A collaborative damping vibration reduction method for wind-induced vibration of ultra-long stay cables

Abstract

The present invention relates to the technical field of bridge vibration reduction, and particularly relates to a collaborative damping vibration reduction method for wind-induced vibration of ultra-long stay cables. The method includes the following steps: determining the order of the controlled mode of wind-induced vibration of the stay cable based on the Strouhal number; determining the number of dampers and the preliminary design installation position ratio based on the order of the controlled mode and the linear viscous damper model; determining the type of the designed damper and the collaborative arrangement mode according to the bridge structure and the damper installation conditions; judging whether the collaborative damping of the damper meets the vibration reduction requirements based on the designed installation position ratio corresponding to the type of the designed damper. If not, adjusting the designed installation position ratio until the collaborative damping meets the vibration reduction requirements. This method can solve the problems in the prior art that the order of the controlled mode of ultra-long stay cables is not clear and the combined vibration reduction measures are difficult to effectively control the vibration of all controlled modes of the stay cables.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge vibration reduction, and particularly relates to a collaborative damping vibration reduction method for wind-induced vibration of ultra-long stay cables. Background Art

[0002] In recent years, with the rapid development of the construction technology of cable-stayed bridges, cable-stayed bridges with main spans exceeding one kilometer have been increasing. The application of long-span cable-stayed bridges has led to the increasing length of stay cables. Currently, the length of stay cables has exceeded 600m. With the increase in highway traffic loads and the construction of highway-railway dual-purpose cable-stayed bridges, the loads borne by stay cables are getting larger and larger. The characteristics of being ultra-long and overweight pose great challenges to the vibration control of stay cables. The traditional vibration control of stay cables mainly focuses on controlling the low and medium-order vibrations of stay cables, and generally adopts the installation of an external damper at the beam end. However, the emergence of ultra-long and overweight stay cables has further reduced the fundamental frequency of stay cables, and high-order vortex-induced vibrations of 40-60 orders may occur under frequently-occurring wind speeds. Such high-order vortex-induced vibrations have been observed on the Sutong Yangtze River Highway Bridge and the Shanghai-Sutong Yangtze River Highway-Railway Bridge. Therefore, compared with traditional stay cables, the vibration control of ultra-long stay cables needs to consider the low, medium, and high-order vibrations of stay cables.

[0003] At present, in order to effectively control the wind-induced vibration of ultra-long stay cables under wind loads, some researchers have proposed relevant dampers and methods. For example, in the invention with the application number CN202011065966.5 and the name "A combined vibration damping device and method for stay cables", aiming at the problem that the external damper has a poor control effect on the high-frequency vibration of stay cables, a combined damper and vibration damping method that combines an external damper and a tuned mass damper is proposed. This method first determines the installation position of the external damper according to the vibration damping requirements of the stay cable, and then determines the design frequency of the tuned mass damper according to the vibration mode frequency of the external damper at the modal node of the stay cable. The vibration of the stay cable is suppressed through the combined action of the dampers. Through analysis, it is found that the method proposed in this invention does not clarify the vibration damping requirements of the stay cable, that is, the controlled modal order of the stay cable. When the controlled modal order is uncertain, it is impossible to clarify whether the combination of the two dampers can completely suppress the low, medium, and high-order vibrations of the stay cable under the controlled mode. For example, in the invention with the application number CN202022844949.3 and the name "A damper system for ultra-long stay cables and a cable-stayed bridge", aiming at the control problems of the low, medium, and high-order modal vibrations of ultra-long stay cables, a damper system is proposed. This system includes a first damping system for suppressing low and medium-order modal vibrations and a second damping system for suppressing high-order modal vibrations. Among them, the first damping system is installed between adjacent cables through a first damper, a support rod, and a cable clamp; the second damping system is installed between the bridge deck and the cable root through a second damper, a connecting rod, and a cable clamp. Through analysis, it is found that the first damping system is installed between two stay cables, and it is difficult for the support stay cable to provide sufficient support stiffness to ensure the vibration damping effect of the first damper.

[0004] In summary, the problems existing in the existing damping and vibration reduction systems and methods are as follows: (1) The controlled modal order of the stay cable is not clear. (2) The combined vibration reduction measures are difficult to effectively control the vibrations of all controlled modes of the stay cable. Summary of the Invention

[0005] Aiming at the defects existing in the prior art, the purpose of the present invention is to provide a collaborative damping and vibration reduction method for the wind-induced vibration of ultra-long stay cables, which can solve the problems that the combined vibration reduction measures in the prior art do not clarify the controlled modal order of the stay cable and are difficult to effectively control the vibrations of all controlled modes of the stay cable.

[0006] To achieve the above purpose, the technical solution adopted by the present invention is:

[0007] The present invention provides a collaborative damping and vibration reduction method for the wind-induced vibration of ultra-long stay cables, including the following steps:

[0008] Based on the Strouhal number, determine the controlled modal order of the wind-induced vibration of the stay cable;

[0009] Based on the controlled modal order and the linear viscous damper model, determine the number of dampers and the preliminary design installation position ratio;

[0010] According to the bridge structure configuration and the damper installation conditions, determine the designed damper type and the collaborative layout method;

[0011] Based on the design installation position ratio corresponding to the designed damper type, determine whether the collaborative vibration damping of the dampers meets the vibration reduction requirements. If not, adjust the design installation position ratio until the collaborative vibration damping meets the vibration reduction requirements.

[0012] In some alternative solutions, if the damper type supported by a bracket or a cable duct is adopted, after the collaborative damping meets the vibration reduction requirements, it is also determined whether the bracket support or the cable duct support meets the design requirements of the support stiffness assurance coefficient. If not, reduce the design installation position ratio until both the collaborative damping and the support stiffness meet the design requirements.

[0013] In some alternative solutions, according to the formula Determine the support stiffness assurance coefficient of the j-th damper for the bracket support or the cable duct support where k j is the support stiffness of the j-th damper, represents the shortest distance between the installation position of the j-th damper and the cable anchorage end, and T is the cable force.

[0014] In some alternative solutions, the determination of the number of dampers and the preliminary design installation position ratio based on the controlled modal order and the linear viscous damper model includes:

[0015] Based on the controlled modal order and the linear viscous damper model, calculate the additional logarithmic decrement of each order of modal vibration provided by the collaborative vibration dampers;

[0016] Determine whether the additional logarithmic decrement meets the vibration reduction requirements. If not, adjust the number of dampers and the preliminary design installation position ratio until the calculated additional logarithmic decrement meets the vibration reduction requirements.

[0017] In some alternative solutions, according to the formula Calculate the additional logarithmic decrement Δ(i) of the i-th order mode under the conditions of the selected number of linear viscous dampers and the preliminary design installation position ratio, is the additional logarithmic decrement provided by the j-th damper for the i-th order mode of the stay cable; k represents the number of dampers used for the stay cable, n is the controlled modal order of the stay cable, represents the shortest distance between the installation position of the j-th damper and the cable anchorage end; l represents the length of the stay cable; represents the installation position ratio of the j-th damper, i = 1... n, j = 1... k.

[0018] In some alternative embodiments, determining the controlled modal order of the cable - stayed cable's wind - induced vibration based on the Strouhal number includes:

[0019] Based on the frequent wind speed and the outer diameter size of the cable - stayed cable, calculate the controlled wind - vibration frequency of the cable - stayed cable through the Strouhal number;

[0020] Based on the cable - stayed cable parameters, determine the fundamental vibration frequency of the cable - stayed cable;

[0021] According to the controlled wind - vibration frequency and the fundamental vibration frequency of the cable - stayed cable, determine the controlled modal order of the cable - stayed cable.

[0022] In some alternative embodiments, according to the formula f v =US t / D, determine the controlled wind - vibration frequency f v ;

[0023] where U is the frequent wind speed; D is the outer diameter size of the cable - stayed cable; S t is the Strouhal number.

[0024] In some alternative embodiments, according to the formula the fundamental vibration frequency f0 of the cable - stayed cable;

[0025] where L is the cable length; T is the cable force; m is the mass per unit length of the cable - stayed cable.

[0026] In some alternative embodiments, according to n = f v / f0, determine the controlled modal order n of the cable - stayed cable, where f0 is the fundamental vibration frequency of the cable - stayed cable, and f v is the controlled wind - vibration frequency.

[0027] In some alternative embodiments, according to the bridge structure configuration and the damper installation conditions, determine the collaborative layout method of the designed damper, including: beam - end collaborative layout, tower - end collaborative layout, and beam - end - tower - end collaborative layout.

[0028] Compared with the prior art, the advantages of the present invention are: (1) The control order of the ultra - long cable - stayed cable is clarified through the Strouhal number and the fundamental frequency calculation formula of the cable - stayed cable; (2) The type and collaborative layout method of the designed damper can be clarified through the bridge structure configuration and the damper installation conditions; (3) The collaborative vibration - damping damper designed by this method comprehensively considers all the controlled modal orders, enables all the controlled orders to meet the design requirements, the vibration - damping effect is predictable, and can effectively control the vibration problems of all the controlled modes of the ultra - long cable - stayed cable. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] To more clearly illustrate the technical solutions in the embodiments of the present application, the following briefly introduces the accompanying drawings required for the description of the embodiments. Obviously, the accompanying drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can be obtained based on these drawings.

[0030] Figure 1 It is a schematic flowchart of a collaborative damping and vibration reduction method for wind-induced vibration of ultra-long stay cables in an embodiment of the present invention;

[0031] Figure 2 It is a schematic diagram of the installation structure of a collaborative damper in an embodiment of the present invention;

[0032] Figure 3 It is a schematic diagram of the vibration reduction effect of a linear viscous damper installed at the tower end in an embodiment of the present invention;

[0033] Figure 4 It is a schematic diagram of the vibration reduction effect of a linear viscous damper installed at the beam end in an embodiment of the present invention;

[0034] Figure 5 It is a schematic diagram of the collaborative vibration reduction effect of the installed linear viscous damper in an embodiment of the present invention;

[0035] Figure 6 It is a schematic diagram of the vibration reduction effect of a lever mass damper installed at the beam end in an embodiment of the present invention;

[0036] Figure 7 It is a schematic diagram of the collaborative vibration reduction effect of the installed designed damper in an embodiment of the present invention.

[0037] In the figure: 1. Stay cable; 2. Main tower; 3. Main beam; 4. Beam-end damper; 5. Tower-end damper. Detailed implementation manners

[0038] To make the objectives, technical solutions, and advantages of the embodiments of the present application clearer, the following clearly and completely describes the technical solutions in the embodiments of the present application with reference to the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are some, but not all, of the embodiments of the present application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present application without creative efforts belong to the scope of protection of the present application.

[0039] The following further elaborates on the embodiments of the present invention with reference to the accompanying drawings.

[0040] As Figure 1 shown, the present invention provides a collaborative damping and vibration reduction method for wind-induced vibration of ultra-long stay cables, including the following steps:

[0041] S1: Determine the order of the controlled mode of the cable - stayed cable's wind - induced vibration based on the Strouhal number.

[0042] In some alternative embodiments, step S1 specifically includes:

[0043] S11: Calculate the controlled wind - induced vibration frequency of the cable - stayed cable based on the frequent wind speed and the outer diameter size of the cable - stayed cable through the Strouhal number.

[0044] In this example, according to the formula f v = US t / D, determine the controlled wind - induced vibration frequency f v ; U is the frequent wind speed; D is the outer diameter size of the cable - stayed cable; S t is the Strouhal number, that is, the Strouhal number.

[0045] S12: Determine the fundamental vibration frequency of the cable - stayed cable based on the parameters of the cable - stayed cable.

[0046] In this example, according to the formula the fundamental vibration frequency f0 of the cable - stayed cable; L is the cable length; T is the cable force; m is the mass per unit length of the cable - stayed cable.

[0047] S13: Determine the order of the controlled mode of the cable - stayed cable according to the controlled wind - induced vibration frequency and the fundamental vibration frequency of the cable - stayed cable.

[0048] In this example, according to n = f v / f0, determine the order of the controlled mode n of the cable - stayed cable, where f0 is the fundamental vibration frequency of the cable - stayed cable, and f v is the controlled wind - induced vibration frequency.

[0049] S2: Based on the order of the controlled mode and the linear viscous damper model, determine the number of dampers and the preliminary design installation position ratio through the complex modal decomposition method.

[0050] In some alternative embodiments, step S2 includes:

[0051] S21: Based on the order of the controlled mode and the linear viscous damper model, calculate the additional logarithmic decrement of each - order modal vibration provided by the cooperative vibration - damping damper through the complex modal decomposition method.

[0052] In this example, according to the formula calculate the additional logarithmic decrement Δ(i) of the i - th order mode under the condition of the selected number and preliminary design installation position ratio of the linear viscous damper, is the additional logarithmic decrement provided by the j - th damper to the i - th order mode of the cable - stayed cable solved by the complex modal decomposition method; k represents the number of dampers used for the cable - stayed cable, and n is the order of the controlled mode of the cable - stayed cable, represents the shortest distance between the installation position of the j-th damper and the cable anchorage end; l represents the length of the stay cable; represents the installation position ratio of the j-th damper, i = 1...n, j = 1...k; Δ(i) represents the sum of the additional logarithmic decrement rates provided by all dampers for the i-th modal vibration of the stay cable. In this example, k takes the value of 2, that is, two dampers are installed on the stay cable. For the convenience and aesthetics of installation, the two dampers are generally installed at the beam end and the tower end respectively.

[0053] S22: Determine whether the additional logarithmic decrement rate meets the vibration reduction requirements. If not, adjust the number of dampers and the preliminary design installation position ratio until the additional logarithmic decrement rate calculated by the complex modal decomposition method meets the vibration reduction requirements.

[0054] In this example, for the additional logarithmic decrement rate of the i-th modal vibration, a linear viscous damper model is used for calculation. Ensure that the additional logarithmic decrement rates of each modal vibration meet the design requirements. In this way, the preliminary design installation position ratio of the theoretical design is obtained using the viscous damper model.

[0055] S3: Determine the type of designed damper and the collaborative layout method according to the bridge structure configuration and damper installation conditions.

[0056] In this example, due to location requirements during on-site installation. According to the bridge structure configuration and damper layout requirements, select the type of damper that works collaboratively. Among them, broadband dampers are preferably used for collaborative damping control. If it is not possible to install broadband dampers simultaneously, broadband and narrowband dampers can be used for collaborative control.

[0057] In this example, according to the bridge structure configuration and damper installation conditions, determine the collaborative layout method of the designed damper, including: collaborative layout at the beam end, collaborative layout at the tower end, and beam end - tower end collaborative layout.

[0058] In this example, the collaborative layout at the beam end means arranging the dampers collaboratively at the beam end, the collaborative layout at the tower end means arranging the dampers collaboratively at the tower end, and the beam end - tower end collaborative layout means arranging the dampers collaboratively at the beam end and the tower end respectively.

[0059] On the premise that the installation conditions are met, in this example, one damper is set at the beam end and the tower end respectively, and they are used to control the low and middle order vibrations and the middle and high order vibrations of the stay cable respectively. The beam end and the tower end satisfy the frequencies that the stay cable needs to be controlled.

[0060] S4: Based on the designed installation position ratio corresponding to the type of designed damper, determine whether the collaborative vibration reduction damping of the damper meets the vibration reduction requirements through the complex modal decomposition method. If not, adjust the designed installation position ratio until the collaborative vibration reduction damping meets the vibration reduction requirements.

[0061] In this example, the formula is also used to calculate the additional logarithmic decrement Δ(i) of the i-th order modal vibration of the designed damper type under the conditions of the selected quantity and the designed installation position ratio. However, the parameters of the actual designed damper type are used for the calculation.

[0062] When specifically adjusting the designed installation position ratio, adjust the installation position of the designed damper i.e., the designed installation position ratio Calculate the additional logarithmic decrement Δ of the cooperative damper on the stay cable under different designed installation position ratios. Among them, the parameters of the actual designed damper type are used for the calculation. When the additional logarithmic decrement Δ meets the corresponding vibration reduction requirements, further determine the corresponding designed installation position ratio at this time as the designed installation position ratio of the damper.

[0063] In some alternative embodiments, if the damper type supported by a bracket or a cable duct is adopted, after the cooperative damping meets the vibration reduction requirements, it is also determined whether the support by the bracket or the cable duct meets the design requirements of the support stiffness guarantee coefficient. If not, reduce the designed installation position ratio until both the cooperative damping and the support stiffness meet the design requirements.

[0064] Specifically, according to the formula determine the support stiffness guarantee coefficient of the j-th damper supported by a bracket or a cable duct where k j is the support stiffness of the j-th damper, represents the shortest distance between the installation position of the j-th damper and the cable anchoring end, and T is the cable force.

[0065] When the damper support stiffness guarantee coefficient meets the design requirements, this step is completed and the design process of the cooperative damper ends; when the damper support stiffness guarantee coefficient does not meet the design requirements, readjust the designed installation position ratio of the damper until the designed installation position ratio meets both the design requirements of the additional logarithmic decrement and the support stiffness guarantee coefficient.

[0066] When there is no damper supported by a bracket or a cable duct in the cooperative damper, when the designed installation position ratio meets the design requirements of the additional logarithmic decrement, the design process of the cooperative damper ends.

[0067] The following gives a more specific embodiment to illustrate the design process of using the cooperative vibration reduction damper:

[0068] A certain bridge is a cable-stayed bridge with a main span of 900 meters. The longest stay cable 1 is 620 meters long, with an outer diameter of 200 mm, a cable force of 12,500 kN, and a unit cable weight of 140 kg / m for stay cable 1. The end anchoring method of stay cable 1 is the anchor plate type. The common wind speed is level 6 wind, and the Strouhal number S t = 0.2. The vibration reduction target of stay cable 1: For the vibration mode frequencies below 3 Hz of the stay cable, that is, for the 3rd - 13th order, the designed logarithmic decrement should reach more than 3.0%, and for the vibration mode frequencies above 3 Hz, that is, for the 14th order and above, the designed logarithmic decrement should reach more than 1.5%. The structure of the main girder 3 is a steel truss girder for both railway and highway use, and the main tower 2 is a concrete tower.

[0069] Adopt the above - mentioned collaborative damping vibration reduction method for the wind - induced vibration of ultra - long stay cables to determine the parameters of the collaborative damper, specifically as follows:

[0070] First, through the formula n = f v / f0, the controlled modal order n of the stay cable in the implementation case is calculated to be 60.

[0071] Combined with the characteristics of the bridge structure, the theoretical installation position ratio range of the damper is given: The beam - end damper 4 controls the medium - high - order vibrations, that is, the (41 - 60)th order, and the installation position ratio is taken as 1.1%, and the installation position The tower - end damper 5 controls the low - medium - order vibrations, that is, the (1 - 33)th order, and the installation position ratio is taken as 1.5%, and the installation position

[0072] According to the formula Determine the sum of the additional logarithmic decrements Δ(i) provided by the collaborative damper for the i - th order modal vibration of the stay cable. Through calculation and analysis, the vibration reduction effect of the tower - end viscous damper is as Figure 3 shown, the vibration reduction effect of the beam - end viscous damper is as Figure 4 , and the collaborative vibration reduction effect of the damper is as Figure 5 shown. It can be seen from the above that the additional logarithmic decrements of the stay cable for the (3 - 60)th order all meet the vibration reduction requirements.

[0073] Determine the wide - band type collaborative damper. Select the lever mass damper for the beam - end damper and the viscous damper for the tower - end damper. As Figure 2 shown.

[0074] Considering that there is a bridge deck support at the beam end, the tower - end damper has installation conditions, and the tower end provides a larger installation position, the tower - end viscous damper is used to control the low - medium - order vibrations of the stay cable, and the beam - end lever mass damper with a smaller installation position ratio is used to control the medium - high - order vibrations of the stay cable.

[0075] According to the theoretical installation position ratio of the dampers, it is determined that the design installation position ratio of the lever mass damper at the beam end is taken as 1.1%, and the design installation position ratio of the viscous damper at the tower end is taken as 1.5%.

[0076] According to the formula Determine the sum of the additional logarithmic decrements Δ(i) provided by the cooperative dampers for the i-th order modal vibration of the stay cables. Through calculation and analysis, the vibration reduction effect of the viscous damper is as Figure 2 shown, and the vibration reduction effect of the lever mass damper is as Figure 6 , and the cooperative vibration reduction effect of the dampers is as Figure 7 shown. It can be seen from the above that the additional logarithmic decrements of the stay cables in the (3 - 60) orders all meet the vibration reduction requirements.

[0077] The damper support stiffness guarantee coefficient should reach above 0.8.

[0078] The support stiffness of the cable duct of the viscous damper at the tower end and the support stiffness of the bracket of the lever mass damper at the beam end need to be checked through the formula . The support stiffness k 1 of the bracket of the lever mass damper at the beam end is 10,000 kN / m, and the stiffness guarantee coefficient . The support stiffness k 2 of the cable duct of the viscous damper at the tower end is 7,000 kN / m, and the stiffness guarantee coefficient The damper support stiffness guarantee coefficients and both reach above the design requirement of 0.80, and the design process of the cooperative dampers ends.

[0079] To sum up, in this scheme, first, based on the Strouhal number, the order of the controlled modes of the wind-induced vibration of the stay cables is determined; then, based on the order of the controlled modes and the linear viscous damper model, the number of dampers and the preliminary design installation position ratio are determined through the complex modal decomposition method; according to the bridge structure configuration and the damper installation conditions, the type of the designed damper and the cooperative layout method are determined; based on the design installation position ratio corresponding to the type of the designed damper, it is judged whether the cooperative vibration reduction damping of the dampers meets the vibration reduction requirements through the complex modal decomposition method. If not, the design installation position ratio is adjusted until the cooperative vibration reduction damping meets the vibration reduction requirements. The order of the controlled modes is clear. Considering all the orders of the controlled modes comprehensively, all the controlled orders can meet the design requirements, and the vibration reduction effect is predictable. The support stiffness of the designed damper also needs to be checked. If the support stiffness does not meet the requirements, the design installation position ratio is reduced and returned to S4 for recalculation and analysis until both the vibration reduction requirements and the support stiffness meet the design requirements. Considering the order of the controlled modes, whether it is effective for all the orders of the controlled modes, and the requirements of the support stiffness in the design stage, both the vibration reduction effect and the feasibility can be predicted, improving the efficiency of design and construction.

[0080] In the description of the present application, it should be noted that the orientation or positional relationship indicated by terms such as "upper" and "lower" is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present application and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, it should not be construed as a limitation to the present application. Unless otherwise clearly specified and defined, the terms "installed", "connected", and "coupled" should be understood in a broad sense. For example, it may be a fixed connection, a detachable connection, or an integral connection; it may be a mechanical connection or an electrical connection; it may be directly connected or indirectly connected through an intermediate medium, and it may be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present application can be understood according to specific circumstances.

[0081] It should be noted that in the present application, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprising", "including" or any other variant thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements not only includes those elements, but also includes other elements not expressly listed, or further includes elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "comprising one..." does not exclude the existence of additional identical elements in the process, method, article or device including the said element.

[0082] The above are only specific embodiments of the present application, enabling those skilled in the art to understand or implement the present application. Various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to these embodiments shown herein, but rather to the broadest scope consistent with the principles and novel features claimed herein.

Claims

1. A collaborative damping vibration reduction method for wind-induced vibration of ultra-long stay cables, characterized in that, Including the following steps: Based on the Strouhal number, determine the order of the controlled mode of the cable wind-induced vibration; including: Based on the frequently encountered wind speed and the outer diameter size of the stay cable, calculate the controlled wind vibration frequency of the stay cable through the Strouhal number; according to the formula , determine the controlled wind vibration frequency ; where U is the frequently encountered wind speed; D is the outer diameter size of the stay cable; S t is the Strouhal number; Based on the cable parameters, determine the fundamental vibration frequency of the stay cable; according to the formula , the fundamental vibration frequency of the stay cable f 0; where L is the cable length; T is the cable force; m is the mass per unit length of the stay cable; Determine the controlled modal order of the stay cable according to the controlled wind-induced vibration frequency and the vibration fundamental frequency of the stay cable; according to n = f v / f 0, determine the controlled modal order of the stay cable n , f 0 is the vibration fundamental frequency of the stay cable, is the controlled wind-induced vibration frequency; Based on the order of the controlled mode and the linear viscous damper model, determine the number of dampers and the preliminary design installation position ratio; including: Based on the controlled modal order and the linear viscous damper model, calculate the additional logarithmic decrement of each order of modal vibration provided by the cooperative vibration damping damper; according to the formula , calculate the additional logarithmic decrement of the i -th order mode of the linear viscous damper under the conditions of the selected number and the preliminary design installation position ratio , is the additional logarithmic decrement provided by the j -th damper to the i -th order mode of the stay cable; k represents the number of dampers used for the stay cable, n is the controlled modal order of the stay cable, represents the shortest distance between the installation position of the j -th damper and the anchorage end of the cable; represents the length of the stay cable; represents the installation position ratio of the j -th damper, i = 1...n, j = 1...k; Judge whether the additional logarithmic decrement meets the vibration reduction requirements. If not, adjust the number of dampers and the preliminary design installation position ratio until the calculated additional logarithmic decrement meets the vibration reduction requirements; According to the bridge structure and the damper installation conditions, determine the type of the designed damper and the collaborative layout method; Based on the design installation position ratio corresponding to the type of the designed damper, judge whether the collaborative vibration reduction damping of the damper meets the vibration reduction requirements. If not, adjust the design installation position ratio until the collaborative vibration reduction damping meets the vibration reduction requirements.

2. The collaborative damping and vibration reduction method for wind-induced vibration of an ultra-long stay cable according to claim 1, characterized in that, If the damper type of support by bracket or cable duct support is adopted, after the collaborative damping meets the vibration reduction requirements, it is also judged whether the support by bracket or cable duct support meets the design requirements of the support stiffness guarantee coefficient. If not, reduce the design installation position ratio until both the collaborative damping and the support stiffness meet the design requirements.

3. The collaborative damping vibration reduction method for wind-induced vibration of an ultra-long stay cable according to claim 2, characterized in that, According to the formula , determine the bracket support or cable duct support stiffness guarantee coefficient j of the th damper; where is the support stiffness of the j th damper, represents the shortest distance between the installation position of the j th damper and the cable anchorage end, T is the cable force.

4. The collaborative damping vibration reduction method for wind-induced vibration of an ultra-long stay cable according to claim 1, characterized in that: According to the bridge structure and the damper installation conditions, determine the collaborative layout method of the designed damper, including: collaborative layout at the beam end, collaborative layout at the tower end, and collaborative layout between the beam end and the tower end.

Images