A double-annular strong magnetic array nonlinear dynamic vibration absorber for suspension rod vibration reduction and design method

Abstract

The present invention discloses a double-annular strong magnetic array nonlinear dynamic vibration absorber and design method for suspension vibration reduction, which belongs to the field of structural vibration control. The installation position and quantity are designed according to the vibration reduction requirements, and one is usually installed at the midpoint of the suspension. The vibration absorber comprises inner and outer magnetic ring arrays, counterweights, universal wheels and a base. It feeds back the control force in the opposite direction of the suspension vibration during movement, so that the suspension vibration energy is transferred to the vibration absorber and then less returned to the suspension, and the energy is dissipated through friction between the universal wheel and the base, the installation of air dampers and other measures. It introduces nonlinear stiffness, so that the optimal parameter domain range is expanded from the line domain to the surface domain, and thus has the outstanding advantages of easy parameter tuning and high vibration reduction robustness, and is easy to install, durable, and requires no or less maintenance. It is applicable to single, double and four-cable suspensions, and is expected to achieve the goal of good vibration reduction effect throughout the life cycle of the suspension, which has positive significance for ensuring driving and bridge safety and extending the service life of the suspension.

Description

Technical Field

[0001] The present invention belongs to the technical field of engineering structure vibration control, specifically the field of passive structure control based on nonlinear dynamic vibration absorbers, and its specific application is the vibration control of hangers and other cable structures of suspension bridges and arch bridges. Background Art

[0002] Long-span cable-supported bridges are often important transportation hubs. They are often built in areas with complex terrain, intense atmospheric activity and frequent strong winds, such as rivers, lakes, and deep mountains and canyons. As the key load-bearing components of suspension bridges and arch bridges, the hangers become thinner, longer and more flexible as the span of the bridge gradually increases. In addition, their characteristics such as low damping lead to the influence of prominent wind-induced dynamic effects and the accumulation of fatigue damage caused by long-term reciprocating vibration. These problems have become one of the key challenges facing their long-term safe service and service life. In recent years, the video recordings of the monitoring systems of some long-span suspension bridges show that the hangers have repeatedly vibrated violently in extreme weather, which has attracted more and more attention from researchers and engineers. Therefore, effective vibration reduction measures need to be taken to control the vibration of the hangers to ensure their service and driving safety and extend their service life.

[0003] At present, the commonly used method is to install a separator or a tuned mass damper (TMD): (1) It is impossible to install a separator on a single hanger, and the requirements for achieving optimal control of TMD are often more stringent, the optimal parameter selection range in the design is narrow, and the TMD is prone to spring fatigue, corrosion and aging problems during long-term service, which leads to changes in its frequency, greatly reducing the vibration reduction effect of TMD; at the same time, TMD has the undesirable phenomenon of increased vibration response of the controlled structure under loads in a specific frequency band range, and it is necessary to narrow the bandwidth of this frequency band and reduce the vibration response amplitude within this range. (2) Installing a separator between the cables of double-cable and four-cable hangers can effectively avoid the cable collision phenomenon; but the separator has little vibration reduction effect in the direction perpendicular to the double hanger plane; for the four-cable hanger, it has a certain vibration reduction effect in both directions, but the galloping aerodynamic interference still causes its vibration problems to be prominent. Therefore, the hanger still lacks a set of vibration control solutions with good vibration reduction effect, easy parameter tuning, strong control robustness, easy maintenance and relatively wide applicability.

[0004] The present invention proposes a double-ring strong magnet array nonlinear dynamic vibration absorber for suspension vibration reduction, which is a passive structural control device. The linear stiffness and nonlinear stiffness are controlled by changing the geometric parameters and physical parameters of the inner and outer ring strong magnet arrays, and the friction between the universal wheel and the vibration absorber base or the installation of air dampers are used to dissipate energy, thereby suppressing the vibration of the suspension to be controlled. Due to the introduction of nonlinear stiffness, the optimal parameter domain range has been greatly expanded, the robustness of the vibration reduction effect has been effectively improved, and the undesirable phenomenon of increasing the vibration response of the controlled structure under loads in a specific frequency band range has been greatly improved compared to TMD; These characteristics make it possible to achieve good vibration reduction effects when applied to suspensions, and have the advantages of easy parameter tuning, strong durability, easy maintenance, and applicability to single / double / four-cable suspensions.

[0005] The present invention provides a convenient and practical solution for vibration control of long-span bridge suspenders, and provides support for ensuring the safe service and service life of the suspenders. This specification only uses the application background of long-span bridge suspenders as an example, and the present invention is also applicable to vibration control of other cable structures. Summary of the invention

[0006] The present invention provides a double-annular strong magnet array nonlinear dynamic vibration absorber for reducing vibration of a bridge hanger, which can reduce the horizontal dynamic response of the hanger under various excitations and suppress its vibration.

[0007] The technical solution of the present invention:

[0008] A double-ring strong magnetic array nonlinear dynamic vibration absorber for boom vibration reduction, comprising an inner magnetic ring array (2), an outer magnetic ring array (3), a counterweight (4), a universal wheel (5) and a base (6); wherein, when used on a boom (1) in service, the inner magnetic ring array (2) is composed of two inner ring split bodies (7) spliced ​​together, each inner ring split body (7) having a designed number of slots, each slot having an inner ring magnetic tile (8), an inner ring limit steel ring (9) being fixed to the corresponding inner ring split body (7) by bolts, an anti-skid washer being added to the inner side of the inner ring split body (7), and the inner magnetic ring array (2) being fixed to the boom (1). The outer magnetic ring array (3) is similar in structure to the inner magnetic ring array (2). Each outer magnetic tile (16) is placed in a designed slot and fixed to the outer ring split body 1 (17) and the outer ring split body 2 (18) by means of an outer ring limiting steel ring (15). The outer magnetic ring array (3) is connected to the counterweight (4) and the universal wheel (5) respectively by bolts. The counterweight (4) is installed on the periphery of the outer magnetic ring array (3) and fixed thereto. The counterweight (4) is a square body composed of four rectangular mass blocks spliced ​​together by bolts. The base (6) is spliced ​​together by two identical base split bodies (21). An anti-slip gasket is provided on the inner side thereof. The base (6) is fixed to the installation position of the suspension rod (1) by bolts and is used to support the outer magnetic ring array (3) thereon. A counterweight (4) and a universal wheel (5); the universal wheel (5) is in direct contact with a base (6), can rotate in any direction, and provides damping through friction with the base (6), the magnitude of the damping provided being adjusted by changing the friction coefficient between the universal wheel (5) and the base (6); energy is dissipated by damping provided by friction, or by installing an air damper between the inner magnetic ring array (2) and the outer magnetic ring array (3); the size of the counterweight (4), the size of the inner magnetic ring tile (8), and the size of the outer magnetic ring tile (16) are designed according to the basic parameters of the suspension rod (1) to be controlled, and the magnetic force between the inner magnetic ring array (2) and the outer magnetic ring array (3) ensures that the outer magnetic ring array (3) does not collide with the inner magnetic ring array (2) during movement; the installation position and number of the double annular strong magnetic array nonlinear dynamic vibration absorber on the suspension rod (1) are designed according to the dynamic characteristics of the suspension rod (1) to be controlled and its vibration reduction requirements, and at least one is installed at the midpoint position.

[0009] A design method for a double annular strong magnet array nonlinear dynamic vibration absorber for suspension rod vibration reduction, the steps are as follows:

[0010] Step 1: obtain the basic characteristics of the controlled boom (1) by field survey or reviewing the design parameters: the outer diameter including the sheath and the natural frequency;

[0011] Step 2: Determine the basic design parameters of the double annular strong magnet array nonlinear dynamic vibration absorber to be designed:

[0012] 1) The ratio of the sum of the mass of the outer magnetic ring array (3) and the counterweight (4) to the modal mass of the suspension rod (1): 1% to 5%. The greater the mass ratio within this range, the better the vibration reduction effect. The ratio should be determined based on the vibration reduction requirements of the suspension rod (1);

[0013] 2) Damping ratio of vibration absorber: The design damping ratio of the vibration absorber is the design damping ratio of the optimal tuned mass damper under the same mass ratio;

[0014] 3) Linear stiffness and cubic stiffness of vibration absorber: The numerical model of the suspension rod-vibration absorber system is established as shown in formula (1):

[0015]

[0016] Among them, w(t) represents the vector composed of displacements corresponding to each degree of freedom of the suspender, and They correspond to their velocity and acceleration respectively; M is the mass matrix of the hanger; C is the damping matrix of the hanger, using Rayleigh damping; K is the stiffness matrix of the hanger; F(t) is the sum of the external load on the hanger and the reaction force of the vibration absorber on the hanger; m, c, k1, k2 represent the mass, damping, linear stiffness and nonlinear stiffness of the vibration absorber respectively; v represents the displacement of the vibration absorber, denote its velocity and acceleration respectively; one end of the suspension rod is the starting point of the x-axis, x is the x-axis coordinate of the point on the suspension rod, d is the installation position of the vibration absorber on the x-axis, and δ(xd) is the Dirac function;

[0017] Formula (2) is the parameter optimization objective function,

[0018]

[0019] Among them, Δ, Δ con Respectively represent the root mean square value, variance or other vibration reduction effect evaluation index of the displacement or velocity time history response of a point on the hanger under the same white noise load when it is uncontrolled and controlled, and are selected or established according to the vibration reduction requirements;

[0020] According to the optimal linear stiffness of TMD, the linear stiffness and nonlinear stiffness parameter optimization range of the nonlinear vibration absorber are determined. The dynamic response of the hanger is calculated by calling the numerical model of the hanger-absorber system under the action of multi-point white noise load, and the optimal linear stiffness and optimal nonlinear stiffness values ​​are obtained by automatic optimization.

[0021] 4) Geometric parameters of inner and outer magnetic ring arrays: comprehensively considering the cost of the vibration absorber and the cross-sectional dimensions of the suspension rod to be controlled, determine the number of magnetic tiles, the central angle of the magnetic tiles, and the inner diameter of the magnetic tiles of the inner magnetic ring array (2) and the outer magnetic ring array (3); establish a parameterized electromagnetic field numerical model of a double-ring strong magnetic array nonlinear dynamic vibration absorber system, and adjust the thickness and height of the magnetic tiles so that the inner and outer magnetic ring array assembly composed of the inner magnetic ring array (2) and the outer magnetic ring array (3) reaches the designed linear stiffness value and the designed cubic stiffness value;

[0022] 5) Geometric parameters of the vibration absorber counterweight (4): the mass of the vibration absorber counterweight (4) is obtained by subtracting the mass of the outer magnetic ring array (3) from the total mass of the vibration absorber. The length, width and height of the counterweight (4) are then designed according to the density of the counterweight block;

[0023] Step 3, processing and manufacturing a double annular strong magnetic array nonlinear dynamic vibration absorber according to the design parameters obtained in step 2;

[0024] Step 4: Install the manufactured double-annular strong magnet array nonlinear dynamic vibration absorber on the laboratory suspension rod, use a dynamometer and a ruler to measure the force-displacement relationship of the double-annular strong magnet array nonlinear dynamic vibration absorber to ensure that its linear stiffness and cubic stiffness are the designed values; allow it to move freely, measure its displacement signal, and determine its damping ratio using methods such as the free vibration attenuation method, and adjust the damping ratio by adjusting the friction between the universal wheel (5) and the base (6) or by setting other damping methods to achieve or approach the optimal damping ratio.

[0025] The beneficial effect of the present invention is that the double annular strong magnet array nonlinear dynamic vibration absorber installed on the bridge hanger can effectively reduce the vibration displacement response and vibration velocity response of the hanger, ensure the safety of the hanger's service and driving, and reduce the fatigue damage of the hanger to effectively extend its service life; since the invention introduces nonlinear stiffness and linear stiffness at the same time, it has the advantages of easy parameter tuning, high robustness of vibration reduction effect, easy installation, no or only a small amount of maintenance and easy maintenance, and is applicable to single, double and four-cable hangers, etc., and is expected to achieve the goal of good vibration reduction effect throughout the life cycle of the hanger. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a schematic diagram of the invented suspension rod double annular strong magnet array nonlinear dynamic vibration absorber.

[0027] Figure 2 It is a schematic diagram of the inner magnetic ring array.

[0028] Figure 3 It is a schematic diagram of the outer magnetic ring array.

[0029] Figure 4 It is a schematic diagram of the counterweight split.

[0030] Figure 5 This is a schematic diagram of the base split.

[0031] In the figure: 1 suspension rod; 2 inner magnetic ring array; 3 outer magnetic ring array; 4 counterweight; 5 universal wheel; 6 base; 7 inner ring split; 8 inner ring magnetic tile; 9 inner ring limiting steel ring; 10 first bolt hole; 11 second bolt hole; 12 third bolt hole; 13 fourth bolt hole; 14 fifth bolt hole; 15 outer ring limiting steel ring; 16 outer ring magnetic tile; 17 outer ring split one; 18 outer ring split two; 19 sixth bolt hole; 20 seventh bolt hole; 21 base split. DETAILED DESCRIPTION

[0032] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions. Taking a suspension rod of a suspension bridge as an example, the vibration absorber size parameter design method and installation process of the present invention are described in detail, and the effect of the present invention on suspension rod vibration reduction is explained in conjunction with numerical simulation results.

[0033] The selected suspension bridge hanger has an effective calculated length of 60.954m and a hanger mass of 2961Kg. The first-order natural frequency of the hanger is 1.952Hz through finite element modeling and analysis. According to the steps proposed in the present invention, the size of the double-ring strong magnetic array nonlinear dynamic vibration absorber is designed. The sum of the outer magnetic ring array and the counterweight is 39.09Kg, and the mass ratio to the controlled hanger is set to 1.32%. The optimal damping value of the vibration absorber is calculated to be 70N / (m / s), the optimal linear stiffness value is 4438N / m, and the optimal cubic stiffness value is 1.511× 10 6 N / m 3 . Based on the electromagnetic field finite element analysis software MAXWELL, a parametric electromagnetic field numerical model of the double-ring strong magnetic array is established, and the parameters of the double-ring strong magnetic array nonlinear dynamic vibration absorber are calculated as follows: the number of magnetic tiles of the inner and outer magnetic ring arrays is 9, the thickness is 0.018m, the height is 0.1m, the center angle is 30 degrees, the inner radius of the magnetic tile of the inner magnetic ring array is 61.5mm, and the inner radius of the magnetic tile of the outer magnetic ring array is 129.5mm; the four counterweights are the same, and the height of each counterweight is 0.1m, the thickness is 0.04m, and the length is 0.36m. When the mass ratio changes, these parameters change accordingly.

[0034] In order to verify the vibration reduction effect of the vibration absorber, a finite element model of the controlled boom was established based on SIMULINK software. The transient analysis method was used to obtain the dynamic responses of the boom before and after the installation of the double annular strong magnet array nonlinear dynamic vibration absorber. The displacement and velocity dynamic response results before and after the installation of the damper at the midpoint of the boom show that under exactly the same excitation, the displacement and velocity response of the midpoint of the boom are significantly reduced after the vibration absorber is installed.

[0035] Table 1 shows the comparison results of the dynamic response of the midpoint of a certain suspension rod under the same band-limited white noise excitation with and without the double annular strong magnet array nonlinear dynamic vibration absorber. These results are the average values ​​of 20 sets of dynamic response calculation results under random white noise excitation. It can be seen that: after the invented vibration absorber is installed, the displacement and velocity vibration responses of the midpoint of the suspension rod are significantly reduced, and the vibration reduction effect becomes better with the increase of the mass ratio; the invented double annular strong magnet array nonlinear dynamic vibration absorber has a significant inhibitory effect on the vibration of the suspension rod.

[0036] Table 1. The reduction of the midpoint vibration response index of a certain suspension rod after the invented nonlinear dynamic vibration absorber is installed

[0037]

Claims

1. A double annular strong magnet array nonlinear dynamic vibration absorber for suspension rod vibration reduction, characterized in that: The double-ring strong magnetic array nonlinear dynamic vibration absorber comprises an inner magnetic ring array (2), an outer magnetic ring array (3), a counterweight (4), a universal wheel (5) and a base (6); wherein, when used for an in-service boom (1), the inner magnetic ring array (2) is composed of two inner ring split bodies (7) spliced ​​together, each inner ring split body (7) has a designed number of slots, each slot is provided with an inner ring magnetic tile (8), an inner ring limiting steel ring (9) is fixed to the corresponding inner ring split body (7) by bolts, an anti-slip gasket is added on the inner side of the inner ring split body (7), and the inner magnetic ring array (2) is fixed to the outer magnetic ring array (3). The outer magnetic ring array (3) is fixed at the installation position of the suspension rod (1); the structure of the outer magnetic ring array (3) is similar to that of the inner magnetic ring array (2); each outer magnetic tile (16) is placed in a designed slot and fixed to the outer ring split body 1 (17) and the outer ring split body 2 (18) through the outer ring limiting steel ring (15); the outer magnetic ring array (3) is connected to the counterweight (4) and the universal wheel (5) respectively by bolts; the counterweight (4) is installed on the periphery of the outer magnetic ring array (3) and fixed thereto; the counterweight (4) is a square body composed of four rectangular mass blocks spliced ​​by bolts; the base (6) It is composed of two identical base parts (21) spliced ​​together, with an anti-skid washer on the inner side thereof, which is fixed to the installation position of the suspension rod (1) by bolts, and is used to support the outer magnetic ring array (3), the counterweight (4) and the universal wheel (5) thereon; the universal wheel (5) is in direct contact with the base (6), can rotate in any direction, and provides damping through friction between the universal wheel (5) and the base (6), and the magnitude of the damping provided is adjusted by changing the friction coefficient between the universal wheel (5) and the base (6); the damping provided by friction, or between the inner magnetic ring array (2) and the outer magnetic ring array (3) An air damper is installed between the two suspension rods to dissipate energy; the size of the counterweight (4), the size of the inner ring magnetic tile (8) and the size of the outer ring magnetic tile (16) are designed according to the basic parameters of the suspension rod (1) to be controlled, and the magnetic force between the inner magnetic ring array (2) and the outer magnetic ring array (3) ensures that the outer magnetic ring array (3) does not collide with the inner magnetic ring array (2) during movement; the installation position and number of the double annular strong magnetic array nonlinear dynamic vibration absorber on the suspension rod (1) are designed according to the dynamic characteristics of the suspension rod (1) to be controlled and its vibration reduction requirements, and at least one is installed at the midpoint position.

2. The design method of a double annular strong magnetic array nonlinear dynamic vibration absorber for suspension rod vibration reduction according to claim 1 is characterized in that: Here are the steps: Step 1: obtain the basic characteristics of the controlled boom (1) by field survey or reviewing the design parameters: the outer diameter including the sheath and the natural frequency; Step 2: Determine the basic design parameters of the double annular strong magnet array nonlinear dynamic vibration absorber to be designed: 1) The ratio of the sum of the mass of the outer magnetic ring array (3) and the counterweight (4) to the modal mass of the suspension rod (1) is 1% to 5%. The greater the mass ratio within this range, the better the vibration reduction effect. The ratio should be determined based on the vibration reduction requirements of the suspension rod (1); 2) Damping ratio of vibration absorber: The design damping ratio of the vibration absorber is the design damping ratio of the optimal tuned mass damper under the same mass ratio; 3) Linear stiffness and cubic stiffness of vibration absorber: The numerical model of the suspension rod-vibration absorber system is established as shown in formula (1): Among them, w(t) represents the vector composed of displacements corresponding to each degree of freedom of the suspender, and They correspond to their velocity and acceleration respectively; M is the mass matrix of the hanger; C is the damping matrix of the hanger, using Rayleigh damping; K is the stiffness matrix of the hanger; F(t) is the sum of the external load on the hanger and the reaction force of the vibration absorber on the hanger; m, c, k1, k2 represent the mass, damping, linear stiffness and nonlinear stiffness of the vibration absorber respectively; v represents the displacement of the vibration absorber, denote its velocity and acceleration respectively; one end of the suspension rod is the starting point of the x-axis, x is the x-axis coordinate of the point on the suspension rod, d is the installation position of the vibration absorber on the x-axis, and δ(xd) is the Dirac function; Formula (2) is the parameter optimization objective function, Among them, Δ, Δ con Respectively represent the root mean square value, variance or other vibration reduction effect evaluation index of the displacement or velocity time history response of a point on the hanger under the same white noise load when it is uncontrolled and controlled, and are selected or established according to the vibration reduction requirements; According to the optimal linear stiffness of TMD, the linear stiffness and nonlinear stiffness parameter optimization range of the nonlinear vibration absorber are determined. The dynamic response of the hanger is calculated by calling the numerical model of the hanger-absorber system under the action of multi-point white noise load, and the optimal linear stiffness and optimal nonlinear stiffness values ​​are obtained by automatic optimization. 4) Geometric parameters of inner and outer magnetic ring arrays: comprehensively considering the cost of the vibration absorber and the cross-sectional dimensions of the suspension rod to be controlled, determine the number of magnetic tiles, the central angle of the magnetic tiles, and the inner diameter of the magnetic tiles of the inner magnetic ring array (2) and the outer magnetic ring array (3); establish a parameterized electromagnetic field numerical model of a double-ring strong magnetic array nonlinear dynamic vibration absorber system, and adjust the thickness and height of the magnetic tiles so that the inner and outer magnetic ring array assembly composed of the inner magnetic ring array (2) and the outer magnetic ring array (3) reaches the designed linear stiffness value and the designed cubic stiffness value; 5) Geometric parameters of the vibration absorber counterweight (4): the mass of the vibration absorber counterweight (4) is obtained by subtracting the mass of the outer magnetic ring array (3) from the total mass of the vibration absorber. The length, width and height of the counterweight (4) are then designed according to the density of the counterweight block; Step 3, processing and manufacturing a double-annular strong magnetic array nonlinear dynamic vibration absorber according to the design parameters obtained in step 2; Step 4: Install the manufactured double-annular strong magnet array nonlinear dynamic vibration absorber on a laboratory suspension rod, use a dynamometer and a ruler to measure the force-displacement relationship of the double-annular strong magnet array nonlinear dynamic vibration absorber to ensure that its linear stiffness and cubic stiffness are the designed values; allow it to move freely, measure its displacement signal, and determine its damping ratio using a free vibration attenuation method or other methods, and adjust the damping ratio by adjusting the friction between the universal wheel (5) and the base (6) or by setting other damping methods, so that it reaches or approaches the optimal damping ratio.

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