A pendulum tuned mass damper and a calculation method

Abstract

A single pendulum type tuned mass damper, including horizontal velocity sensor, circuit board, frequency adjustment mechanism, damping adjustment mechanism; A precise self-adjusting frequency algorithm of a single pendulum type tuned mass damper, including the steps of initial frequency adjustment and subsequent fine frequency adjustment. The present application relates to the technical field of damper, through the improvement of damper structure and algorithm, the frequency and damping of damper can be precisely adjusted.

Description

Technical Field

[0001] This invention belongs to the field of damper technology, specifically relating to a pendulum-type tuned mass damper and its calculation method. Background Technology

[0002] The rapid proliferation of rail transit, human-induced vibrations on lightweight, large-span structures, and increasing construction activity in cities have brought unavoidable vibration problems, which can adversely affect neighboring buildings and the people inside. Numerous examples have demonstrated the effectiveness of vibration reduction measures for buildings, such as the frequently used tuned mass dampers (TMDs).

[0003] While TMDs come in various forms, their core principles are similar: frequency, damping, and mass are key parameters. The pendulum type, a common TMD, is frequently used in high-rise buildings such as wind towers to reduce wind-induced vibrations. Traditional pendulum TMDs mainly consist of a pendulum rod, a mass sphere (or block), and damping components. Traditional PTMDs (Passive Tuned Mass Dampers) struggle to achieve precise frequency and damping adjustments. Furthermore, calculations often differ from actual conditions, preventing PTMDs from achieving optimal frequency and damping. This results in a complex and inaccurate construction process, hindering optimal vibration reduction. Since parameters calculated using finite element models or other algorithms may differ from reality, and TMDs often cannot be manufactured after project completion, a TMD that can be tested on-site after delivery and then adjusted is needed. However, traditional pendulum TMDs struggle to achieve quantitative adjustments. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, this invention discloses a single-pendulum tuned mass damper and its calculation method. This invention aims to improve three problems in existing technologies, as follows:

[0005] 1. The frequency modulation method of PTMD has been improved, with initial frequency modulation and subsequent precise frequency modulation to achieve the best vibration reduction effect.

[0006] 2. In existing designs of self-adjusting frequency PTMDs, only the frequency can generally be adjusted. Damping, due to the difficulty in fine-tuning, is often estimated within a reasonable range in practical engineering. This invention sets up a lower suspension device submerged in the damping fluid. The oscillation of the lower suspension device in the damping fluid provides damping for the PTMD. By changing the relative sliding amplitude between the sliding block and the positioning block, the contact area with the damping fluid is altered, allowing for autonomous and fine-tuning of the damping.

[0007] 3. Improve the algorithm for precisely adjusting the PTMD frequency.

[0008] To achieve the above objectives, the technical solution of the present invention is as follows:

[0009] A pendulum-type tuned mass damper includes a horizontal velocity sensor, a circuit board, a frequency adjustment mechanism, and a damping adjustment mechanism. The horizontal velocity sensor is fixedly mounted on the bottom of the structure to be damped and is used to detect the natural frequency of the structure and the dynamic response frequency when subjected to external excitation. The horizontal velocity sensor is connected to the circuit board via a wire. The frequency adjustment mechanism and the damping adjustment mechanism are respectively connected to the bottom of the structure and work together. The circuit board is configured to control the frequency adjustment mechanism and the damping adjustment mechanism.

[0010] Preferably, the structure has a rectangular mounting frame fixed at the bottom, and the frequency adjustment mechanism includes a first servo motor located at the four corners of the rectangular mounting frame. The output shaft of the first servo motor is fixedly connected to a first winding roller, and edge swing ropes are wound on the first winding roller. A support box with an open top is provided below the rectangular mounting frame. The support box is uniformly filled with a mass block. The support box is horizontally positioned, and the bottom ends of the four edge swing ropes are respectively connected to the four corners of the top of the support box. The circuit board is electrically connected to the first servo motor through wires and is used to control the lifting height of the mass block.

[0011] Preferably, the damping adjustment mechanism includes a second servo motor located at the center of the rectangular mounting frame. The output shaft of the second servo motor is fixedly connected to a second winding roller. A central swing rope is wound on the second winding roller. The central swing rope passes downward along the axis of the rectangular mounting frame, through a through hole preset at the center of the mass block, and through the bottom of the support box. The bottom end of the central swing rope is connected to a suspension device with adjustable surface area. The suspension device is connected to damping fluid, which is placed in a container. The container is fixedly connected to the ground or the wall of the building structure. The circuit board is electrically connected to the second servo motor through wires.

[0012] Preferably, the lower suspension device includes a positioning block, a multi-section tubular telescopic rod, and a sliding block. The positioning block has a cavity, and a first sliding hole and a second sliding hole are respectively provided at the top and bottom of the cavity along the axis of the positioning block. The upper end of the sliding block is open and covers the outer periphery of the positioning block. The bottom end of the sliding block has a sliding rod extending upward and penetrating through the second sliding hole. The top end of the sliding rod is fixedly connected to a limit block, which is slidably connected to the inner wall of the cavity. The outer surface of the lowest section of the multi-section tubular telescopic rod is slidably and sealingly connected to the inner surface of the first sliding hole. The sliding rod is slidably and sealingly connected to the second sliding hole. The inner surface of the sliding block is slidably and sealingly connected to the outer surface of the positioning block. The central swing rope passes through the multi-section tubular telescopic rod along the through hole and is connected to the top end of the limit block. The bottom end of the lowest section of the multi-section tubular telescopic rod is fixedly connected to the top end of the limit block. The top end of the multi-section tubular telescopic rod is fixedly connected to the bottom end of the support box. The multi-section tubular telescopic rod is coaxial with the through hole.

[0013] Preferably, both the positioning block and the sliding block are cubic structures. The multi-section tubular telescopic rod is also provided with four edge limiting rods along the vertical direction on its outer periphery. The upper end of the edge limiting rod is fixedly connected to the bottom end of the support box, and the lower end is fixedly connected to the corner of the top of the positioning block.

[0014] Preferably, the circuit board is equipped with a calculation module. This module calculates the natural frequency and dynamic response frequency of the structure using Fourier transform based on the data collected by the horizontal velocity sensor. The circuit board controls the rotation of the first servo motor to raise and lower the mass block, thereby adjusting the vibration frequency of the damper. It also controls the raising and lowering of the sliding block to achieve relative sliding between the sliding block and the positioning block. Both the sliding block and the positioning block are immersed in damping fluid, and the relative sliding adjusts the contact area with the damping fluid. The circuit board adjusts the lengths of the central and edge swing ropes based on real-time data measured by the horizontal velocity sensor. After obtaining the calculated damping and frequency through the calculation module, if the discrete time-domain data has a certain error after Fourier transform due to insufficient sensor sensitivity, the circuit board uses a precise self-tuning algorithm to fine-tune the frequency error.

[0015] A precise self-tuning algorithm for a pendulum tuned mass damper includes the following steps:

[0016] (1) Initial frequency tuning: Apply a steady-state continuous excitation to the structure to be vibration reduced or directly under environmental excitation. The horizontal velocity sensor connected to the structure collects vibration data within a certain period of time. The circuit board initially calculates the natural frequency and dynamic response frequency of the structure and controls the first servo motor to adjust the length of the edge swing rope.

[0017] (2) Subsequent fine-tuning of frequency: During the algorithm process, the first servo motor first extends the edge swing rope. If the test speed of the horizontal speed sensor shows a decreasing trend, it proves that the swing rope adjustment direction is correct. The circuit board records the swing rope length and speed value at each adjustment until the speed changes from a decreasing trend to an increasing trend, and stops adjusting the swing rope length. The extreme value corresponding to the swing rope length is output. If the speed shows an increasing trend when the first servo motor first extends the swing rope, the swing rope length is shortened, and the above steps are repeated.

[0018] Preferably, step (1) includes the following specific steps:

[0019] The natural frequency of the structure is calculated as shown in equation (1). The obtained vibration time-domain data is converted into frequency-domain data to obtain the spectral density function of the signal, from which the natural frequency of the structure can be obtained:

[0020]

[0021] In the formula:

[0022] x(t) represents time-domain data, and in this invention specifically refers to velocity;

[0023] X(ω) is frequency domain data;

[0024] ω is the frequency;

[0025] t represents time;

[0026] j is an imaginary number;

[0027] Since the sensor measures discrete time-domain data, the calculated amplitude density can only be a finite number of frequencies, which is the Discrete Fourier Transform (DFT). The DFT definition of a finite-length discrete signal x(n), (n=0,1,2……,N-1) is shown in equation (2):

[0028]

[0029] In the formula: k = 0, 1, 2, ..., N-1;

[0030] X(k) is divided into two parts: n is even and n is odd, where x1 is even and x2 is odd, as shown in equation (3).

[0031] x(n)=x1(n)+x2(n) (3)

[0032] Then equation (2) becomes:

[0033]

[0034] because Then equation (4) becomes:

[0035]

[0036] Since both even and odd sequences in equation (5) are based on... If it is a period, then Therefore, equation (5) can be expressed as:

[0037]

[0038] In equations (2)-(6), k takes the same value, k = 0, 1, 2, ..., N-1. That is, if we obtain X(k), we can necessarily obtain... After converting the measured time-domain data into the frequency domain, the structure's natural frequency can be obtained. The first servo motor adjusts the length of the edge swing rope according to the calculation results to complete the initial frequency tuning.

[0039] The beneficial effects of the present invention, a pendulum-type tuned mass damper and its calculation method, are as follows:

[0040] This invention proposes a self-adjusting frequency and damping PTMD (Pendulum-Modulated Mass Damper). The PTMD incorporates a built-in feedback adjustment system (circuit board, horizontal velocity sensor, first servo motor, second servo motor) and a classic PTMD structure. The circuit board controls the servo motors to change the length of the pendulum rope based on the structure's natural frequency, adjusting the damping and frequency to the theoretically calculated results. The feedback adjustment system then performs precise self-frequency tuning to achieve optimal vibration reduction. The structure is improved to address the limitation of traditional PTMDs, which can only roughly estimate damping, allowing for precise damping adjustment. The algorithm for precise self-frequency adjustment in the feedback control system is optimized, making it more accurate, simpler, and easier to implement compared to traditional PTMDs. Attached Figure Description

[0041] Figure 1 A schematic diagram of the structure of the present invention;

[0042] Figure 2 The algorithm flowchart of this invention;

[0043] Figure 3 A schematic diagram of the lower suspension device;

[0044] Figure 4 A schematic diagram showing the maximum contact area between the lower suspension device and the damping fluid;

[0045] 1-Horizontal speed sensor, 2-Circuit board, 3-First servo motor, 4-Central swing rope, 5-Edge swing rope, 6-Mass block, 7-Support box, 8-Lower suspension device, 9-Damping fluid, 81-Multi-section tubular telescopic rod, 811-Telescopic area, 82-Edge limiting rod, 83-Sliding block, 84-Positioning block. Detailed Implementation

[0046] The following description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0047] Example 1

[0048] A pendulum-type tuned mass damper, such as Figure 1 , 3 As shown in Figure 4, the structure includes a horizontal velocity sensor 1, a circuit board 2, a frequency adjustment mechanism, and a damping adjustment mechanism. The horizontal velocity sensor is fixedly installed at the bottom of the structure to be vibration-damped and is used to detect the natural frequency of the structure and the dynamic response frequency when subjected to external excitation. The horizontal velocity sensor 1 is connected to the circuit board 2 via a wire. The frequency adjustment mechanism and the damping adjustment mechanism are respectively connected to the bottom of the structure and work together. The circuit board 2 is configured to control the frequency adjustment mechanism and the damping adjustment mechanism.

[0049] Example 2

[0050] Based on Example 1, this example discloses:

[0051] like Figure 1 As shown, a rectangular mounting frame (not shown in the figure) is fixedly provided at the bottom of the structure. The frequency adjustment mechanism includes a first servo motor 3 located at the four corners of the rectangular mounting frame. The output shaft of the first servo motor 3 is fixedly connected to a first winding roller (not shown in the figure). An edge swing rope 5 is wound on the first winding roller. A support box 7 with an open top is provided below the rectangular mounting frame. Mass blocks 6 are evenly filled in the support box 7. The support box 7 is set horizontally. The bottom ends of the four edge swing ropes 5 are respectively connected to the four corners of the top of the support box 7. The circuit board 2 is electrically connected to the first servo motor 3 through wires and is used to control the lifting height of the mass blocks.

[0052] like Figure 1 , 3 As shown in Figure 4, the damping adjustment mechanism includes a second servo motor (not marked in the figure) located at the center of the rectangular mounting frame. The output shaft of the second servo motor is fixedly connected to a second winding roller. A central swing rope 4 is wound on the second winding roller. The central swing rope 4 passes downward along the axis of the rectangular mounting frame, passes through a through hole preset at the center of the mass block 6, and passes through the bottom end of the support box. The bottom end of the central swing rope 4 is connected to a lower suspension device with adjustable surface area. The lower suspension device is connected to the damping fluid 9. The damping fluid 6 is placed in a container. The container is fixedly connected to the ground or the wall of the building structure. The circuit board 2 is electrically connected to the second servo motor through wires.

[0053] Example 3

[0054] Based on Example 2, this example discloses:

[0055] like Figure 1 , 3As shown in Figure 4, the lower suspension device 8 includes a positioning block 84, a multi-section tubular telescopic rod 81, and a sliding block 83. The positioning block 84 has a cavity. A first sliding hole (not shown) and a second sliding hole (not shown) are respectively located at the top and bottom of the cavity along the axis of the positioning block. The upper end of the sliding block 83 is open and covers the outer periphery of the positioning block 84. The bottom end of the sliding block has a sliding rod (not shown) extending upwards and penetrating through the second sliding hole. A limit block (not shown) is fixedly connected to the top of the sliding rod. The limit block is slidably connected to the inner wall of the cavity. The multi-section... The outer surface of the lowest section of the tubular telescopic rod is sealed and slidably connected to the inner surface of the first sliding hole; the sliding rod is sealed and slidably connected to the second sliding hole; the inner surface of the sliding block 83 is sealed and slidably connected to the outer surface of the positioning block 84; the central swing rope passes through the through hole and is connected to the top of the limiting block; the bottom end of the lowest section of the multi-section tubular telescopic rod is fixedly connected to the top of the limiting block to ensure that the mass block and the sliding block rotate synchronously; the top end of the multi-section tubular telescopic rod 81 is fixedly connected to the bottom end of the support box 7; and the multi-section tubular telescopic rod is coaxial with the through hole.

[0056] Example 4

[0057] Based on Example 3, this example discloses:

[0058] like Figure 1 , 3 As shown in Figure 4, both the positioning block 84 and the sliding block 83 are cubic structures. The multi-section tubular telescopic rod 81 is also provided with four edge limiting rods 82 along the vertical direction on its outer periphery. The upper end of the edge limiting rod is fixedly connected to the bottom end of the support box, and the lower end is fixedly connected to the corner of the top of the positioning block to ensure that the positioning block and the mass block rotate synchronously.

[0059] Example 5

[0060] Based on the above embodiment 3, this embodiment discloses:

[0061] like Figure 2As shown, the circuit board is equipped with a calculation module. This module calculates the natural frequency and dynamic response frequency of the structure using Fourier transform based on the data collected by the horizontal velocity sensor 1. The circuit board controls the rotation of the first servo motor to raise and lower the mass block, thereby adjusting the vibration frequency of the damper. It also controls the raising and lowering of the sliding block to achieve relative sliding between the sliding block and the positioning block. Both the sliding block and the positioning block are immersed in damping fluid, and the relative sliding adjusts the contact area with the damping fluid, thus regulating the damping force. The circuit board 2 adjusts the length of the central pendulum rope 4 and the edge pendulum rope 5 based on the real-time data measured by the horizontal velocity sensor 1. After calculating the damping and frequency through the calculation module, due to insufficient sensor sensitivity, the discrete time-domain data has a certain error after Fourier transform. Therefore, the circuit board uses a precise self-tuning frequency algorithm to fine-tune the frequency error.

[0062] Example 6

[0063] Based on Example 5, such as Figure 2 As shown, this embodiment discloses:

[0064] Since the effect of fine adjustments to damping relative to frequency is not significant, fine-tuning the PTMD frequency is sufficient. Therefore, this invention simplifies the algorithm for precise self-frequency modulation, and its algorithm flow is as follows: Figure 2 As shown.

[0065] A precise self-tuning algorithm for a pendulum tuned mass damper includes the following steps:

[0066] (1) First initial frequency tuning: Apply a steady-state continuous excitation to the structure to be vibration reduced or directly under environmental excitation. The horizontal velocity sensor connected to the structure collects vibration data within a certain period of time. The circuit board calculates the natural frequency and dynamic response frequency of the structure and controls the first servo motor to adjust the length of the edge swing rope.

[0067] (2) Subsequent fine-tuning of frequency: During the algorithm process, the first servo motor first extends the edge swing rope. If the test speed of the horizontal speed sensor shows a decreasing trend, it proves that the swing rope adjustment direction is correct. The circuit board records the swing rope length and speed value at each adjustment until the speed changes from a decreasing trend to an increasing trend, and stops adjusting the swing rope length. The extreme value corresponding to the swing rope length is output. If the speed shows an increasing trend when the first servo motor first extends the swing rope, the swing rope length is shortened, and the above steps are repeated.

[0068] Example 7

[0069] Based on Example 6, such as Figure 2 As shown, this embodiment discloses:

[0070] Step (1) includes the following specific steps:

[0071] The natural frequency of the structure is calculated as shown in equation (1). The obtained vibration time-domain data is converted into frequency-domain data to obtain the spectral density function of the signal, from which the natural frequency of the structure can be obtained:

[0072]

[0073] In the formula, x(t) represents time-domain data, which specifically refers to velocity in this invention;

[0074] X(ω) is frequency domain data;

[0075] ω is the frequency;

[0076] t represents time;

[0077] j is an imaginary number;

[0078] Since the sensor measures discrete time-domain data, the calculated amplitude density can only be a finite number of frequencies, which is the Discrete Fourier Transform (DFT). The DFT definition of a finite-length discrete signal x(n), n = 0, 1, 2, ..., N-1 is shown in equation (2):

[0079]

[0080] In the formula: k = 0, 1, 2, ..., N-1;

[0081] X(k) is divided into two parts: n is even and n is odd, where x1 is even and x2 is odd, as shown in equation (3).

[0082] x(n)=x1(n)+x2(n) (3)

[0083] Then equation (2) becomes:

[0084]

[0085] because Then equation (4) becomes:

[0086]

[0087] Since both even and odd sequences in equation (5) are based on... If it is a period, then Therefore, equation (5) can be expressed as:

[0088]

[0089] In equations (2)-(6), k takes the same value, k = 0, 1, 2, ..., N-1. That is, if we obtain X(k), we can necessarily obtain... Compared to DFT, FFT (Fast Fourier Transform) can significantly shorten the calculation process. After converting the measured time-domain data into the frequency domain, the natural frequency of the structure can be obtained. The motor adjusts the swing rope according to the calculation results to complete the initial frequency tuning.

Claims

1. A pendulum tuned mass damper characterized by: The horizontal velocity sensor is fixed on the bottom of the structure to be damped and is used to detect the natural frequency of the structure and the dynamic response frequency when the structure is excited by external excitation, the horizontal velocity sensor is signal connected with the circuit board through wires, the frequency adjusting mechanism and the damping adjusting mechanism are respectively connected with the bottom of the structure and are used in cooperation, and the circuit board is configured to control the frequency adjusting mechanism and the damping adjusting mechanism. The frequency adjusting mechanism includes a first servo motor arranged at four corners of the rectangular mounting frame, an output shaft of the first servo motor is fixedly connected with a first winding roller, and an edge pendulum rope is wound on the first winding roller. The damping adjusting mechanism includes a second servo motor arranged at the center of the rectangular mounting frame, an output shaft of the second servo motor is fixedly connected with a second winding roller, and a central pendulum rope is wound on the second winding roller. The central pendulum rope passes through a through hole arranged at the center of the mass block and penetrating the bottom end of the support box along the axis of the rectangular mounting frame, and the bottom end of the central pendulum rope is connected with a lower suspension device with an adjustable surface area.

2. A pendulum tuned mass damper as claimed in claim 1, characterised in that: The lower suspension device is connected with damping liquid, the damping liquid is arranged in a container, and the container is fixedly connected with the ground or the wall of the building structure. The lower suspension device includes a positioning block, a multi-section tubular telescopic rod and a sliding block, the positioning block is internally provided with a cavity, a first sliding hole and a second sliding hole are arranged at the axis of the positioning block and at the top end and the bottom end of the cavity respectively, the sliding block is open at the top end and is wrapped around the outer periphery of the positioning block, the bottom end of the sliding block is provided with a slide rod extending upward and penetrating the second sliding hole, the top end of the slide rod is fixedly connected with a limiting block, the limiting block is slidingly connected with the inner wall of the cavity, the outer surface of the lowermost section of the multi-section tubular telescopic rod is sealingly and slidingly connected with the inner surface of the first sliding hole, the slide rod is sealingly and slidingly connected with the second sliding hole, the inner surface of the sliding block is sealingly and slidingly connected with the outer surface of the positioning block, the central pendulum rope passes through the multi-section tubular telescopic rod along the through hole and is connected with the top end of the limiting block, the bottom end of the lowermost section of the multi-section tubular telescopic rod is fixedly connected with the top end of the limiting block, the top end of the multi-section tubular telescopic rod is fixedly connected with the bottom end of the support box, and the multi-section tubular telescopic rod is coaxial with the through hole. The positioning block and the sliding block are both cubic structures, and four edge limiting rods are vertically arranged on the outer periphery of the multi-section tubular telescopic rod, the top end of each edge limiting rod is fixedly connected with the bottom end of the support box, and the bottom end of each edge limiting rod is fixedly connected with the corner of the top end of the positioning block.

3. A pendulum tuned mass damper as claimed in claim 2, characterised in that: The circuit board is provided with a calculation module, the calculation module calculates the inherent frequency and dynamic response frequency of the structure through Fourier transform for the collected data of the horizontal velocity sensor, the circuit board realizes the lifting of the mass block to adjust the vibration frequency of the damper by controlling the rotation of the first servo motor, the relative sliding of the sliding block and the positioning block is realized by controlling the lifting of the sliding block, the sliding block and the positioning block are immersed in the damping liquid, the size of the contact area with the damping liquid is adjusted through relative sliding, the circuit board adjusts the length of the central swing rope and the edge swing rope according to the data measured by the horizontal velocity sensor in real time, after the calculation of the calculation module, the discrete time domain data has a certain error after Fourier transform due to the insufficient sensitivity of the sensor, at this time, the circuit board fine tunes the frequency error through the precise self-tuning frequency algorithm.

4. A precision self-tuning algorithm for a pendulum tuned mass damper as claimed in claim 3, characterized in that, It comprises the following steps: (1) initial frequency tuning: a stable and continuous excitation is applied to the structure to be damped or the horizontal velocity sensor connected to the structure directly measures the vibration data within a certain time under the environmental excitation, the circuit board initially calculates the inherent frequency and dynamic response frequency of the structure, and controls the first servo motor to adjust the length of the edge swing rope; (2) subsequent frequency fine tuning: in the algorithm process, the first servo motor first lengthens the edge swing rope, if the test speed of the horizontal velocity sensor shows a decreasing trend, it proves that the swing rope adjustment direction is correct, the circuit board records the swing rope length and speed value at each adjustment, until the speed changes from a decreasing trend to an increasing trend, the adjustment of the swing rope length is stopped, and the output records the extreme swing rope length; if the first servo motor first lengthens the swing rope, the speed shows an increasing trend, then shorten the swing rope length, and repeat the above steps.

5. The precise self-tuning frequency algorithm of the single pendulum tuned mass damper according to claim 4, characterized in that the step (1) comprises the following specific steps: The calculation of the inherent frequency of the structure is shown in formula (1), the obtained vibration time domain data is converted into frequency domain data, the frequency spectrum density function of the signal is obtained, and the inherent frequency of the structure is obtained: ； In the formula: For time domain data, in the present invention specifically refers to velocity; is the frequency domain data; f is the frequency; t is time; j is an imaginary number; Since the sensor measures discrete time domain data, the calculated amplitude density can only correspond to a limited number of frequencies, that is, discrete Fourier transform, the discrete Fourier transform of the finite length discrete signal x(n) (n=0, 1, 2……, N-1) is defined as formula (2): ； In the formula: k=0, 1, 2……, N-1; X(k) is divided into two parts of n as even and n as odd, x1 is even, and x2 is odd, as shown in formula (3); ； Then formula (2) becomes: ； Since then equation (4) becomes: ； Since both the even and odd sequences in Equation (5) are periodic with periodicity of 2N, then Thus, Equation (5) is expressed as: ； In formula (2) - formula (6), k is all the same value, k = 0, 1, 2,..., N-1; that is, only need to get Then the inherent frequency of the structure can be obtained After converting the measured time domain data into frequency domain, the inherent frequency of the structure can be obtained, and the first servo motor adjusts the length of the edge pendulum to complete the initial frequency adjustment.

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