A shock absorber and shock avoidance method based on the principle of self-participation internal resonance

Abstract

The application discloses a kind of based on independent parametric internal resonance principle's shock absorber and shock absorbing method, the shock absorber includes: power transmission wire;Several cantilever shock absorbers are fixed on the power transmission wire by fastening screw and nut;The spatial position of the power transmission wire and cantilever shock absorber is orthogonal, and the ratio of natural frequency is preset value;The cantilever shock absorber and power transmission wire constitute independent parametric internal resonance system, and the modal damping of cantilever shock absorber is obtained by simulating the independent parametric internal resonance system under the condition that the ratio of natural frequency is preset value and the shock absorbing effect of cantilever shock absorber is best, so as to adjust the modal frequency of cantilever shock absorber.The application utilizes independent parametric internal resonance principle, realizes the substantial absorption of power transmission line vibration energy to achieve the purpose of passive shock absorbing.

Description

Technical Field

[0001] This invention belongs to the field of power transmission line technology, specifically relating to a vibration damper and vibration isolation method based on the principle of autonomous parametric internal resonance. Background Technology

[0002] In power transmission lines, vibration dampers are an important protective device, primarily used to reduce vibrations caused by wind, earthquakes, or other external forces, thereby improving the stability and reliability of the lines. Overhead power transmission lines have high pole positions and large spans. When the conductors are subjected to wind, they vibrate and gallop. This causes the transmission lines to bend periodically, resulting in fatigue effects at the bends. By suspending vibration dampers at appropriate locations on the transmission lines, the dampers move in the opposite direction to the conductors during vibration, thus eliminating or reducing the vibration and extending the service life of the transmission lines.

[0003] A vibration damper is a tuned vibration reduction device. When its natural frequency matches the vibration frequency of the power transmission line, it achieves optimal vibration reduction, transferring more of the transmission line's vibration energy to the damper system, where the damper itself dissipates this energy through its damping effect. Currently, the wind speeds causing light vibrations in power transmission lines typically range from 0.5 to 10 m / s, with vibration frequencies between 2 and 140 Hz, and the vibration direction is variable. Most existing vibration dampers can only resonate with the power transmission line in a single direction under natural conditions, and their vibration energy absorption efficiency is low, failing to provide effective vibration reduction. Therefore, there is an urgent need to develop a multi-directional vibration damper adapted to the vibration environment of power transmission lines to absorb the vibration energy generated by the power transmission lines and achieve a vibration reduction effect. Summary of the Invention

[0004] To overcome the aforementioned deficiencies of the prior art, the present invention provides a vibration damper based on the principle of autonomous parametric internal resonance, the vibration damper comprising:

[0005] Power transmission lines;

[0006] Several cantilevered vibration dampers are fixed to the power transmission line by fastening screws and nuts;

[0007] The spatial positions of the power transmission line and the cantilever vibration damper are orthogonal, and the ratio of their natural frequencies is a preset value.

[0008] The cantilever vibration damper and the transmission line constitute an autonomous parametric internal resonance system. The first two modes of the system structure are the first bending modes of the vertical cantilever beam and the transmission line in the cantilever vibration damper, respectively defined as the direct excitation mode and the parametric excitation mode.

[0009] By simulating the autonomous parametric internal resonance system, the optimal modal damping of the cantilever vibration damper is obtained under the condition that the ratio of the natural frequency to the transmission line and the cantilever vibration damper is a preset value, thereby adjusting the modal damping of the cantilever vibration damper.

[0010] Furthermore, the shock absorber includes:

[0011] The cantilevered shock absorber includes:

[0012] The clamp is provided with several threaded holes, and the fastening screws and nuts are used to fix the clamp to the power transmission line through the threaded holes;

[0013] A vertical cantilever beam, one end of which is fixed to the clamp, is used to adjust the length of the vertical cantilever beam so that the ratio of the transmission line frequency to the natural frequency of the cantilever vibration damper is a preset value.

[0014] A spherical mass block is fixed to the other end of the vertical cantilever beam. The size of the spherical mass block is determined according to the modal frequency of the required cantilever vibration damper. The modal frequency is changed by adjusting the radius of the spherical mass block to match the modal frequency of the transmission line.

[0015] Furthermore, the preset value is 1:2.

[0016] Furthermore, there are four cantilever shock absorbers, which are equidistant from each other.

[0017] A vibration reduction method based on the principle of autonomous parametric internal resonance includes the following steps:

[0018] Step S1: Measure the modal frequency ω2 of the transmission line;

[0019] Step S2: Select a vertical cantilever beam and a spherical mass block of specific dimensions so that the modal frequencies of the cantilever vibration damper and the transmission line satisfy the relationship ω1:ω2=1:2, and construct a model based on this:

[0020] The model is a lumped parameter model of an autonomous parametric internal resonance system, which is described by the following dimensionless global coupled motion equations, expressed as:

[0021]

[0022] Where x represents the horizontal displacement, i.e., the displacement of the parametric excitation mode; y represents the vertical displacement, i.e., the displacement of the directly excitation mode; μ1 represents the horizontal modal damping coefficient; u2 represents the vertical modal damping coefficient; ω1 represents the horizontal modal frequency; ω2 represents the vertical modal frequency; α1 represents the horizontal nonlinear coupling coefficient; α2 represents the vertical nonlinear coupling coefficient; G0 represents the driving amplitude; Ω represents the driving angular frequency; and ε represents the small perturbation parameter.

[0023] Equations (1) and (2) are second-order ordinary differential equations with weak quadratic coupling terms. The multi-scale method is used to derive these equations to quantify the system's response characteristics and obtain approximate solutions to equations (1) and (2). These solutions are expressed as functions of the fast variable time scale T0 and the slow variable time scale T1, specifically:

[0024] y(t,ε)=y0(T0,T1)+εy1(T0,T1)+o(ε 2 (32);

[0025] x(t,ε)=x0(T0,T1)+εx1(T0,T1)+o(ε 2 (33);

[0026] Where y(t,ε) represents the approximate solution in the vertical direction, x(t,ε) represents the approximate solution in the horizontal direction, y0(T0,T1) represents the principal solution in the vertical direction without the influence of small perturbation parameters, x0(T0,T1) represents the principal solution in the horizontal direction without the influence of small perturbation parameters, y1(T0,T1) represents the first correction of the system response in the vertical direction due to small perturbation parameters, εx1(T0,T1) represents the first correction of the system response in the horizontal direction due to small perturbation parameters, and o(ε 2 ) represents a higher-order small quantity;

[0027] Using the chain rule and ignoring higher-order terms of second order and above, the first and second derivatives with respect to time are expressed as follows:

[0028]

[0029] in, This represents the first derivative with respect to time t. This represents the second derivative with respect to time t. Let T0 be the partial derivative of the fast variable at the time scale. This represents the partial derivative of the slow variable at the time scale T1;

[0030] Substituting equations (5) and (6) into equations (1) and (2) and separating the two-order components ε 0 and ε 1 We can obtain:

[0031] Class ε 0 :

[0032] D0 2 y0+ω1 2 y0=0(36);

[0033] D0 2 x0+ω2 2x0 = 0(37);

[0034] Among them, formula (7) represents the 0th order equation in the vertical direction, and formula (8) represents the 0th order equation in the horizontal direction;

[0035] Class ε 1 :

[0036] D0 2 y1+ω2 2 y1=-2D0D1y0-2u2D0y0-α2[(D0x0) 2 +x0D0 2 x0]+G0cos(ΩT0) (38);

[0037] D0 2 x1+ω1 2 x1=-2D0D1x0-2u1D0x0-α1x0D0 2 y0 (39);

[0038] Wherein, formula (9) represents the first-order correction equation in the vertical direction, formula (10) represents the first-order correction equation in the horizontal direction, x1 represents the first-order correction solution in the horizontal direction, and y1 represents the first-order correction solution in the vertical direction;

[0039] The analytical solutions to equations (9) and (10) are further expressed as:

[0040]

[0041] Where A1(T1) represents the first-order approximate magnitude term to be determined in the horizontal direction, A2(T1) represents the first-order approximate magnitude term to be determined in the vertical direction, and cc is the conjugate complex term of each term in the formula;

[0042] The first frequency detuning parameter σ is imported to describe the detuning level between the modal frequency ω2 of the directly excited mode and the driving frequency Ω. The second frequency detuning parameter σ1 is imported to describe the detuning level between the modal frequencies ω2 and ω1 of the directly excited mode and the parametric excited mode, expressed as:

[0043] Ω=ω2+εσ(42);

[0044] ω2=2ω1+εσ1(43);

[0045] Substituting equations (11)-(14) into equations (9) and (10), we get:

[0046]

[0047] Among them, D0 2 y1+ω2 2y1 represents the dynamic equation of the first-order correction term in the vertical direction, and -2jω2(D1A2+u2A2) represents the influence of the slow variable time scale and the damping effect in the vertical direction. This represents the effect of nonlinear coupling in the horizontal direction on the vertical direction. This represents the effect of the external driving force on the vertical direction, and -2jω1(D1A1+u1A1) represents the effect of the slow variable time scale and damping effect in the horizontal direction.

[0048] In equation (15), the long-term term In the sum (16) long term Since the coefficients are all zero, we can obtain:

[0049]

[0050] Wherein, formula (17) represents the steady-state equation in the vertical direction, and formula (18) represents the steady-state equation in the horizontal direction. Indicates the complex conjugate of A1;

[0051] Furthermore, we import polar coordinates to represent A1 and A2:

[0052]

[0053] Among them, A i and The first-order approximate amplitudes A of the parametric excitation mode and the direct excitation mode are respectively. i The real part of the signal and the phase difference between the vibration response and the periodic driving signal;

[0054] Substituting equation (19) into equations (17) and (18), and separating the real and imaginary parts, we obtain the following averaged equation:

[0055]

[0056] in, This represents the phase difference between the external driving force and the vertical vibration phase. This represents the phase difference between the horizontal and vertical vibration phases.

[0057] When the autonomous parametric internal resonance system reaches a steady-state vibration state under the excitation of the driving signal, both the amplitude and phase remain stable.

[0058] Meet the conditions The steady-state conditions are as follows:

[0059]

[0060] Substituting equations (24) and (25) into equations (20)-(23), we obtain the steady-state equations of motion for the self-excited internal resonance system:

[0061] 2a2ω2σ+α2a1 2 ω1 2 cosθ2+G0cosθ1=0(55);

[0062] 2u2a2ω2+α2a1 2 ω1 2 sinθ2+G0sinθ1=0(56);

[0063] 2(σ+σ1)ω1+α1ω2 2 a2cosθ2=0(57);

[0064] 4u1ω1-α1ω2 2 a2sinθ2=0(58);

[0065] The effects of modal damping on the amplitude-frequency response curve of the direct excitation mode were verified by numerical simulation of equations (26)-(29) using MATLAB iterative programs, and the optimal modal damping was obtained.

[0066] Step S3: Assemble the clamp, vertical cantilever beam and spherical mass block 103 into a cantilever vibration damper according to the modal damping in step S2. Then fix four identical cantilever vibration dampers to the appropriate positions on the power transmission line, i.e. the power transmission conductor, using multiple fastening screws and nuts.

[0067] Step S4: Observe whether the cantilever vibration damper vibrates when the transmission line vibrates at low frequency under the action of external force, and at the same time suppress the vibration intensity of the transmission line.

[0068] If the cantilever vibration damper vibrates, then vibration reduction has been successfully achieved; otherwise, replace the vertical cantilever beam 102 with one of different lengths and continuously observe the vibration reduction effect until the cantilever vibration damper can vibrate significantly, thus achieving the vibration reduction effect.

[0069] Compared with the prior art, the beneficial effects of the present invention are:

[0070] 1) This invention utilizes the principle of autonomous parametric internal resonance to achieve a significant absorption of the vibration energy of transmission lines, thereby achieving passive vibration reduction.

[0071] 2) By setting four anti-vibration hammers in different directions as the same low-frequency resonant unit, which together with the high-frequency resonant unit form an autonomous parametric internal resonance system, the present invention can realize the rapid absorption of multi-directional vibration energy. Attached Figure Description

[0072] Figure 1 This is a schematic diagram of the anti-vibration hammer based on the principle of autonomous parametric internal resonance of the present invention;

[0073] Figure 2 This is a schematic diagram of the low-frequency resonant unit of the vibration damper based on the principle of autonomous parametric internal resonance of the present invention;

[0074] Figure 3 The figure shows the finite element simulation of the parametric excitation modes of the autonomous parametric internal resonance system of the present invention.

[0075] Figure 4 The image shows the finite element simulation of the direct excitation mode of the autonomous parametric internal resonance system of this invention.

[0076] Figure 5 This is the lumped parameter model of the autonomous parametric internal resonance system of this invention;

[0077] Figure 6 The dimensionless amplitude-frequency characteristic curves of the direct excitation modes of different modal damping coefficients u1 in the autonomous parametric internal resonance system of this invention are shown.

[0078] Figure 7 The dimensions-free amplitude-frequency characteristic curves of the direct excitation modes of different modal damping coefficients u2 in the autonomous parametric internal resonance system of this invention are shown.

[0079] Figure 8 This invention relates to the relationship between the amplitude variation of the directly excited mode and the modal damping coefficient of the parametric excited mode in the autonomous parametric internal resonance system within the autonomous parametric internal resonance region.

[0080] Among them: 1 cantilever vibration damper, 2 power transmission line, 3 fastening screw, 4 nut, 101 clamp, 1011 fastening threaded hole, 1012 connecting threaded hole, 102 vertical cantilever beam, 102, 103 spherical mass block. Detailed Implementation

[0081] 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 some embodiments of the present invention, and not all 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.

[0082] Reference Figure 1 and Figure 2 A vibration damper based on the principle of autonomous parametric internal resonance, in one example, the vibration damper includes:

[0083] 2. Transmission line;

[0084] Several cantilevered shock absorbers 1 are fixed to the power transmission line 2 by fastening screws 3 and nuts 4;

[0085] The spatial positions of the power transmission line 2 and the cantilever vibration damper 1 are orthogonal, and the ratio of their natural frequencies is a preset value of 1:2.

[0086] The cantilever vibration damper 1 and the transmission line 2 constitute an autonomous parametric internal resonance system. The first two modes of the system structure are the first bending modes of the vertical cantilever beam 102 in the cantilever vibration damper 1 and the transmission line 2, which are defined as the direct excitation mode and the parametric excitation mode, respectively.

[0087] By simulating the autonomous parametric internal resonance system, the optimal modal damping of the cantilever vibration damper is obtained under the condition that the ratio of the natural frequency to the transmission line and the cantilever vibration damper is a preset value, thereby adjusting the modal damping of the cantilever vibration damper.

[0088] To ensure the vibration damper remains stable in harsh outdoor environments and does not put too much pressure on power transmission lines, the cantilever vibration damper 11 is made of lightweight and corrosion-resistant aluminum alloy.

[0089] Furthermore, the shock absorber includes:

[0090] The cantilevered shock absorber 1 includes:

[0091] The clamp 101 is provided with several threaded holes, and the fastening screws 3 and nuts 4 fix the clamp 101 to the power transmission line 2 through the threaded holes;

[0092] A vertical cantilever beam 102 is fixed at one end to the clamp 101. The length of the vertical cantilever beam 102 is adjusted so that the ratio of the natural frequency of the power transmission line 2 to the natural frequency of the cantilever vibration damper 1 is a preset value.

[0093] A spherical mass block 103 is fixed to the other end of the vertical cantilever beam 102. The size of the spherical mass block 103 is determined according to the required modal frequency of the cantilever vibration damper 1. The modal frequency is changed by adjusting the radius of the spherical mass block 103 to match the modal frequency of the transmission line 2.

[0094] Furthermore, the preset value is 1:2.

[0095] Furthermore, there are four cantilever shock absorbers 1, which are equidistant from each other.

[0096] A vibration reduction method based on the principle of autonomous parametric internal resonance includes the following steps:

[0097] Step S1: Measure the modal frequency ω2 of the transmission line 2;

[0098] Step S2: Select a vertical cantilever beam 102 and a spherical mass block 103 of specific dimensions so that the modal frequencies of the cantilever vibration damper 1 and the transmission line 2 satisfy the relationship ω1:ω2=1:2, and construct a model based on this:

[0099] See Figure 3 and Figure 4 Their modal frequencies are 8.2398 Hz and 16.46 Hz, respectively.

[0100] See Figure 5 This is a lumped parameter model of an autonomous parametric internal resonance system consisting of a cantilevered vibration damper 11 and a power transmission conductor 22. Masses M1 and M2 represent two vibration modes in the system; in the formula, M1 and M2 correspond to the horizontal and vertical displacements, respectively. Springs K1 and K2 represent the elastic restoring forces in the system; in the formula, K1 and K2 correspond to the squares of the modal frequencies in the horizontal and vertical directions, respectively. Dampers C1 and C2 represent the energy dissipation in the system; in the formula, C1 and C2 correspond to the modal damping coefficients in the horizontal and vertical directions, respectively.

[0101] The model is a lumped parameter model of an autonomous parametric internal resonance system, which is described by the following dimensionless global coupled motion equations, expressed as:

[0102]

[0103] Where x represents the horizontal displacement, i.e., the displacement of the parametric excitation mode; y represents the vertical displacement, i.e., the displacement of the directly excitation mode; μ1 represents the horizontal modal damping coefficient; u2 represents the vertical modal damping coefficient; ω1 represents the horizontal modal frequency; ω2 represents the vertical modal frequency; α1 represents the horizontal nonlinear coupling coefficient; α2 represents the vertical nonlinear coupling coefficient; G0 represents the driving amplitude; Ω represents the driving angular frequency; and ε represents the small perturbation parameter.

[0104] Equations (1) and (2) are second-order ordinary differential equations with weak quadratic coupling terms. The multi-scale method is used to derive these equations to quantify the system's response characteristics and obtain approximate solutions to equations (1) and (2). These solutions are expressed as functions of the fast variable time scale T0 and the slow variable time scale T1, specifically:

[0105] y(t,ε)=y0(T0,T1)+εy1(T0,T1)+o(ε 2 (61);

[0106] x(t,ε)=x0(T0,T1)+εx1(T0,T1)+o(ε 2 (62);

[0107] Where y(t,ε) represents the approximate solution in the vertical direction, x(t,ε) represents the approximate solution in the horizontal direction, y0(T0,T1) represents the principal solution in the vertical direction without the influence of small perturbation parameters, x0(T0,T1) represents the principal solution in the horizontal direction without the influence of small perturbation parameters, y1(T0,T1) represents the first correction of the system response in the vertical direction due to small perturbation parameters, εx1(T0,T1) represents the first correction of the system response in the horizontal direction due to small perturbation parameters, and o(ε 2 ) represents a higher-order small quantity;

[0108] Using the chain rule and ignoring higher-order terms of second order and above, the first and second derivatives with respect to time are expressed as follows:

[0109]

[0110] in, This represents the first derivative with respect to time t. This represents the second derivative with respect to time t. Let T0 be the partial derivative of the fast variable at the time scale. This represents the partial derivative of the slow variable at the time scale T1;

[0111] Substituting equations (5) and (6) into equations (1) and (2) and separating the two-order components ε 0 and ε 1 We can obtain:

[0112] Class ε 0 :

[0113] D0 2 y0+ω1 2 y0=0(65);

[0114] D0 2 x0+ω2 2 x0 = 0(66);

[0115] Among them, formula (7) represents the 0th order equation in the vertical direction, and formula (8) represents the 0th order equation in the horizontal direction;

[0116] Class ε 1 :

[0117] D0 2 y1+ω2 2 y1=-2D0D1y0-2u2D0y0-α2[(D0x0) 2 +x0D0 2 x0]+G0cos(ΩT0) (67);

[0118] D0 2 x1+ω12 x1=-2D0D1x0-2u1D0x0-α1x0D0 2 y0 (68);

[0119] Wherein, formula (9) represents the first-order correction equation in the vertical direction, formula (10) represents the first-order correction equation in the horizontal direction, x1 represents the first-order correction solution in the horizontal direction, and y1 represents the first-order correction solution in the vertical direction;

[0120] The analytical solutions to equations (9) and (10) are further expressed as:

[0121]

[0122] Where A1(T1) represents the first-order approximate magnitude term to be determined in the horizontal direction, A2(T1) represents the first-order approximate magnitude term to be determined in the vertical direction, and cc is the conjugate complex term of each term in the formula;

[0123] The first frequency detuning parameter σ is imported to describe the detuning level between the modal frequency ω2 of the directly excited mode and the driving frequency Ω. The second frequency detuning parameter σ1 is imported to describe the detuning level between the modal frequencies ω2 and ω1 of the directly excited mode and the parametric excited mode, expressed as:

[0124] Ω=ω2+εσ(71);

[0125] ω2=2ω1+εσ1(72);

[0126] Substituting equations (11)-(14) into equations (9) and (10), we get:

[0127]

[0128] Among them, D0 2 y1+ω2 2 y1 represents the dynamic equation of the first-order correction term in the vertical direction, and -2jω2(D1A2+u2A2) represents the influence of the slow variable time scale and the damping effect in the vertical direction. This represents the effect of nonlinear coupling in the horizontal direction on the vertical direction. This represents the effect of the external driving force on the vertical direction, and -2jω1(D1A1+u1A1) represents the effect of the slow variable time scale and damping effect in the horizontal direction.

[0129] In equation (15), the long-term term In the sum (16) long term Since the coefficients are all zero, we can obtain:

[0130]

[0131] Wherein, formula (17) represents the steady-state equation in the vertical direction, and formula (18) represents the steady-state equation in the horizontal direction. Indicates the complex conjugate of A1;

[0132] Furthermore, we import polar coordinates to represent A1 and A2:

[0133]

[0134] Among them, A i and The first-order approximate amplitudes A of the parametric excitation mode and the direct excitation mode are respectively. i The real part of the signal and the phase difference between the vibration response and the periodic driving signal;

[0135] Substituting equation (19) into equations (17) and (18), and separating the real and imaginary parts, we obtain the following averaged equation:

[0136]

[0137] in, This represents the phase difference between the external driving force and the vertical vibration phase. This represents the phase difference between the horizontal and vertical vibration phases.

[0138] When the autonomous parametric internal resonance system reaches a steady-state vibration state under the excitation of the driving signal, both the amplitude and phase remain stable.

[0139] Meet the conditions The steady-state conditions are as follows:

[0140]

[0141] Substituting equations (24) and (25) into equations (20)-(23), we obtain the steady-state equations of motion for the self-excited internal resonance system:

[0142] 2a2ω2σ+α2a1 2 ω1 2 cosθ2+G0cosθ1=0(84);

[0143] 2u2a2ω2+α2a1 2 ω1 2 sinθ2+G0sinθ1=0(85);

[0144] 2(σ+σ1)ω1+α1ω2 2 a2cosθ2=0(86);

[0145] 4u1ω1-α1ω2 2 a2sinθ2=0(87);

[0146] The effects of modal damping on the amplitude-frequency response curve of the direct excitation mode were verified by numerical simulation of equations (26)-(29) using MATLAB iterative programs, and the optimal modal damping was obtained.

[0147] Where u1 is the modal damping coefficient of the parametrically excited mode, and u2 is the modal damping coefficient of the directly excited mode. Figure 6 and Figure 7 It can be seen that under the condition of low damping, that is, when u1 = 0.1 and u2 = 0.1, the modal amplitude of the system is the lowest, splitting from the original single peak into a double peak, and a trough of amplitude appears at the original resonance peak, which means that the vibration energy of the transmission line 22 is absorbed by a large amount, thereby achieving the purpose of vibration reduction.

[0148] As the modal damping coefficient u1 of the parametrically excited mode increases from 0.1 to 2.0, the amplitude-frequency response curve of the directly excited mode in the autonomous parametric internal resonance region becomes increasingly flat, and the magnitude of the mode amplitude reduction becomes smaller, meaning that the vibration energy absorbed by the transmission conductor 22 also decreases. Conversely, as the modal damping coefficient u2 of the directly excited mode increases from 0.1 to 2.0, its quality factor continuously decreases, and the double resonance peak becomes increasingly blunt, such as... Figure 7 .

[0149] Figure 8 The amplitude variation ΔA of the directly excited mode within the autonomous parametric resonance region was quantitatively characterized. 2_ The relationship between (max-min) and the modal damping coefficient u1 of the parametric excitation mode. It can be seen that ΔA 2_ (max-min) gradually approaches zero at a decreasing rate as u1 increases. The smaller the modal damping, the more significant the amplitude change; that is, the largest amplitude difference occurs when u1 = 0.1, resulting in the most significant damping effect. When u1 = 2.0, ΔA... 2_ (max-min) is almost equal to 0, resulting in the worst damping effect. Therefore, when fixing the cantilever damper 11, it should be fully secured with clamps 101 to reduce the negative impact of support damping on the damping effect.

[0150] Step S3: Assemble the clamp 101, vertical cantilever beam 102 and spherical mass block 103 into a cantilever shock absorber 1 according to the modal damping in step S2. Then fix the four identical cantilever shock absorbers 1 to the appropriate positions on the power transmission line, i.e. the power transmission conductor 2, using multiple fastening screws 3 and nuts 4.

[0151] Step S4: When the transmission line 2 experiences low-frequency vibration under external force, observe whether the cantilever vibration damper 1 vibrates, and at the same time suppress the vibration intensity of the transmission line 2.

[0152] If the cantilever vibration damper 1 vibrates, then vibration reduction is successfully achieved; otherwise, replace the vertical cantilever beam 102 with one of different lengths and continuously observe the vibration reduction effect until the cantilever vibration damper 1 can vibrate significantly, thus achieving the vibration reduction effect.

[0153] Finally, it should be noted that the above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A vibration reduction method based on the principle of autonomous parametric internal resonance, wherein the vibration damper includes: Power transmission lines; Several cantilevered vibration dampers are fixed to the power transmission line by fastening screws and nuts; The spatial positions of the power transmission line and the cantilever vibration damper are orthogonal, and the ratio of their natural frequencies is a preset value. The cantilever vibration damper and the transmission line constitute an autonomous parametric internal resonance system. The first two modes of the system structure are the first bending modes of the vertical cantilever beam and the transmission line in the cantilever vibration damper, respectively defined as the direct excitation mode and the parametric excitation mode. By simulating the autonomous parametric internal resonance system, the optimal modal damping of the cantilever vibration damper is obtained under the condition that the ratio of the natural frequency to the transmission line and the cantilever vibration damper is a preset value, thereby adjusting the modal damping of the cantilever vibration damper. Its characteristic is that it includes the following steps: Step S1: Measure the modal frequencies of the transmission line. ; Step S2: Select a vertical cantilever beam and a spherical mass block of specific dimensions so that the modal frequencies of the cantilever vibration damper and the transmission line satisfy... The relationship, and build a model based on this: The model is a lumped parameter model of an autonomous parametric internal resonance system, which is described by the following dimensionless global coupled motion equations, expressed as: ； ； in, This represents the displacement in the horizontal direction, which is also the displacement of the parametric excitation mode. This represents the vertical displacement, which is also the displacement of the directly excited mode. This represents the modal damping coefficient in the horizontal direction. This represents the modal damping coefficient in the vertical direction. Represents the modal frequencies in the horizontal direction. Indicates the modal frequency in the vertical direction; Represents the nonlinear coupling coefficient in the horizontal direction. Represents the nonlinear coupling coefficient in the vertical direction; Indicates the driving amplitude. Indicates the driving angular frequency. Indicates the parameters of small perturbations; Equations (1) and (2) are second-order ordinary differential equations with weak quadratic coupling terms. They are derived using the multi-scale method to quantitatively study the response characteristics of the system and obtain approximate solutions to equations (1) and (2), which are expressed as fast variable time scales. and slow variable time scale The function is as follows: ； ； in, This represents an approximate solution in the vertical direction. This represents an approximate solution in the horizontal direction. This represents the principal solution in the vertical direction when it is not affected by small perturbation parameters. This represents the principal solution in the horizontal direction when it is not affected by small perturbation parameters. This represents the first correction to the system response in the vertical direction caused by a small disturbance parameter. This represents the first correction to the system response in the horizontal direction caused by small perturbation parameters. Indicates a higher-order minima; Using the chain rule and ignoring higher-order terms of second order and above, the first and second derivatives with respect to time are expressed as follows: ； ； in, This represents the first derivative with respect to time t. This represents the second derivative with respect to time t. , indicating the time scale of fast variables The partial derivatives, , representing the time scale of slow variables The partial derivatives; Substitute equations (5) and (6) into equations (1) and (2) and separate the two-order components. and We can obtain: class : ； ； Among them, formula (7) represents the 0th order equation in the vertical direction, and formula (8) represents the 0th order equation in the horizontal direction; class : ； ； Wherein, formula (9) represents the first-order correction equation in the vertical direction, and formula (10) represents the first-order correction equation in the horizontal direction. This represents the first-order corrected solution in the horizontal direction. The first-order corrected solution in the vertical direction; The analytical solutions to equations (9) and (10) are further expressed as: ； ； in, This represents the undetermined first-order approximate magnitude term in the horizontal direction. This represents the undetermined first-order approximate magnitude term in the vertical direction. Let be the conjugate complex term of each term in the formula; Import first frequency detuning parameters Modal frequencies used to describe directly excited modes With drive frequency The detuning level between them, import the second frequency detuning parameter Modal frequencies of directly excited modes and parametrically excited modes and The level of detuning between them is expressed as: ； ； Substituting equations (11)-(14) into equations (9) and (10), we get: ； ； in, The dynamic equation representing the first-order correction term in the vertical direction. This represents the effects of slow variables on time scales and damping effects in the vertical direction. This represents the effect of nonlinear coupling in the horizontal direction on the vertical direction. This indicates the effect of external driving force on the vertical direction. This represents the time-scale effects and damping effects of slow variables in the horizontal direction; In equation (15), the long-term term In the long term of the sum (16) Since the coefficients are all zero, we can obtain: ； ； Wherein, formula (17) represents the steady-state equation in the vertical direction, and formula (18) represents the steady-state equation in the horizontal direction. express The complex conjugate; Furthermore, polar coordinates are imported for representation. and : ； in, and These are the first-order approximate amplitudes of the parametric excitation mode and the direct excitation mode, respectively. The real part of the signal and the phase difference between the vibration response and the periodic driving signal; Substituting equation (19) into equations (17) and (18), and separating the real and imaginary parts, we obtain the following averaged equation: ； ； ； ； in, This represents the phase difference between the external driving force and the vertical vibration phase. This represents the phase difference between the horizontal and vertical vibration phases; When the autonomous parametric internal resonance system reaches a steady-state vibration state under the excitation of the driving signal, both the amplitude and phase remain stable. Meet the conditions , The steady-state conditions are as follows: ； ； Substituting equations (24) and (25) into equations (20)-(23), we obtain the steady-state equation of motion for the self-excited internal resonance system: ； ； ； ； The effects of modal damping on the amplitude-frequency response curve of the direct excitation mode were verified by numerical simulation of equations (26)-(29) using MATLAB iterative programs, and the optimal modal damping was obtained. Step S3: Assemble the clamp, vertical cantilever beam and spherical mass block into a cantilever vibration damper according to the modal damping in step S2. Then fix four identical cantilever vibration dampers to the appropriate position on the power transmission line, i.e. the power transmission conductor, using multiple fastening screws and nuts. Step S4: Observe whether the cantilever vibration damper vibrates when the transmission line vibrates at low frequency under the action of external force, and at the same time suppress the vibration intensity of the transmission line. If the cantilever vibration damper vibrates, then vibration reduction has been successfully achieved; otherwise, replace the vertical cantilever beam with one of different lengths and continuously observe the vibration reduction effect until the cantilever vibration damper can vibrate significantly, thus achieving the vibration reduction effect.

2. The vibration reduction method according to claim 1, characterized in that, The vibration damper includes: The cantilevered shock absorber includes: The clamp is provided with several threaded holes, and the fastening screws and nuts are used to fix the clamp to the power transmission line through the threaded holes; A vertical cantilever beam, one end of which is fixed to the clamp, is used to adjust the length of the vertical cantilever beam so that the ratio of the transmission line frequency to the natural frequency of the cantilever vibration damper is a preset value. A spherical mass block is fixed to the other end of the vertical cantilever beam. The size of the spherical mass block is determined according to the modal frequency of the required cantilever vibration damper. The modal frequency is changed by adjusting the radius of the spherical mass block to match the modal frequency of the transmission line.

3. The vibration reduction method according to claim 2, characterized in that, The preset value is 1:

2.

4. The vibration reduction method according to claim 2, characterized in that, There are four cantilevered shock absorbers, which are equidistant from each other.

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