounting holes 20112 are formed on the side of the groove 20111. The fixing block 2012 is fixed to the mounting holes 20112 by a pin 2013.
[0040] In this embodiment, by setting four energy harvesting mechanisms 1, the vibration frequencies of the four energy harvesting mechanisms 1 can be set according to the vibration frequency of the railway, further increasing the power generation efficiency. The four energy harvesting mechanisms 1 share the same auxiliary mechanism 2, and the number of second magnets 202 on the auxiliary mechanism 2 is the same as the number of energy harvesting mechanisms 1. It should be noted that, in order to prevent interference between the vibrations of the energy harvesting mechanisms 1, there should be gaps in the base plate 101 of the energy harvesting mechanism 1. Of course, in other embodiments, different numbers of energy harvesting mechanisms can be used, with multiple energy harvesting mechanisms sharing the same auxiliary mechanism.
[0041] Optionally, it also includes a plurality of partition plates 3; the plurality of partition plates 3 are respectively installed between the energy harvesting mechanism 1 and the auxiliary mechanism 2, and the partition plates 3 are used to isolate different magnet regions to prevent interference between different magnet regions.
[0042] In this embodiment, the partition plate 3 serves to isolate different magnet areas.
[0043] Optionally, setting the vibration frequency of the energy harvesting mechanism 1 includes the following steps: S1. Obtain bridge vibration parameters; Interferometric radar is used to collect bridge vibration parameters. When using it, the interferometric radar is placed at a distance of about 30 meters from the bridge, and the crosshair of the interferometric radar is aligned with the mid-span of the bridge. The interferometric radar can use the IBIS-FS system (IBIS-FS is an advanced remote monitoring system based on microwave interferometry), and its displacement measurement accuracy can reach the sub-millimeter level.
[0044] S2, using the existing REMD+MSST signal processing method (REMD is an advanced computational method for molecular simulation, and MSST is multi-scale synchronous compression transform), the vibration parameters are decomposed into signals, and the time-frequency plots of the IMF signals representing the bridge's free vibration and / or forced vibration are extracted and displayed. REMD decomposes the bridge vibration signal and extracts the main vibration information of the bridge, filtering out other information. MSST displays the extracted information in a time-frequency manner to obtain the time-frequency characteristics of different types of bridge vibration.
[0045] S3, extract the free vibration frequency and / or forced vibration frequency based on the time-frequency diagram displayed; S4, set the vibration frequency of the energy harvesting mechanism 1 according to the free vibration frequency and / or forced vibration frequency.
[0046] In this embodiment, the vibration frequency of the energy harvesting mechanism 1 is adjusted to match the free vibration frequency and / or the forced vibration frequency to form a resonance phenomenon, thereby enhancing the power generation efficiency.
[0047] Optionally, the energy harvesting mechanism 1 has four components; In step S3, the first-order free vibration frequency, the second-order free vibration frequency, the third-order free vibration frequency, and the forced vibration frequency are extracted from the time-frequency diagram displayed on the time-frequency display. In step S4, the vibration frequencies of the four energy harvesting mechanisms 1 are set according to the first-order free vibration frequency, the second-order free vibration frequency, the third-order free vibration frequency, and the forced vibration frequency, respectively.
[0048] In this embodiment, as Figure 8 As shown, based on the measured results, the first-order free vibration frequency, second-order free vibration frequency, third-order free vibration frequency, and forced vibration frequency are approximately 6.5Hz, 9.9Hz, 13.2Hz, and 3.4Hz, respectively. Therefore, the vibration frequencies of the four energy harvesting mechanisms 1 are set to 3.4Hz, 6.5Hz, 9.9Hz, and 13.2Hz, respectively. It should be noted that the above data are from a single measurement, and the results may vary at different bridge locations. The stiffness and mass of the energy harvesting mechanism are calculated using the following formula: ; in: The vibration frequency, To measure the stiffness of the collection mechanism, The mass of the energy harvesting mechanism.
[0049] The above description is only a preferred embodiment of the present invention and does not limit the scope of the present invention. All equivalent structural transformations made under the inventive concept of the present invention using the contents of the present invention specification and drawings, or direct / indirect applications in other related technical fields, are included within the protection scope of the present invention.
Claims
1. A frictional nanovibration energy harvesting device based on a high-speed railway bridge, characterized in that, The energy collection mechanism comprises a bottom plate, a first friction assembly and a second friction assembly. The first friction assembly comprises a first mounting plate, a copper foil tape, a wire and a negative friction layer; the first mounting plate is mounted on the bottom plate, the copper foil tape is mounted on the first mounting plate, the negative friction layer is mounted on the copper foil tape, and the wire is connected with the copper foil tape. The second friction assembly comprises a stand, a counterweight, a positive friction layer and a first magnet; the stand is mounted on the bottom plate, the counterweight is slidingly connected with the stand, the negative friction layer is mounted on the first end of the counterweight, and the negative friction layer is in contact with the positive friction layer; the first magnet is mounted on the second end of the counterweight. The auxiliary mechanism comprises a mounting assembly and a second magnet; the second magnet is mounted on the mounting assembly, the second magnet is close to the first magnet, and the second magnet repels the first magnet. The second friction assembly further comprises a base, a top plate, a first elastic member and a second elastic member. The base is mounted on the bottom plate, the bottom of the stand is mounted on the base, the top plate is mounted on the top of the stand, the first elastic member is mounted between the base and the counterweight, and the second elastic member is mounted between the top plate and the counterweight.
2. The high-speed rail bridge based frictional nanovibrational energy harvesting device of claim 1, wherein, The second friction assembly further comprises a second mounting plate and an insulating layer; the second mounting plate is mounted on the first end of the counterweight, the insulating layer is mounted on the second mounting plate, and the negative friction layer is mounted on the insulating layer. The first friction assembly further comprises a support table; the first mounting plate is mounted on the support table; the support table is slidingly connected with the bottom plate, and the support table is used to adjust the tightness between the negative friction layer and the positive friction layer.
3. The high-speed rail bridge based frictional nanovibrational energy harvesting device of claim 1, wherein, The energy collection mechanism further comprises a sliding rail; the sliding rail has a groove, the side edge of the negative friction layer is located in the groove, and the side edge of the positive friction layer is slidingly connected in the groove.
4. The high-speed rail bridge based frictional nanovibrational energy harvesting device of claim 1, wherein, The copper foil tape is provided in two, the two copper foil tapes are arranged in an upper and lower manner, and there is a gap between the two copper foil tapes.
5. The high-speed rail bridge based frictional nanovibrational energy harvesting device of claim 1, wherein, The energy collection mechanism is provided in four, the four energy collection mechanisms surround the auxiliary mechanism, the auxiliary mechanism is provided with four second magnets, the four second magnets are arranged in one-to-one correspondence with the four first magnets on the four energy collection mechanisms, and four groups of magnet areas are formed.
6. The high-speed rail bridge based frictional nanovibrational energy harvesting device of claim 1, wherein, A plurality of partition plates are further included; the plurality of partition plates are respectively mounted between the energy collection mechanisms and the auxiliary mechanism, and the partition plates are used to isolate different magnet areas to prevent interference between different magnet areas.
7. The high-speed rail bridge based frictional nanovibrational energy harvesting device of claim 1, wherein, The vibration frequency of the energy collection mechanism is set 8. The high-speed rail bridge based frictional nanovibrational energy harvesting device of claim 7, wherein, The method comprises the following steps:
9. The high-speed rail bridge based frictional nanovibrational energy harvesting device of claim 1, wherein, S1, obtaining a bridge vibration parameter; S2, using a REMD+MSST signal processing method to perform signal decomposition on the vibration parameter, and extracting an IMF signal time-frequency display of a time-frequency diagram representing bridge free vibration and / or forced vibration; S3, extracting a free vibration frequency and / or a forced vibration frequency according to the time-frequency diagram of the time-frequency display; S4, setting vibration frequencies of the energy collecting mechanisms according to the free vibration frequencies and / or forced vibration frequencies.
10. The high-speed rail bridge based frictional nanovibrational energy harvesting device of claim 9, wherein, The energy collecting mechanisms are four in total; In the step S3, a first-order free vibration frequency, a second-order free vibration frequency, a third-order free vibration frequency and a forced vibration frequency are extracted according to the time-frequency diagram of the time-frequency display; In the step S4, vibration frequencies of the four energy collecting mechanisms are set respectively according to the first-order free vibration frequency, the second-order free vibration frequency, the third-order free vibration frequency and the forced vibration frequency.
Citation Information
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