A vibration damping device for inhibiting vibration of an ultra-long cable-stayed cable and a parameter optimization method thereof

Abstract

This invention discloses a vibration damping device and its parameter optimization method for suppressing the vibration of ultra-long cable-stayed bridges. The vibration damping device includes a first damper and a second damper disposed between the cable-stayed bridge and the bridge deck. The intersection of the cable-stayed bridge and the bridge deck is the anchorage end. The distance between the installation point of the first damper and the anchorage end of the cable-stayed bridge is a1, and the distance between the installation point of the second damper and the anchorage end of the cable-stayed bridge is a2, where a1 < a2. The dimensionless damping coefficient of the first damper is η1, where η1 = c1 / (Tm). 0.5 The dimensionless damping coefficient of the second damper is η2, where η2 = c2 / (Tm). 0.5 The value of η1 ranges from η1,opt3 to η1,opt1, and η2 ≈ 1. In the damping device of this invention, the first damper is mainly for low-order modal vibration, and the second damper is mainly for high-order modal vibration, so that each damper can play its best role. This allows the damping device to effectively suppress different modal vibrations of the cable-stayed bridge, avoid excessive or insufficient control of the cable vibration, and improve the structural safety and comfort of the bridge.

Description

Technical Field

[0001] This invention relates to the field of structural vibration control technology, and in particular to a vibration reduction device for suppressing the vibration of ultra-long cable-stayed bridges and a method for optimizing its parameters. Background Technology

[0002] Currently, vibration control devices on cable-stayed bridges mainly include viscoelastic dampers, viscous dampers, eddy current dampers, and magnetorheological dampers. With the development of science and technology and the application of new materials and technologies, the length of cable-stayed bridges continues to break new records; currently, the cable-stayed bridges on the Sutong Yangtze River Bridge exceed 500 meters. Under dynamic loads such as wind and vehicles, vibration problems are particularly significant, causing a huge adverse impact on the long-term service performance of the cable-stayed bridges. The most common vibration reduction scheme for cable-stayed bridges today is to install only one set of external dampers on each cable. This set of dampers is set with a large damping coefficient. This scheme can only improve the damping ratio of the first few modes of the cable-stayed bridge and suppress the occurrence of wind and rain vibrations. However, in recent years, high-order vortex-induced vibration events have frequently occurred in ultra-long cable-stayed bridges. Traditional damper setting and parameter optimization methods cannot effectively suppress their high-order modal vibrations, leading to damage and breakage of the cable-stayed bridge dampers. Summary of the Invention

[0003] The purpose of this invention is to overcome the problem that traditional single dampers can only suppress low-order mode vibrations of stay cables but not high-order mode vibrations, and to provide a vibration reduction device for suppressing the vibration of ultra-long stay cables and a method for optimizing its parameters.

[0004] To achieve the above-mentioned objectives, the present invention provides the following technical solution:

[0005] A vibration damping device for suppressing the vibration of ultra-long cable-stayed bridges includes a first damper and a second damper disposed between the cable-stayed bridge and the bridge deck. The intersection of the cable-stayed bridge and the bridge deck is the anchorage end. The distance between the first damper and the installation point of the cable-stayed bridge and the anchorage end is [missing information]. a 1. Unit: m. The distance between the installation point of the second damper on the cable and the anchorage end is... a 2, unit: m a 1 < a 2; The dimensionless damping coefficient of the first damper is or 1, or 1= c 1 / ( Tm ) 0.5 The dimensionless damping coefficient of the second damper is or 2, or 2= c 2 / ( Tm ) 0.5 , c 1 represents the damping coefficient of the first damper, in Ns / m;c 2 represents the damping coefficient of the second damper, in Ns / m; T is the cable tension, in N; m is the mass per unit length of cable, in kg / m; the dimensionless damping coefficient of the first damper... or The range of values ​​for 1 is or 1,opt3~ or 1,opt1, where, , , l The length of the stay cable, in meters; the dimensionless damping coefficient of the second damper. or 2≈1.

[0006] The vibration damping device of this invention comprises a first damper and a second damper installed between the bridge deck and the stay cables, with the first damper positioned closer to the anchorage end of the stay cable relative to the bridge deck than the second damper. The dimensionless damping coefficient of the first damper is specified. or 1 =h 1,opt3~ or 1,opt1, the dimensionless damping coefficient of the second damper. or The value of 2≈1 means that the No. 1 damper is mainly for low-order modal vibrations, such as first to third-order vibrations caused by wind and rain excitation; the No. 2 damper is mainly for high-order modal vibrations, such as fourth-order and higher-order vibrations caused by end motion. Therefore, the No. 1 damper can be used to suppress low-order modal vibrations, and the No. 2 damper can be used to suppress high-order modal vibrations, so that each damper can play its best role. This allows the vibration reduction device to effectively suppress different modal vibrations of the cable-stayed bridge, avoid excessive or insufficient control of the cable vibration, and improve the structural safety and comfort of the bridge.

[0007] Preferably, the first damper and the second damper are fixed to the stay cable by buckles, and the other end of the first damper and the second damper are connected to the bridge deck.

[0008] With this structural arrangement, both the No. 1 and No. 2 dampers are connected to the stay cables via buckles, which ensures the stability of the connection between the dampers and the stay cables and improves the damping effect of the dampers.

[0009] Preferably, the first damper and the second damper are respectively connected to the bridge deck via support columns, which are pre-embedded in the bridge deck.

[0010] Connecting dampers No. 1 and No. 2 to the bridge deck via support columns avoids directly installing dampers on the bridge deck, reducing the impact on the bridge deck structure and improving the stability of the bridge structure. Setting support columns pre-embedded in the bridge deck ensures the stability of the support columns.

[0011] Preferably, a connecting rod is provided between the support column and the first damper, and between the support column and the second damper, and the first damper and the second damper are respectively connected to the support column through the connecting rod.

[0012] By installing a connecting rod between the damper and the support column, the support column and the damper can be connected more tightly.

[0013] Preferably, the first damper and the second damper are viscous dampers, magnetorheological dampers, or eddy current dampers.

[0014] Preferably, the buckle includes an upper ring and a lower ring, which are connected by bolts, and the stay cable is located within the space enclosed by the upper ring and the lower ring.

[0015] The stay cables are secured by upper and lower rings, which are then fastened with bolts, ensuring a stable connection between the stay cables and the damper.

[0016] A vibration reduction parameter optimization method for designing a vibration reduction device for suppressing the vibration of ultra-long cable-stayed bridges, comprising the following steps:

[0017] S1. Calculate the installation of the first damper at... a 1 distance n First-order modal damping ratio g n(1,a1) The second damper is installed on a At a distance of 2 n First-order modal damping ratio g n(2,a2-a1) :

[0018]

[0019] ;

[0020] S2. Calculate S1 g n(1,a1) and g n(2,a2-a1) The damping ratios of each mode are obtained by adding them together when the first damper and the second damper work together. n总 :

[0021] ;

[0022] S3. If in S2 n总 If the design meets the engineering vibration reduction requirements, it is considered complete; otherwise, adjustments are needed. or 1、 or 2、a 1. a 2 -a 1, until n总 It meets the requirements for vibration reduction in engineering projects.

[0023] This invention provides a dual-damper parameter design method for simultaneously controlling low-order and high-order multimodal vibrations of stay cables. The vibration reduction device designed using this method, by arranging two sets of dampers on a single cable, can simultaneously control both low-order and high-order modal vibrations, solving the problem that commonly used single-damper schemes can only control low-order modal vibrations while failing to suppress high-order modal vibrations. This provides a novel application method for cable-stayed vibration reduction structures.

[0024] Preferably, after adjusting the installation position of the first damper, the location is redefined. or The range of values ​​for 1.

[0025] A vibration reduction device is designed using the aforementioned vibration reduction parameter optimization method.

[0026] Compared with the prior art, the beneficial effects of the present invention are:

[0027] 1. The damping device of the present invention comprises a first damper and a second damper installed between the bridge deck and the stay cables, wherein the first damper 1 is closer to the anchorage end of the stay cable 3 and the bridge deck 4 than the second damper 2. The dimensionless damping coefficient of the first damper is set. or 1 =h 1,opt3~ or 1,opt1, the dimensionless damping coefficient of the second damper. or The value of 2≈1 means that the No. 1 damper is mainly for low-order modal vibrations, such as first to third-order vibrations caused by wind and rain excitation; the No. 2 damper is mainly for high-order modal vibrations, such as fourth-order and higher-order vibrations caused by end motion. Therefore, the No. 1 damper can be used to suppress low-order modal vibrations, and the No. 2 damper can be used to suppress high-order modal vibrations, so that each damper can play its best role. This allows the vibration reduction device to effectively suppress different modal vibrations of the cable-stayed bridge, avoid excessive or insufficient control of the cable vibration, and improve the structural safety and comfort of the bridge.

[0028] 2. Both dampers No. 1 and No. 2 are connected to the stay cables via buckles. The stay cables are held tightly by the upper and lower rings of the buckles, which are then secured with bolts. This ensures the stability of the connection between the stay cables and the dampers, thereby improving the vibration reduction effect of the dampers.

[0029] 3. This invention also provides a dual-damper parameter design method for simultaneously controlling low-order and high-order multimodal vibrations of stay cables. The vibration reduction device designed using this method, by arranging two sets of dampers on a single cable, can simultaneously control both low-order and high-order modal vibrations of the cable, solving the problem that commonly used single-damper schemes can only control low-order modal vibrations but cannot suppress high-order modal vibrations. This provides a novel application method for cable vibration reduction structural systems. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the arrangement of the shock absorption device of the present invention;

[0031] Figure 2 for Figure 1 Sectional view along axis AA;

[0032] Figure 3 This is a schematic diagram of the buckle structure;

[0033] Figure 4 The damping ratio of the first 40 modes is given when different damper arrangement schemes are used in Example 2.

[0034] Attached reference numerals: 1-Damper No. 1, 2-Damper No. 2, 3-Stay cable, 4-Bridge deck, 5-Ring, 51-Upper ring, 52-Lower ring, 53-Bolt, 6-Support column, 61-Connecting rod. Detailed Implementation

[0035] The present invention will be further described in detail below with reference to experimental examples and specific embodiments. However, this should not be construed as limiting the scope of the above-mentioned subject matter of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0036] Example 1

[0037] like Figure 1-3 As shown, this invention discloses a vibration damping device for suppressing the vibration of ultra-long cable-stayed bridges, including a first damper 1 for suppressing low-order mode vibration and a second damper 2 for suppressing high-order mode vibration. The first damper 1 is closer to the anchorage end of the cable-stayed bridge 3 and the bridge deck 4 than the second damper 2.

[0038] In this embodiment, the distance between the installation point of the first damper 1 and the anchor end of the stay cable 3 is set to... a 1. Unit: m. The distance between the installation point of damper 2 on cable 3 and the anchorage end is: a 2, unit: m. a 1 < a 2. To enable this damping device to suppress different modal vibrations of the cable-stayed bridge, we set the dimensionless damping coefficient of damper 1 to be [value missing]. or 1, or 1=c 1 / ( Tm ) 0.5 ,and or 1 =h 1,opt3~ or 1,opt1; The dimensionless damping coefficient of damper 2 is or 2, or 2= c 2 / ( Tm ) 0.5 , or The value of 2 can range from 0.8 to 1.2. In this embodiment... or 2≈1, where c 1 represents the damping coefficient of the first damper 1, in Ns / m; c 2 represents the damping coefficient of the second damper 2, in Ns / m; T is the cable tension, in N; m is the mass of the cable per unit length, in kg / m.

[0039] or 1,opt3 represents the optimal damping coefficient for the third mode when damper 1 is installed alone on cable 3, where or 1,opt1 represents the optimal damping coefficient for the first mode when damper 1 is installed alone on cable 3, where, , , l The length of the cable 3 is given in meters (m).

[0040] In this embodiment, both damper 1 and damper 2 are positioned between the stay cable 3 and the bridge deck 4. One end of damper 1 is connected to the stay cable 3 via a retaining ring 5, and the other end is connected to a support column 6. One end of damper 2 is connected to the stay cable 3 via another retaining ring 5, and the other end is connected to another support column 6. To ensure the stability of the connection, connecting rods 61 can also be installed between the support column 6 and damper 1, and between the support column 6 and damper 2. Damper 1 and damper 2 are connected to the support column 6 via connecting rods 61, and both support columns 6 are pre-embedded in the bridge deck 4.

[0041] To better lock the stay cable 3 and secure the connection between the stay cable 3 and the damper, in this embodiment, the retaining ring 5 is configured as a ring structure including an upper ring 51 and a lower ring 52. The upper ring 51 and the lower ring 52 are connected together by bolts 53 and can clamp the stay cable 3 inside. It is foreseeable that the specific structure of the retaining ring 5 in this invention is not limited to the ring structure of the upper ring 51 and the lower ring 52 described above, that is, as long as it can clamp the stay cable 3 and make the connection between the stay cable 3 and the damper stable, it is acceptable.

[0042] In this embodiment, damper 1 and damper 2 can be viscous dampers, magnetorheological dampers, or eddy current dampers. The vibration damping device of the present invention, by setting damper 1 and damper 2 between the bridge deck and the stay cables and defining the relevant parameters of damper 1 and damper 2, ensures that damper 1 primarily targets low-order modal vibrations, such as first to third-order vibrations caused by wind and rain excitation; damper 2 primarily targets high-order modal vibrations, such as fourth-order and higher-order vibrations caused by end motion. Damper 1 can be used to suppress low-order modal vibrations, and damper 2 can be used to suppress high-order modal vibrations, allowing each damper to achieve its optimal effect. This vibration damping device can effectively suppress different modal vibrations of the stay bridge, avoiding excessive or insufficient control of the stay cable vibrations, and improving the structural safety and comfort of the bridge.

[0043] Example 2

[0044] The present invention also provides a method for optimizing vibration reduction parameters, comprising the following steps:

[0045] S1. Design the modal damping ratio of damper 1 (first damper) for controlling low-order modal vibration and the modal damping ratio of damper 2 (second damper) for controlling high-order modal vibration. Damper 1 is installed... a 1 distance n First-order modal damping ratio g n(1,a1) The calculation formula is:

[0046]

[0047] Damper No. 2 is installed a At a distance of 2 n First-order modal damping ratio g n(2,a2-a1) The calculation formula is:

[0048]

[0049] From the above equation, it can be seen that the modal damping ratio n From the dimensionless damping coefficient or Modal order n Installation position of damper a / l Decision. During its design process, adjustments can be made... a 1 and / or a 2 -a 1. To achieve the desired damping ratio for each. a 1 indicates the distance of damper 1 from the anchor end, in meters; a 2 indicates the distance of the second damper 2 from the anchor end.

[0050] S2. Calculate S1 g n(1,a1) and g n(2,a2-a1) The summation yields the modal damping ratios when damper 1 and damper 2 work together. n总 :

[0051] ;

[0052] S3. Verify the design results, and compare the damping ratios of each mode when they act together in S2. n总 Compared with the target damping ratio set in the actual engineering design targ For comparison, if the design meets the engineering requirements, it is completed; otherwise, it is adjusted. or 1、 or 2 、 a 1. a 2 -a 1, until n总 It meets the requirements for vibration reduction in engineering projects.

[0053] It is worth noting that even or 1 was identified as or 1,opt3 or or 1 , opt2 , or 1. The specific value is still subject to a Due to the influence of 1, recalculation is required every time the installation position of damper 1 is adjusted. or 1.

[0054] In this embodiment, when designing and using the vibration damping device in Embodiment 1, the first damper 1 is installed close to the anchoring end of the stay cable 3. a At point 1, a larger damping coefficient is set. c 1. To control low-order modal vibrations; then, the second damper 2 is installed at a distance from the anchoring end of the stay cable 3. a Two locations were selected, and a smaller damping coefficient was set. c 2. To control higher-order modal vibrations. The optimized parameter scheme for the dual-damper system, capable of simultaneously suppressing both lower-order and higher-order modal vibrations of the stay cable, is as follows:

[0055] (1)

[0056] In the formula, or 1 represents the dimensionless damping coefficient of damper 1. or2 represents the dimensionless damping coefficient of damper 2; or 1,optn This represents the optimal damping coefficient for the nth mode when damper 1 is installed alone on cable 3.

[0057] We believe that when or 1 is much greater than or At 2 o'clock, or 1,optn =1 / sin ( no 1 / l ), or 2,optn =1 / sin ( no 2 / l ).

[0058] In actual engineering, dampers can often only be installed very close to the anchorage end of the stay cable 3, therefore a 1. a 2 are much smaller than l Based on the characteristics that dampers with different parameters have different effects on the mode shape of the cable, damper 1 and damper 2 are arranged according to formula (1). When only one damper with an appropriate damping coefficient is installed on the cable 3, the damping force generated by the damper causes the mode shape of the cable to be divided into two sine curves, and a slope inflection point is formed at the point of action of the damper.

[0059] Consider two extreme cases: when the damping coefficient of the damper approaches 0, the damper has no effect on the mode shape of cable 3, and the mode shape of cable 3 is a complete sine curve; when the damping coefficient approaches infinity, the mode displacement of cable 3 at its connection point with the damper approaches 0, and the damper acts approximately as a new anchoring end.

[0060] When damper 1 and damper 2 are arranged according to formula (1), we discuss the mode shape characteristics of cable 3 in low-order and high-order modes respectively:

[0061] Low-order modes: According to formula (1), the dimensionless damping coefficient of damper 2 is... or 2≈1, which is much smaller than the optimal dimensionless damping coefficient of the lower-order modes, therefore we believe that or 2 approaches 0. At this point, the low-order mode shape curve of the double-damped system of cable 3 is equivalent to that of the case where only damper 1 is installed.

[0062] Higher-order modes: The optimal dimensionless damping coefficient of the higher-order modes is close to 1. According to formula (1), the dimensionless damping coefficient of damper 1 is much larger than the optimal dimensionless damping coefficient of the higher-order modes. Therefore, we believe that... or1 approaches ∞. At this point, damper 1 is considered the new anchoring end, and the mode shape curve of the double-damped system of cable 3 is equivalent to shortening the cable length of cable 3 to... l - a 1, and in a 2- a The case where damper 2 is installed at point 1.

[0063] To visually compare the control performance of the single-damper and double-damper schemes, the load response of cable 3 with different damper schemes was calculated. To ensure the fairness of the comparison, we assume that due to site installation limitations, all dampers can only be installed at a distance from the anchorage end of cable 3. a / l = within 0.02.

[0064] To demonstrate the advantages of the vibration reduction device and its design method designed in this invention, we take an ultra-long cable-stayed bridge cable 3 as an example. The cable 3 is 551m long, with an outer diameter of 0.152m, a cable force of 6300kN, a weight per meter of cable of 92kg / m, and a cable inclination angle of 21.9°. Three different damper arrangement schemes are proposed for this cable 3:

[0065] Option 1: Install only one set of dampers a / l At a value of 0.02, to suppress low-order modal vibrations, the damper parameters are adjusted according to... or =7.3 Design.

[0066] Option 2: Use a damper to suppress higher-order modal vibrations, with the dimensionless damping coefficient set to... or =1.5, which can effectively improve the damping ratio of most high-order modes.

[0067] Option 3 uses the vibration reduction device and design method provided by this invention to design two sets of dampers to simultaneously suppress low-order and high-order modal vibrations. The positions of the two sets of dampers are as follows: a 1 / l = 0.01、( a 2- a 1) / l =0.01.

[0068] The parameters of the three damper schemes are shown in Table 1 below.

[0069] Table 1. Parameters of three damper schemes

[0070]

[0071] When using the above three schemes, the first 40 modal damping of the cable-stayed bridge is as follows: Figure 4As shown in the figure, it can be seen that when using Scheme 1, the first 10 modes of the stay cable 3 can obtain a large damping ratio, but the damping ratio of most higher-order modes is relatively small; when using Scheme 2, the damping ratio of most higher-order modes of the stay cable 3 is significantly improved, but the damping ratio of the first 3 modes is relatively small; while when the stay cable 3 is controlled by Scheme 3, that is, the vibration reduction device and its design method provided by the present invention, the damping ratio of the first 40 modes is effectively improved to above 0.4%.

[0072] The comparison shows that the dual-damper parameter design method provided by this invention, which can simultaneously control the low-order and high-order multimodal vibrations of a cable-stayed bridge, and the vibration reduction device designed using this method, can simultaneously control the low-order and high-order modal vibrations of a cable-stayed bridge by arranging two sets of dampers on a single cable. This solves the problem that the commonly used single-damper scheme can only control the low-order or high-order modal vibrations of cables, and provides a new application method for cable vibration reduction structure systems.

[0073] Example 3

[0074] The present invention also provides a vibration damping device, which is designed using the vibration damping parameter optimization method of Example 2.

[0075] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A vibration damping device for suppressing the vibration of an ultra-long cable-stayed bridge, comprising a first damper (1) and a second damper (2) disposed between the cable-stayed bridge (3) and the bridge deck (4), wherein the intersection of the cable-stayed bridge (3) and the bridge deck (4) is the anchorage end, characterized in that, The distance between the installation point of the first damper (1) and the anchor end of the stay cable (3) is... a 1, unit m, the distance between the installation point of the second damper (2) on the cable (3) and the anchoring end is... a 2, unit: m a 1 < a 2; The dimensionless damping coefficient of the first damper (1) is η 1, η 1= c 1 / ( Tm ) 0.5 The dimensionless damping coefficient of the second damper (2) is η 2, η 2= c 2 / ( Tm ) 0.5 , c 1 represents the damping coefficient of the first damper (1), in Ns / m; c 2 represents the damping coefficient of the second damper (2), in Ns / m; T represents the cable tension in N; m represents the mass per unit length of cable in kg / m; the dimensionless damping coefficient of the first damper (1) is... η The range of values ​​for 1 is η 1,opt3~ η 1,opt1, where, , , l The length of the stay cable (3), in meters; the dimensionless damping coefficient of the second damper (2). η 2≈1.

2. The vibration damping device for suppressing the vibration of ultra-long cable-stayed bridges according to claim 1, characterized in that, The first damper (1) and the second damper (2) are respectively fixed to the cable (3) by a buckle (5), and the other end of the first damper (1) and the second damper (2) are connected to the bridge deck (4).

3. The vibration damping device for suppressing the vibration of ultra-long cable-stayed bridges according to claim 2, characterized in that, The first damper (1) and the second damper (2) are respectively connected to the bridge deck (4) through support columns (6), and the support columns (6) are pre-embedded in the bridge deck (4).

4. The vibration damping device for suppressing the vibration of ultra-long cable-stayed bridges according to claim 3, characterized in that, A connecting rod (61) is provided between the support column (6) and the first damper (1), and between the support column (6) and the second damper (2). The first damper (1) and the second damper (2) are respectively connected to the support column (6) through the connecting rod (61).

5. A vibration damping device for suppressing the vibration of ultra-long cable-stayed bridges according to claim 1, characterized in that, The first damper (1) and the second damper (2) are viscous dampers, magnetorheological dampers, or eddy current dampers.

6. A vibration damping device for suppressing the vibration of ultra-long cable-stayed bridges according to any one of claims 2-4, characterized in that, The buckle (5) includes an upper ring (51) and a lower ring (52), which are connected by bolts (53), and the cable (3) is located in the space enclosed by the upper ring (51) and the lower ring (52).

7. A method for optimizing vibration reduction parameters, characterized in that, The method for designing a vibration damping device as described in any one of claims 1-6 includes the following steps: S1. Calculate the installation of the first damper (1) at the following locations. a 1 distance n First-order modal damping ratio ζ n(1,a1) The second damper (2) is installed on a At a distance of 2 n First-order modal damping ratio ζ n(2,a2-a1) : ； S2. Calculate S1 ζ n(1,a1) and ζ n(2,a2-a1) The damping ratios of each mode when the first damper (1) and the second damper (2) work together are obtained by adding them together. n总 : ； S3. If in S2 n总 If the design meets the engineering vibration reduction requirements, it is considered complete; otherwise, adjustments are needed. η 1、 η 2 、 a 1. a 2 -a 1, until n总 It meets the requirements for vibration reduction in engineering projects.

8. The vibration reduction parameter optimization method according to claim 7, characterized in that, After adjusting the installation position of the first damper (1), the location is redefined. η The range of values ​​for 1.

9. A vibration damping device, characterized in that, The design is performed using a vibration reduction parameter optimization method as described in any one of claims 7-8.

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