Shock-proof hammer based on autonomous parametric excitation internal resonance principle and shock-proof method

Abstract

The invention discloses a stockbridge damper based on an autonomous parameterized excitation internal resonance principle and a damping method. The stockbridge damper comprises a power transmission conductor, the plurality of cantilever type shock-proof hammers are fixed on the power transmission conductor through fastening screws and nuts; the spatial position of the power transmission conductor is orthogonal to that of the cantilever type shock-proof hammer, and the ratio of the inherent frequency is a preset value; an autonomous parametric excitation internal resonance system is formed by the cantilever type shock-proof hammer and a power transmission wire, and the modal damping of the cantilever type shock-proof hammer is obtained by simulating the autonomous parametric excitation internal resonance system under the condition that the power transmission wire and the cantilever type shock-proof hammer meet the condition that the shock-proof effect of the cantilever type shock-proof hammer is the best under the condition that the ratio of the inherent frequency is a preset value. Therefore, the modal frequency of the cantilever type shock-proof hammer is adjusted. Based on the principle of autonomous parametric excitation internal resonance, the vibration energy of the power transmission line is greatly absorbed so as to achieve the purpose of passive damping.

Description

Technical Field

[0001] The invention belongs to the technical field of power transmission lines, and in particular relates to a shock-proof hammer and a shock-proof method based on the principle of autonomous parametric internal resonance. Background Art

[0002] In power transmission lines, the anti-vibration hammer is an important protective device, mainly used to reduce the vibration of power transmission lines caused by wind, earthquake or other external forces, so as to improve the stability and reliability of the lines. The poles of overhead power transmission lines are high and the span is large. When the wires are affected by wind, they will vibrate and dance. At this time, the transmission lines will bend periodically and produce fatigue effects at the bends. At this time, after the anti-vibration hammer is hung at a suitable position on the transmission line, the anti-vibration hammer will move in the opposite direction of the wire during the vibration of the transmission line, thereby eliminating or weakening the vibration of the transmission line, thereby extending the service life of the transmission line.

[0003] The shock-absorbing hammer is a tuned vibration reduction device. When its natural frequency matches the vibration frequency of the transmission line, it can produce the best vibration reduction effect, thereby transferring more of the vibration energy of the transmission line to the shock-absorbing hammer system, and consuming this energy through the damping effect of the shock-absorbing hammer itself. At present, the wind speed range that causes breeze vibration of the transmission line is generally 0.5-10m / s, the vibration frequency is between 2-140Hz, and the vibration direction is variable. Most of the existing shock-absorbing hammers can only resonate with the transmission line in the natural environment in a single direction, and the vibration energy absorption efficiency is low, and it cannot achieve a good shock-absorbing effect. Therefore, it is urgent to propose a shock-absorbing hammer that can adapt to the vibration environment of the transmission line in multiple directions, which is used to absorb the vibration energy generated by the transmission line to achieve the effect of shock reduction. Summary of the invention

[0004] In order to overcome the above-mentioned defects of the prior art, the present invention provides a shock-absorbing hammer based on the principle of self-parametric internal resonance, the shock-absorbing hammer comprising:

[0005] Transmission lines;

[0006] A plurality of cantilever shock-absorbing hammers are fixed on the transmission wire by fastening screws and nuts;

[0007] The transmission wire and the cantilever shock-absorbing hammer are orthogonal in spatial position, and the ratio of the natural frequencies is a preset value;

[0008] The cantilever shock-absorbing hammer and the transmission line form an autonomous parametrically excited internal resonance system, and the first two modes of the system structure are the first-order bending modes of the vertical cantilever beam in the cantilever shock-absorbing hammer and the transmission line, which are defined as direct excitation mode and parameter excitation mode respectively;

[0009] The optimal modal damping of the cantilever shock-absorbing hammer is obtained by simulating the autonomous parametrically excited internal resonance system when the ratio of the natural frequencies of the transmission line and the cantilever shock-absorbing hammer is a preset value, thereby adjusting the modal damping of the cantilever shock-absorbing hammer.

[0010] Furthermore, the shock-proof hammer comprises:

[0011] The cantilever shock-absorbing hammer comprises:

[0012] A clamp is provided with a plurality of threaded holes, and the fastening screws and nuts are passed through the threaded holes to fix the clamp on the power transmission wire;

[0013] A vertical cantilever beam, one end of which is fixed on the fixture, and the ratio of the natural frequency of the power transmission wire and the cantilever shock-absorbing hammer is made to be a preset value by adjusting the length of the vertical cantilever beam;

[0014] The spherical mass block is fixed on the other end of the vertical cantilever beam. The size of the spherical mass block is determined according to the required modal frequency of the cantilever shock-absorbing hammer. The modal frequency of the spherical mass block 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-absorbing hammers, which are arranged equidistantly from each other.

[0017] A vibration reduction method based on the principle of self-parametric internal resonance comprises the following steps:

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

[0019] Step S2: Select a vertical cantilever beam and a spherical mass block of a specific size so that the modal frequencies of the cantilever shock-absorbing hammer and the transmission line satisfy the relationship of ω1:ω2=1:2, and build a model based on this:

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

[0021]

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

[0023] Among them, equations (1) and (2) are second-order ordinary differential equations with weak quadratic coupling terms. The multi-scale method is used to derive them to quantitatively study the response characteristics of the system and obtain approximate solutions of equations (1) and (2), which 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] Among them, 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 main solution in the vertical direction when it is not affected by the small disturbance parameter, x0(T0,T1) represents the main solution in the horizontal direction when it is not affected by the small disturbance parameter, y1(T0,T1) represents the first correction of the system response in the vertical direction due to the small disturbance parameter, εx1(T0,T1) represents the first correction of the system response in the horizontal direction due to the small disturbance parameter, o(ε 2 ) represents a high-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:

[0028]

[0029] in, represents the first-order derivative with respect to time t, represents the second-order derivative with respect to time t, represents the partial derivative of the fast variable time scale T0, represents the partial derivative of the slow variable time scale T1;

[0030] Substitute equations (5) and (6) into equations (1) and (2) and separate the two-order components ε 0 and ε 1 We can get:

[0031] Class ε 0 :

[0032] D0 2 y0+ω1 2 y0=0(36);

[0033] D0 2 x0+ω2 2x0=0(37);

[0034] Wherein, 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 of equations (9) and (10) are further expressed as:

[0040]

[0041] Wherein, A1(T1) represents the first-order approximate amplitude term to be determined in the horizontal direction, A2(T1) represents the first-order approximate amplitude 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 introduced to describe the detuning level between the modal frequency ω2 of the direct excitation mode and the driving frequency Ω, and the second frequency detuning parameter σ1 is introduced to describe the detuning level between the modal frequencies ω2 and ω1 of the direct excitation mode and the parameter excitation mode, which is expressed as:

[0043] Ω=ω2+εσ(42);

[0044] ω2=2ω1+εσ1(43);

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

[0046]

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

[0048] The medium and long term term in formula (15) The medium and long term terms in formula (16) The coefficients of are zero respectively, so:

[0049]

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

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

[0052]

[0053] Among them, A i and are the first-order approximate amplitudes A of the parameter excitation mode and the direct excitation mode respectively. i The real part of 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 can obtain the following averaged equation:

[0055]

[0056] in, Represents the phase difference between the external driving force and the vertical vibration phase, Indicates the phase difference between the horizontal and vertical vibration phases;

[0057] When the self-parametrically excited internal resonance system reaches a steady-state vibration state under the excitation of the driving signal, both the amplitude and phase remain stable and unchanged;

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

[0059]

[0060] Substituting equations (24) and (25) into equations (20)-(23), we can obtain the steady-state motion equation of the self-parametrically 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] By writing an iterative program in MATLAB, numerical simulation is performed on equations (26)-(29) to verify the influence of modal damping on the amplitude-frequency response curve of the direct excitation modal and obtain the optimal modal damping;

[0066] Step S3: assembling the fixture, the vertical cantilever beam and the spherical mass block 103 into a cantilever shock-absorbing hammer according to the modal damping of step S2, and then fixing four identical cantilever shock-absorbing hammers to appropriate positions on the transmission line, i.e., the transmission conductor, by means of a plurality of fastening screws and nuts;

[0067] Step S4: observing whether the cantilever shock-absorbing hammer vibrates when the transmission wire vibrates at a low frequency under the action of an external force, and suppressing the vibration intensity of the transmission wire;

[0068] If the cantilever shock-absorbing hammer vibrates, the shock absorption is successfully achieved; otherwise, the vertical cantilever beam 102 of different lengths is replaced, and the shock absorption effect is continuously observed until the cantilever shock-absorbing hammer can vibrate significantly and achieve the shock absorption effect.

[0069] Compared with the prior art, the present invention has the following beneficial effects:

[0070] 1) The present invention utilizes the principle of self-parametric internal resonance to achieve a large absorption of the vibration energy of the transmission line to achieve the purpose of passive vibration reduction.

[0071] 2) The present invention arranges four shock-absorbing hammers in different directions as the same low-frequency resonance units to form an autonomous parametric internal resonance system with the high-frequency resonance unit, thereby realizing rapid absorption of multi-directional vibration energy. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0073] Figure 2 It is a schematic diagram of a low-frequency resonance unit of a shock-absorbing hammer based on the principle of self-parametric internal resonance of the present invention;

[0074] Figure 3 It is a finite element simulation diagram of the parameter excitation mode of the self-parametrically excited internal resonance system of the present invention;

[0075] Figure 4 It is a finite element simulation diagram of the direct excitation mode of the self-parametrically excited internal resonance system of the present invention;

[0076] Figure 5 It is a lumped parameter model of the self-parametrically excited internal resonance system of the present invention;

[0077] Figure 6 It is the dimensionless amplitude-frequency characteristic curve of the direct excitation mode with different modal damping coefficients u1 in the self-parametric excited internal resonance system of the present invention;

[0078] Figure 7 The dimensionless amplitude-frequency characteristic curve of the direct excitation mode with different modal damping coefficients u2 in the self-parametrically excited internal resonance system of the present invention;

[0079] Figure 8 The present invention implements the relationship between the amplitude variation of the direct excitation mode in the self-parametric excitation internal resonance region and the modal damping coefficient of the parameter excitation mode in the self-parametric excitation internal resonance system;

[0080] Wherein: 1 cantilever shock-absorbing hammer, 2 power transmission wire, 3 fastening screws, 4 nuts, 101 clamp, 1011 fastening threaded hole, 1012 connecting threaded hole, 102 vertical cantilever beam 102, 103 spherical mass block. DETAILED DESCRIPTION

[0081] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0082] Reference Figure 1 and Figure 2 , a shock-absorbing hammer based on the principle of self-parametric internal resonance, in one example, the shock-absorbing hammer comprises:

[0083] Transmission line 2;

[0084] A plurality of cantilever shock-absorbing hammers 1 are fixed on the transmission wire 2 by means of fastening screws 3 and nuts 4;

[0085] The transmission conductor 2 and the cantilever shock-absorbing hammer 1 are orthogonal in spatial position, and the ratio of the natural frequencies is a preset value, which is 1:2;

[0086] The cantilever shock-absorbing hammer 1 and the transmission line 2 constitute an autonomous parametrically excited internal resonance system, and the first two modes of the system structure are the first-order bending modes of the vertical cantilever beam 102 in the cantilever shock-absorbing hammer 1 and the transmission line 2, which are defined as direct excitation mode and parameter excitation mode respectively;

[0087] The optimal modal damping of the cantilever shock-absorbing hammer is obtained by simulating the autonomous parametrically excited internal resonance system when the ratio of the natural frequencies of the transmission line and the cantilever shock-absorbing hammer is a preset value, thereby adjusting the modal damping of the cantilever shock-absorbing hammer.

[0088] In order to ensure that the shock-absorbing hammer remains stable for a long time in a harsh outdoor environment and its weight does not cause too much pressure on the transmission line, the overall material of the cantilever shock-absorbing hammer 11 is selected from lightweight and corrosion-resistant aluminum alloy.

[0089] Furthermore, the shock-proof hammer comprises:

[0090] The cantilever shock-absorbing hammer 1 comprises:

[0091] The clamp 101 is provided with a plurality of threaded holes, and the fastening screws 3 and nuts 4 are used to fix the clamp 101 on the power transmission wire 2 through the threaded holes;

[0092] A vertical cantilever beam 102, one end of which is fixed on the fixture 101, and the ratio of the natural frequency of the power transmission wire 2 and the cantilever shock-absorbing hammer 1 is made to be a preset value by adjusting the length of the vertical cantilever beam 102;

[0093] The spherical mass block 103 is fixed on 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 shock-absorbing hammer 1. The modal frequency of the spherical mass block 103 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-absorbing hammers 1 which are arranged equidistantly from each other.

[0096] A vibration reduction method based on the principle of self-parametric internal resonance comprises the following steps:

[0097] Step S1: measuring 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 a specific size, so that the modal frequencies of the cantilever shock-absorbing hammer 1 and the transmission line 2 satisfy the relationship of ω1:ω2=1:2, and construct a model based on this:

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

[0100] See also Figure 5 It is a lumped parameter model of an autonomous parametrically excited internal resonance system consisting of a cantilever shock-absorbing hammer 11 and a transmission line 22. Among them, the mass blocks M1 and M2 represent the two vibration modes in the system; in the formula, M1 and M2 correspond to the displacements in the horizontal and vertical directions, respectively. The 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. The dampers C1 and C2 represent the energy dissipation in the system, and 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 parametrically excited internal resonance system, which is described by the following dimensionless global coupled motion equations:

[0102]

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

[0104] Among them, equations (1) and (2) are second-order ordinary differential equations with weak quadratic coupling terms. The multi-scale method is used to derive them to quantitatively study the response characteristics of the system and obtain approximate solutions of equations (1) and (2), which 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] Among them, 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 main solution in the vertical direction when it is not affected by the small disturbance parameter, x0(T0,T1) represents the main solution in the horizontal direction when it is not affected by the small disturbance parameter, y1(T0,T1) represents the first correction of the system response in the vertical direction due to the small disturbance parameter, εx1(T0,T1) represents the first correction of the system response in the horizontal direction due to the small disturbance parameter, o(ε 2 ) represents a high-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:

[0109]

[0110] in, represents the first-order derivative with respect to time t, represents the second-order derivative with respect to time t, represents the partial derivative of the fast variable time scale T0, represents the partial derivative of the slow variable time scale T1;

[0111] Substitute equations (5) and (6) into equations (1) and (2) and separate the two-order components ε 0 and ε 1 We can get:

[0112] Class ε 0 :

[0113] D0 2 y0+ω1 2 y0=0(65);

[0114] D0 2 x0+ω2 2 x0=0(66);

[0115] Wherein, 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 of equations (9) and (10) are further expressed as:

[0121]

[0122] Wherein, A1(T1) represents the first-order approximate amplitude term to be determined in the horizontal direction, A2(T1) represents the first-order approximate amplitude 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 introduced to describe the detuning level between the modal frequency ω2 of the direct excitation mode and the driving frequency Ω, and the second frequency detuning parameter σ1 is introduced to describe the detuning level between the modal frequencies ω2 and ω1 of the direct excitation mode and the parameter excitation mode, which is expressed as:

[0124] Ω=ω2+εσ(71);

[0125] ω2=2ω1+εσ1(72);

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

[0127]

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

[0129] The medium and long term term in formula (15) The medium and long term terms in formula (16) The coefficients of are zero respectively, so:

[0130]

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

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

[0133]

[0134] Among them, A i and are the first-order approximate amplitudes A of the parameter excitation mode and the direct excitation mode respectively. i The real part of 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 can obtain the following averaged equation:

[0136]

[0137] in, Represents the phase difference between the external driving force and the vertical vibration phase, Indicates the phase difference between the horizontal and vertical vibration phases;

[0138] When the self-parametrically excited internal resonance system reaches a steady-state vibration state under the excitation of the driving signal, both the amplitude and phase remain stable and unchanged;

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

[0140]

[0141] Substituting equations (24) and (25) into equations (20)-(23), we can obtain the steady-state motion equation of the self-parametrically 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 iterative program written in MATLAB is used to perform numerical simulation on equations (26)-(29) to verify the influence of modal damping on the amplitude-frequency response curve of the direct excitation modal and obtain the optimal modal damping.

[0147] Among them, u1 is the modal damping coefficient of the parametric excitation mode, and u2 is the modal damping coefficient of the direct excitation mode. Figure 6 and Figure 7 It can be seen that under the condition of small 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 double peaks, and an amplitude trough appears at the original resonance peak, which means that the vibration energy of the transmission line 22 is greatly absorbed, thereby achieving the purpose of shock absorption.

[0148] As the modal damping coefficient u1 of the parametric excitation mode increases from 0.1 to 2.0, the amplitude-frequency response curve of the direct excitation mode in the self-parametric internal resonance region becomes flatter and the amplitude of the modal decreases, that is, the vibration energy absorbed by the transmission line 22 also decreases. On the contrary, as the modal damping coefficient u2 of the direct excitation mode increases from 0.1 to 2.0, its own quality factor continues to decrease, and the double resonance peak becomes more and more blunt, such as Figure 7 .

[0149] Figure 8 The amplitude change ΔA of the directly excited mode in the self-parametric internal resonance region is quantitatively characterized. 2_ (max-min) and the modal damping coefficient u1 of the parameter excitation mode. It can be seen that ΔA 2_ (max-min) gradually approaches zero at a decreasing rate as u1 increases. When the modal damping is smaller, the amplitude change is more obvious, that is, when u1=0.1, there is the largest amplitude difference and the shock absorption effect is the most obvious. When u1=2.0, ΔA 2_ (max-min) is almost equal to 0, and the shock absorption effect is the worst. Therefore, when fixing the cantilever shock-absorbing hammer 11, it is necessary to fully fix it by the clamp 101 to reduce the negative impact of the support damping on the shock absorption effect.

[0150] Step S3: assembling the fixture 101, the vertical cantilever beam 102 and the spherical mass block 103 into a cantilever shock-absorbing hammer 1 according to the modal damping of step S2, and then fixing four completely identical cantilever shock-absorbing hammers 1 to appropriate positions on the transmission line, i.e., the transmission conductor 2, by means of a plurality of fastening screws 3 and nuts 4;

[0151] Step S4: observing whether the cantilever shock-absorbing hammer 1 vibrates when the transmission wire 2 vibrates at a low frequency under the action of an external force, and suppressing the vibration intensity of the transmission wire 2;

[0152] If the cantilever shock-absorbing hammer 1 vibrates, shock absorption is successfully achieved; otherwise, the vertical cantilever beam 102 of different lengths is replaced, and the shock absorption effect is continuously observed until the cantilever shock-absorbing hammer 1 can vibrate significantly and achieve the shock absorption effect.

[0153] Finally, it should be noted that the above are only 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 aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A shock-absorbing hammer based on the principle of self-parametric internal resonance, characterized in that: The shock-proof hammer comprises: Transmission lines; A plurality of cantilever shock-absorbing hammers are fixed on the transmission wire by fastening screws and nuts; The transmission wire and the cantilever shock-absorbing hammer are orthogonal in spatial position, and the ratio of the natural frequencies is a preset value; The cantilever shock-absorbing hammer and the transmission line form an autonomous parametrically excited internal resonance system, and the first two modes of the system structure are the first-order bending modes of the vertical cantilever beam in the cantilever shock-absorbing hammer and the transmission line, which are defined as direct excitation mode and parameter excitation mode respectively; The optimal modal damping of the cantilever shock-absorbing hammer is obtained by simulating the autonomous parametrically excited internal resonance system when the ratio of the natural frequencies of the transmission line and the cantilever shock-absorbing hammer is a preset value, thereby adjusting the modal damping of the cantilever shock-absorbing hammer.

2. The anti-vibration hammer based on the principle of self-parametric internal resonance according to claim 1, characterized in that: The shock-proof hammer comprises: The cantilever shock-absorbing hammer comprises: A clamp is provided with a plurality of threaded holes, and the fastening screws and nuts are passed through the threaded holes to fix the clamp on the power transmission wire; A vertical cantilever beam, one end of which is fixed on the fixture, and the ratio of the natural frequency of the power transmission wire and the cantilever shock-absorbing hammer is made to be a preset value by adjusting the length of the vertical cantilever beam; The spherical mass block is fixed on the other end of the vertical cantilever beam. The size of the spherical mass block is determined according to the required modal frequency of the cantilever shock-absorbing hammer. The modal frequency of the spherical mass block is changed by adjusting the radius of the spherical mass block to match the modal frequency of the transmission line.

3. The anti-vibration hammer based on the principle of self-parametric internal resonance according to claim 2, characterized in that: The preset value is 1:

2.

4. The anti-vibration hammer based on the principle of self-parametric internal resonance according to claim 2, characterized in that: There are four cantilever shock-absorbing hammers, which are arranged equidistantly from each other.

5. A shock reduction method based on the principle of autonomous parametric internal resonance, based on the shock-absorbing hammer based on the principle of autonomous parametric internal resonance as claimed in any one of claims 1 to 4, characterized in that: The following steps are involved: Step S1: measuring the modal frequency ω2 of the transmission line; Step S2: Select a vertical cantilever beam and a spherical mass block of a specific size so that the modal frequencies of the cantilever shock-absorbing hammer and the transmission line satisfy the relationship of ω1:ω2=1:2, and build a model based on this: The model is a lumped parameter model of an autonomous parametrically excited internal resonance system, which is described by the following dimensionless global coupled motion equations: Wherein, x represents the displacement in the horizontal direction, i.e., the displacement of the parameter excitation mode, y represents the displacement in the vertical direction, i.e., the displacement of the direct excitation mode, μ1 represents the modal damping coefficient in the horizontal direction, u2 represents the modal damping coefficient in the vertical direction, ω1 represents the modal frequency in the horizontal direction, ω2 represents the modal frequency in the vertical direction; α1 represents the nonlinear coupling coefficient in the horizontal direction, α2 represents the nonlinear coupling coefficient in the vertical direction; G0 represents the driving amplitude, Ω represents the driving angular frequency, and ε represents the small disturbance parameter; Among them, equations (1) and (2) are second-order ordinary differential equations with weak quadratic coupling terms. The multi-scale method is used to derive them to quantitatively study the response characteristics of the system and obtain approximate solutions of equations (1) and (2), which are expressed as functions of the fast variable time scale T0 and the slow variable time scale T1, specifically: y(t,ε)=y0(T0,T1)+εy1(T0,T1)+o(ε 2 ) (3); x(t,ε)=x0(T0,T1)+εx1(T0,T1)+o(ε 2 ) (4); Among them, 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 main solution in the vertical direction when it is not affected by the small disturbance parameter, x0(T0,T1) represents the main solution in the horizontal direction when it is not affected by the small disturbance parameter, y1(T0,T1) represents the first correction of the system response in the vertical direction due to the small disturbance parameter, εx1(T0,T1) represents the first correction of the system response in the horizontal direction due to the small disturbance parameter, o(ε 2 ) represents a high-order small quantity; 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: in, represents the first-order derivative with respect to time t, represents the second-order derivative with respect to time t, represents the partial derivative of the fast variable time scale T0, represents the partial derivative of the slow variable time scale T1; Substitute equations (5) and (6) into equations (1) and (2) and separate the two-order components ε 0 and ε 1 We can get: Class ε 0 : D0 2 y0+ω1 2 y0=0 (7); D0 2 x0+ω2 2 x0=0 (8); Wherein, formula (7) represents the 0th order equation in the vertical direction, and formula (8) represents the 0th order equation in the horizontal direction; Class ε 1 : D0 2 y1+ω2 2 y1=-2D0D1y0-2u2D0y0-α2[(D0x0) 2 +x0D0 2 x0]+G0cos(ΩT0) (9); D0 2 x1+ω1 2 x1=-2D0D1x0-2u1D0x0-α1x0D0 2 y0 (10); 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; The analytical solutions of equations (9) and (10) are further expressed as: Wherein, A1(T1) represents the first-order approximate amplitude term to be determined in the horizontal direction, A2(T1) represents the first-order approximate amplitude term to be determined in the vertical direction, and cc is the conjugate complex term of each term in the formula; The first frequency detuning parameter σ is introduced to describe the detuning level between the modal frequency ω2 of the direct excitation mode and the driving frequency Ω, and the second frequency detuning parameter σ1 is introduced to describe the detuning level between the modal frequencies ω2 and ω1 of the direct excitation mode and the parameter excitation mode, which is expressed as: Ω=ω2+εσ(13); ω2=2ω1+εσ1(14); Substituting equations (11)-(14) into equations (9) and (10), we obtain: Among them, D0 2 y1+ω2 2 y1 represents the dynamic equation of the first-order correction term in the vertical direction, -2jω2(D1A2+u2A2) represents the influence of the slow variable time scale and damping effect in the vertical direction, represents the influence of the nonlinear coupling effect in the horizontal direction on the vertical direction, represents the influence of the external driving force on the vertical direction, -2jω1(D1A1+u1A1) represents the influence of the slow variable time scale and the damping effect in the horizontal direction; The medium and long term term in formula (15) The medium and long term terms in formula (16) The coefficients of are zero respectively, so: Among them, formula (17) represents the steady-state equation in the vertical direction, and formula (18) represents the steady-state equation in the horizontal direction. represents the complex conjugate of A1; Furthermore, we can import polar coordinates to represent A1 and A2: Among them, A i and are the first-order approximate amplitudes A of the parameter excitation mode and the direct excitation mode respectively. i The real part of 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 can obtain the following averaged equation: in, Represents the phase difference between the external driving force and the vertical vibration phase, Indicates the phase difference between the horizontal and vertical vibration phases; When the self-parametrically excited internal resonance system reaches a steady-state vibration state under the excitation of the driving signal, both the amplitude and phase remain stable and unchanged; Satisfy the conditions The steady-state conditions are as follows: Substituting equations (24) and (25) into equations (20)-(23), we can obtain the steady-state motion equation of the self-parametrically excited internal resonance system: 2a2ω2σ+α2a1 2 ω1 2 cosθ2+G0cosθ1=0(26); 2u2a2ω2+α2a1 2 ω1 2 sinθ2+G0sinθ1=0(27); 2(σ+σ1)ω1+α1ω2 2 a2cosθ2=0(28); 4u1ω1-α1ω2 2 a2sinθ2=0(29); The iterative program written in MATLAB is used to perform numerical simulation on equations (26)-(29) to verify the influence of modal damping on the amplitude-frequency response curve of the direct excitation modal and obtain the optimal modal damping. Step S3: assembling the fixture, the vertical cantilever beam and the spherical mass block into a cantilever shock-absorbing hammer according to the modal damping of step S2, and then fixing four completely identical cantilever shock-absorbing hammers to appropriate positions on the transmission line, i.e., the transmission conductor, by means of a plurality of fastening screws and nuts; Step S4: observing whether the cantilever shock-absorbing hammer vibrates when the transmission wire vibrates at a low frequency under the action of an external force, and suppressing the vibration intensity of the transmission wire; If the cantilever shock-absorbing hammer vibrates, shock absorption is successfully achieved; otherwise, replace the vertical cantilever beams of different lengths and continuously observe the shock absorption effect until the cantilever shock-absorbing hammer can vibrate obviously and achieve the shock absorption effect.

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