1 / 2 sub-harmonic resonance vibration reduction method for cable-beam combined structure

Abstract

The invention discloses a cable-beam combined structure 1 / 2 subharmonic resonance vibration reduction method. The method comprises the following steps that S1, the optimal damping force needed by a cable in the current motion state is obtained according to a time-lag vibration reduction rule; s2, calculating a target current required by the MR damper according to the obtained optimal damping force; s3, mapping the target current to a current interval which can be actually applied by the MR damper by using a mapping algorithm to obtain a mapping current; s4, adjusting individual overlarge mapping current to obtain applied current; and S5, current is applied to the MR damper so as to control the cable-beam combined structure. According to the method, the optimal damping force and the target current are accurately calculated, and the time-delay selection rule is combined, so that 1 / 2 subharmonic resonance can be accurately inhibited, the vibration amplitude of the cable-beam composite structure under the specific frequency is effectively reduced, the fatigue damage risk of the structure is reduced, and the service life of the bridge is prolonged.

Description

Technical Field

[0001] The invention belongs to the technical field of bridge vibration control, and in particular relates to a 1 / 2 subharmonic resonance vibration reduction method for a cable-beam combined structure. Background Art

[0002] In modern bridge engineering, long-span bridges such as suspension bridges and tied-arch bridges are widely used due to their large span capacity and lightweight structure. However, the cable-beam composite structures in these bridges face severe vibration challenges. Due to the flexible nature of the cable-beam structure, it is prone to large vibrations under external excitation, especially 1 / 2 subharmonic resonance. This resonance occurs when the external excitation frequency is close to twice the natural frequency of the cable, causing the cable-beam structure to produce a strong vibration response. Long-term vibration not only causes fatigue damage to the structure but can also cause component fracture, seriously threatening the safety and service life of the bridge.

[0003] Traditional vibration control methods primarily include passive and active control. Passive control methods, such as the use of oil dampers, are simple and easy to implement, but their damping force is fixed and cannot be adjusted to changes in the vibration environment. This makes them difficult to adapt to dynamic vibration environments, resulting in limited vibration reduction effectiveness. Active control methods suppress vibration by adjusting the control force in real time. While effective, they require a continuous external energy supply, resulting in high energy consumption and the risk of structural instability. This limits their application to large-mass bridge structures.

[0004] Time-delay feedback control, an emerging vibration control method, adjusts the control force by introducing a time-delay term. However, it is currently primarily used for active control. Because it requires a continuous external energy supply, it is difficult to directly apply to the vibration control of large-mass bridge structures. Existing methods also fail to optimize the nonlinear coupled vibration characteristics of cable-beam composite structures, failing to fully realize their potential for vibration reduction. Summary of the Invention

[0005] The main purpose of the present invention is to overcome the shortcomings of the existing technology and propose a 1 / 2 subharmonic resonance vibration reduction method for a cable-beam combination structure to effectively control the 1 / 2 subharmonic resonance of the cable-beam combination structure.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A 1 / 2 subharmonic resonance vibration reduction method for a cable-beam composite structure comprises the following steps:

[0008] S1. Obtain the optimal damping force f required for the current motion state of the cable according to the time-delay vibration reduction law. o ;

[0009] S2, according to the obtained optimal damping force f o , calculate the target current i required for the MR dampero ;

[0010] S3, using the mapping algorithm to target current i o The mapped current is obtained by mapping to the current range that can actually be applied to the MR damper;

[0011] S4, adjusting individual excessively large mapping currents to obtain applied currents;

[0012] S5. Applying current to the MR damper to control the cable-beam structure.

[0013] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0014] 1. The present invention addresses the 1 / 2 subharmonic resonance problem of cable-beam composite structures. By accurately calculating the optimal damping force and target current and combining it with time-delay selection rules, it can accurately suppress this special resonance phenomenon. Compared with traditional vibration control methods, the control effect of 1 / 2 subharmonic resonance is more significant, effectively reducing the vibration amplitude of the cable-beam structure at specific frequencies, lowering the risk of structural fatigue damage, and extending the service life of the bridge.

[0015] 2. Large structures such as long-span bridges usually require a lot of energy to maintain the operation of active control systems, so energy consumption control is particularly important. The present invention uses semi-active control and does not require continuous external energy supply. The MR damper consumes energy only when the damping force needs to be adjusted, greatly reducing the energy consumption of the entire vibration reduction system.

[0016] 3. Active control methods may cause structural vibration instability in some cases. However, the present invention avoids this instability by reasonably selecting the time lag value and adjusting the current of the MR damper; the semi-active control method makes the system more stable and reliable while ensuring the control effect.

[0017] 4. Compared with traditional active control methods, semi-active control methods reduce the system's energy consumption and operating costs while ensuring vibration reduction effects. In addition, through the rational use and maintenance of MR dampers, their service life is extended, further reducing the cost of equipment replacement. For large-scale bridge projects, this has significant economic benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 is a flow chart of the method of the present invention;

[0019] Figure 2 is a schematic diagram of a cable-beam combined structure model in an embodiment;

[0020] Figure 3 It is attached Figure 2 Schematic diagram of the center beam vibration subsystem model;

[0021] Figure 4 It is attached Figure 2 Schematic diagram of the cable vibration subsystem model;

[0022] Figure 5 is the amplitude time history curve of the tuning parameter σ=-10 in the embodiment;

[0023] Figure 6 is the amplitude time history curve of the cable with tuning parameter σ=0 in the embodiment;

[0024] Figure 7 : is the amplitude time history curve of the tuning parameter σ=10 in the embodiment. DETAILED DESCRIPTION

[0025] The present invention will be described in further detail below with reference to the embodiments and drawings, but the embodiments of the present invention are not limited thereto.

[0026] like Figure 1 As shown, the present invention provides a 1 / 2 subharmonic resonance vibration reduction method for a cable-beam combination structure, comprising the following steps:

[0027] S1. Obtain the optimal damping force f required for the current motion state of the cable according to the time-delay vibration reduction law. o ;

[0028] Among them, the 1 / 2 subharmonic resonance of the cable-beam composite structure satisfies ω an =2ω b +ε 2 σ, where ω an ,ω b are the external excitation frequency of the main beam and the natural frequency of the sling, respectively. ε is an independent parameter that is small enough, and σ is a tuning parameter.

[0029] The extended nonlinear hysteresis biviscous model is used as the MR damper model, and its damping force equation is:

[0030]

[0031] Among them, f h is a variable related to the motion state of the damper and is determined by the following formula:

[0032]

[0033] Among them, x, and represent the displacement, velocity and acceleration of the structure respectively; c po 、c pr 、v h and f y is a parameter related to structural motion and is calculated by the following formula:

[0034]

[0035]

[0036]

[0037] In the damping force equation (1), f i (i) is the part related to current and is determined by the following formula:

[0038]

[0039] The above equation contains 10 constant parameters, [f0 I0 a0 a1 a2 a4 k0 k1 k2 k4], which are related to the damper characteristics.

[0040] The motion differential equation of the cable-beam composite structure considering time delay is:

[0041]

[0042]

[0043] Wherein, formula (4) is the differential equation of motion of the beam, and formula (5) is the differential equation of motion of the cable; q i 、 and are the displacement, velocity and acceleration of the cable or beam, ω i is the natural frequency of the cable or beam, ξ i is the damping ratio of the cable or beam, f i is the external load amplitude of the cable or beam, ω in is the external load frequency of the cable or beam, i=a,b; e1, d1 and d2 are the corresponding coefficients; the above parameters are dimensionless parameters;

[0044] The differential equation is solved using the multi-scale method, and the amplitude-frequency relationship of the structure with time lag when the cable-beam composite structure undergoes 1 / 2 subharmonic resonance satisfies the following equation:

[0045]

[0046] in,

[0047] The time lag value when the 1 / 2 subharmonic resonance occurs and the amplitude of the cable reaches the extreme value is obtained by taking the derivative of formula (6) with respect to the time lag, as follows:

[0048]

[0049] Among them, ω b is the cable's natural frequency.

[0050] The optimal damping force f required at the current moment o Equal to the damping force f calculated based on the motion state before time τ h .

[0051] S2, according to the obtained optimal damping force f o , calculate the target current i required for the MR damper o , specifically:

[0052]

[0053]

[0054] Among them, f o is the optimal damping force required for the current motion state of the structure; f h It is a variable that is only related to the motion state of the system and is regarded as a known quantity.

[0055] S3, using the mapping algorithm to target current i o The mapped current is obtained by mapping to the current range that can actually be applied to the MR damper; specifically:

[0056] Map the target current value interval [a, b] to the current interval [0, c] that the damper can apply, and calculate the mapped current i. The calculation formula is:

[0057]

[0058] The method for determining the target current value interval [a, b] is:

[0059] A constant current is applied to the MR damper, and the cable-beam composite structure system is controlled for a preset period of time according to the passive control strategy. The maximum and minimum values ​​of the target current during this period are found. In order to eliminate the possibility that individual maximum points are too large or too small, the maximum current value is appropriately expanded or reduced, and finally the interval [a, b] is determined.

[0060] S4. Adjust the individual excessively large mapped currents to obtain the applied currents; specifically:

[0061] Before applying the mapped current i to the MR damper, it is first checked whether i is within the current range that can be applied to the MR damper. For the current that exceeds the range, the maximum or minimum value allowed by the range is taken to obtain the applied current.

[0062] S5. Applying current to the MR damper to control the cable-beam structure.

[0063] Among them, when the cable amplitude takes the extreme value, the corresponding time lag value is only related to its own frequency and has nothing to do with the external load frequency;

[0064] The mapping algorithm adapts to the output requirements of the MR damper under different working conditions by dynamically adjusting the current range.

[0065] In the vibration reduction method of the present invention, since the MR damper can only exert a force opposite to the structural velocity, the use of the MR damper for semi-active control will not cause the structural vibration to diverge.

[0066] Example

[0067] In this embodiment, an extended nonlinear hysteresis biviscous model is used as the MR damper model.

[0068] Table 1 shows the parameters of the MR damper.

[0069] parameter Numerical parameter Numerical parameter Numerical parameter Numerical parameter Numerical <![CDATA[f0]]> -16 <![CDATA[I0]]> -1.156 <![CDATA[a0]]> 11432 <![CDATA[a1]]> 0.145 <![CDATA[a2]]> 0.901 <![CDATA[k0]]> 23.92 <![CDATA[k1]]> 315.1 <![CDATA[k2]]> 8.051 <![CDATA[k4]]> 0.0811 <![CDATA[a4]]> 2.381

[0070] Table 1

[0071] This embodiment takes a suspension bridge as an example, and its cable-beam parameters are shown in Table 2 below.

[0072] Parameter Symbol Parameter value Parameter Symbol Parameter value Parameter Symbol Parameter value <![CDATA[M a ]]> 9000kg / m <![CDATA[E a ]]> <![CDATA[2.1×10 11 Well]]> <![CDATA[l a ]]> 350m <![CDATA[M b ]]> 34.5kg / m <![CDATA[E b ]]> <![CDATA[1.15×10 11 Well]]> <![CDATA[l b ]]> 90.6m <![CDATA[H b ]]> 2200KN <![CDATA[I a ]]> <![CDATA[7.5m 4 ]]> <![CDATA[g1]]> 17.5m

[0073] Table 2

[0074] In Table 2, M a 、M b are the unit length masses of the main beam and sling respectively; E a 、E b are the elastic moduli of the main beam and sling respectively; l a 、l b are the main beam span and the length of the sling respectively; H b Represents the initial tension of the sling; I a Represents the cross-sectional moment of the main beam; g1 is the distance from the sling to the left end point of the main beam.

[0075] Using the data in Table 2, the beam natural frequency ω can be calculated a =5.35, cable natural frequency ω b =8.76, then the beam external excitation frequency satisfies ω in the case of 1 / 2 subharmonic resonance an =17.53+ε 2 σ, where σ is the tuning parameter. Assume that the external excitation of the beam is f a =0.1, external excitation size f b =0, small enough independent parameter ε=0.1.

[0076] According to the parameters, a cable-beam composite structure coupled vibration model is established in the Simulink module of MATLAB. The model is as follows: Figure 2 As shown; Figure 3 and Figure 4As shown in Figure 2, they are schematic diagrams of the beam vibration subsystem and the cable vibration subsystem, respectively.

[0077] The MR damper is installed on the cable and its own damping is not considered. The beam is not installed with the MR damper and only its own damping is considered, with a damping ratio of 1%.

[0078] According to the time-delay selection rule, the cable natural frequency ω b =8.76, substitute into the formula:

[0079]

[0080] The first extreme point corresponding to the minimum value of the cable amplitude curve is τ = 0.5379, so τ = 0.6 is taken as the time lag value used for time lag vibration reduction control of the cable-beam composite structure.

[0081] To verify the effectiveness of time-delay in controlling system vibration, the system was divided into a time-delay control system and a time-delay-free control system. To ensure that the energy applied to the time-delay control system and the time-delay-free control system was the same, the RMS value of the applied current during time-delay control was recorded and applied as a constant current to the system with only the MR damper and no time-delay control for passive control.

[0082] like Figure 5 、 Figure 6 as well as Figure 7 As shown in FIG, there are respectively the amplitude time history curves of the cable in the time-delay control system and the time-delay-free control system corresponding to different tuning parameters σ. It can be seen from the figure that when the tuning parameter σ takes different values, whether greater than zero or less than zero, when the time delay τ takes 0.6, the structural amplitude of the time-delay control becomes zero faster than that of the time-delay-free control. The conclusion proves that the method of the present invention can effectively realize the control of the MR damper on the vibration of the cable-beam combination structure with 1 / 2 subharmonic resonance.

[0083] It should also be noted that, in this specification, terms such as "comprises", "includes" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or apparatus comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article or apparatus comprising the element.

[0084] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A 1 / 2 subharmonic resonance vibration reduction method for a cable-beam composite structure, characterized in that: The following steps are involved: S1. Obtain the optimal damping force f required for the current motion state of the cable according to the time-delay vibration reduction law. o ; S2, according to the obtained optimal damping force f o , calculate the target current i required for the MR damper o ; S3, using the mapping algorithm to target current i o The mapped current is obtained by mapping to the current range that can actually be applied to the MR damper; S4, adjusting individual excessively large mapping currents to obtain applied currents; S5. Applying current to the MR damper to control the cable-beam structure.

2. The cable-beam composite structure 1 / 2 subharmonic resonance vibration reduction method according to claim 1, characterized in that: The 1 / 2 subharmonic resonance of the cable-beam composite structure satisfies ω an =2ω b +ε 2 σ, where ω an ,ω b are the external excitation frequency of the main beam and the natural frequency of the sling, respectively. ε is an independent parameter that is small enough, and σ is a tuning parameter.

3. The cable-beam combination structure 1 / 2 subharmonic resonance vibration reduction method according to claim 1, characterized in that: The extended nonlinear hysteresis biviscous model is used as the MR damper model, and its damping force equation is: Among them, f h is a variable related to the motion state of the damper and is determined by the following formula: Among them, x, and represent the displacement, velocity and acceleration of the structure respectively; c po 、c pr 、v h and f y is a parameter related to structural motion and is calculated by the following formula: In the damping force equation (1), f i (i) is the part related to current and is determined by the following formula: The above equation contains 10 constant parameters, [f0 I0 a0 a1 a2 a4 k0 k1 k2 k4], which are related to the damper characteristics.

4. The cable-beam composite structure 1 / 2 subharmonic resonance vibration reduction method according to claim 1, characterized in that: In step S1, the motion differential equation of the cable-beam composite structure considering time delay is: Wherein, formula (4) is the differential equation of motion of the beam, and formula (5) is the differential equation of motion of the cable; q i 、 and are the displacement, velocity and acceleration of the cable or beam, ω i is the natural frequency of the cable or beam, ξ i is the damping ratio of the cable or beam, f i is the external load amplitude of the cable or beam, ω in is the external load frequency of the cable or beam, i=a,b; e1, d1 and d2 are the corresponding coefficients; the above parameters are dimensionless parameters; The differential equation is solved using the multi-scale method, and the amplitude-frequency relationship of the structure with time lag when the cable-beam composite structure undergoes 1 / 2 subharmonic resonance satisfies the following equation: in, The time lag value when the 1 / 2 subharmonic resonance occurs and the amplitude of the cable reaches the extreme value is obtained by taking the derivative of formula (6) with respect to the time lag, as follows: Among them, ω b is the cable's natural frequency.

5. The cable-beam combination structure 1 / 2 subharmonic resonance vibration reduction method according to claim 3, characterized in that: In step S1, the optimal damping force f required at the current moment is o Equal to the damping force f calculated based on the motion state before time τ h .

6. The cable-beam combination structure 1 / 2 subharmonic resonance vibration reduction method according to claim 3, characterized in that: In step S2, the target current i required by the MR damper is calculated. o , specifically: Among them, f o is the optimal damping force required for the current motion state of the structure; f h It is a variable that is only related to the motion state of the system and is regarded as a known quantity.

7. The cable-beam combination structure 1 / 2 subharmonic resonance vibration reduction method according to claim 6, characterized in that: Step S3 is specifically as follows: Map the target current value interval [a, b] to the current interval [0, c] that the damper can apply, and calculate the mapped current i. The calculation formula is: The method for determining the target current value interval [a, b] is: A constant current is applied to the MR damper, and the cable-beam composite structure system is controlled for a preset period of time according to the passive control strategy. The maximum and minimum values ​​of the target current during this period are found. In order to eliminate the possibility that individual maximum points are too large or too small, the maximum current value is appropriately expanded or reduced, and finally the interval [a, b] is determined.

8. The cable-beam combination structure 1 / 2 subharmonic resonance vibration reduction method according to claim 7, characterized in that: Step S4 is specifically as follows: Before applying the mapped current i to the MR damper, it is first checked whether i is within the current range that can be applied to the MR damper. For the current that exceeds the range, the maximum or minimum value allowed by the range is taken to obtain the applied current.

9. The cable-beam combination structure 1 / 2 subharmonic resonance vibration reduction method according to claim 4, characterized in that: When the cable amplitude takes an extreme value, the corresponding time lag value is only related to its own frequency and has nothing to do with the frequency of the external load.

10. A 1 / 2 subharmonic resonance vibration reduction method for a cable-beam composite structure according to claim 7, characterized in that: The mapping algorithm adapts to the output requirements of the MR damper under different working conditions by dynamically adjusting the current range.

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