CN107885954B - Vibration reduction design method for suspension type cable-stayed bridge stay cable - Google Patents

Vibration reduction design method for suspension type cable-stayed bridge stay cable Download PDF

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CN107885954B
CN107885954B CN201711221054.0A CN201711221054A CN107885954B CN 107885954 B CN107885954 B CN 107885954B CN 201711221054 A CN201711221054 A CN 201711221054A CN 107885954 B CN107885954 B CN 107885954B
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tmd
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罗帅
朱佳洋
梁超锋
刘伟
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University of Shaoxing
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    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F30/00—Computer-aided design [CAD]
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    • G06F30/13—Architectural design, e.g. computer-aided architectural design [CAAD] related to design of buildings, bridges, landscapes, production plants or roads
    • E—FIXED CONSTRUCTIONS
    • E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
    • E01D—CONSTRUCTION OF BRIDGES, ELEVATED ROADWAYS OR VIADUCTS; ASSEMBLY OF BRIDGES
    • E01D11/00—Suspension or cable-stayed bridges
    • E01D11/04—Cable-stayed bridges
    • E—FIXED CONSTRUCTIONS
    • E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
    • E01D—CONSTRUCTION OF BRIDGES, ELEVATED ROADWAYS OR VIADUCTS; ASSEMBLY OF BRIDGES
    • E01D19/00—Structural or constructional details of bridges
    • E01D19/16—Suspension cables; Cable clamps for suspension cables ; Pre- or post-stressed cables
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Abstract

The invention belongs to the technical field of engineering, and particularly relates to a vibration reduction design method for a suspension type cable-stayed bridge cable, which comprises the following steps: firstly, establishing a stay cable double TMD vibration reduction model by using a numerical analysis model; secondly, analyzing a dynamic balance equation of a mounting TMD position and a TMD system balance equation by using a double TMD vibration reduction model of the stay cables; and thirdly, verifying that the designed double TMD damping system can further effectively reduce the dynamic response of the inhaul cable through example analysis. The invention improves the defect of frequency sensitivity by simultaneously adopting two TMD systems, improves the defect of sensitivity of a single TMD system to vibration frequency by theoretical analysis, and further improves the vibration damping effect of the system.

Description

Vibration reduction design method for suspension type cable-stayed bridge stay cable
Technical Field
The invention belongs to the technical field of engineering, and particularly relates to a vibration reduction design method for a suspension type cable-stayed bridge inhaul cable.
Background
The control strategy of the Tuned Mass Damper (TMD) achieves the aim of dynamic vibration absorption by applying the resonance of the substructure and the controlled structure, and reduces the response of the main structure in the process of continuously absorbing the vibration energy of the main structure and continuously consuming the vibration energy of the substructure by applying the vibration energy of an energy consumption damping material or device consumption substructure. However, according to the Bode diagram of the dynamic response of the guy cable, the single TMD system has the following defects: a single TMD can only control the reaction of the odd-order mode shape of the structure, but the control effect on the even-order mode shape is not obvious. In order to reduce TMD frequency tuning sensitivity, the invention provides a problem of improving frequency sensitivity by simultaneously adopting two TMD systems, and design parameters and installation positions of the TMD systems are further optimized through theoretical analysis and modal characteristic experiments.
Disclosure of Invention
The invention aims to provide a vibration reduction design method for a suspension type cable-stayed bridge stay cable so as to further improve the vibration reduction effect of a system.
In order to achieve the purpose, the invention specifically provides the following technical scheme: a vibration reduction design method for a suspension type cable-stayed bridge inhaul cable comprises the following steps: firstly, establishing a stay cable double TMD vibration reduction model by using a numerical analysis model; secondly, analyzing a dynamic balance equation of a mounting TMD position and a TMD system balance equation by using a double TMD vibration reduction model of the stay cables; and thirdly, verifying that the designed double TMD damping system can further effectively reduce the dynamic response of the inhaul cable through example analysis.
The method for designing the vibration reduction of the inhaul cable of the suspension type cable-stayed bridge is further characterized by comprising the following steps: establishing a stay cable double TMD vibration reduction model by using a numerical analysis model; the cable force is T, the linear density of the cables is m, the inclination angle is theta, the total length of the cables is L, and the TMD is arranged at an anchoring end L away from the cable bridge deck1And l1+l2The position of (a).
A vibration damping design method for a suspension type cable-stayed bridge stay cable, and further comprises a second step of analyzing a dynamic balance equation and a TMD system balance equation of the stay cable at the position where the TMD is installed according to the established vibration damping model, wherein the node number is k,
the dynamic balance equation of the guy cable at the installation TMD position (the node number is k) is as follows:
Figure GDA0001552389850000021
the vertical equilibrium equation of the TMD mounting point is:
Figure GDA0001552389850000022
wherein v isdFor vertical displacement of the damper, withMeanwhile, the TMD system equilibrium equation is:
Figure GDA0001552389850000023
wherein m isk,ck,kkRespectively, the concentrated mass, the damping and the rigidity at the node k, and obtaining a TMD system balance equation according to the formula (1-2):
Figure GDA0001552389850000024
wherein M isT,CT,KTSubstituting the formulas (1-1) and (1-4) into the following formulas (1-4) to derive a new state space equation standard form for the designed TMD mass, damping and rigidity respectively;
the dynamic balance equation of the inhaul cable under the load action is as follows:
Figure GDA0001552389850000031
wherein L is a load vector
u (t) -dynamic load time course.
The invention has the beneficial effects that: the vibration reduction model based on the single TMD-stayed cable system improves the defect of frequency sensitivity by simultaneously adopting two TMD systems, improves the defect of sensitivity of the single TMD system to vibration frequency by theoretical analysis, and further improves the vibration reduction effect of the system.
Drawings
FIG. 1 is a stay cable-dual TMD system vibration damping analysis model; FIG. 2 is a stay cable-dual TMD system vibration damping analysis model; FIG. 3 is a graph of acceleration time history under the action of seismic excitation;
FIG. 4 is a dynamic response time course at a midpoint of a cable; FIG. 5 is a dynamic response time course at the midpoint of the cable.
Detailed Description
The present invention is described in more detail below.
As shown in fig. 1 and 2, the dual TMD is applied to cable damping, and the method comprises the following steps:
(1) on the premise of embodying the nature of the problem, a stay cable-dual TMD vibration damping system shown in the following figure 1 is established by utilizing the deduced stay cable vibration numerical analysis model, the cable force is T, the linear density of the stay cable is m, the inclination angle is theta, the total length of the cable is L, and the TMD is arranged at an anchoring end L away from the bridge floor of the stay cable1And l1+l2The position of (a).
(2) And analyzing a dynamic balance equation of the stay cable at the position where the TMD is installed (the node number is set as k) and a TMD system balance equation according to the established damping system.
The dynamic balance equation of the guy cable at the installation TMD position (the node number is k) is as follows:
Figure GDA0001552389850000041
the vertical equilibrium equation of the TMD mounting point is:
Figure GDA0001552389850000042
wherein v isdFor damper vertical displacement, at the same time, the TMD system equilibrium equation is:
Figure GDA0001552389850000043
wherein m isk,ck,kkRespectively, the concentrated mass, the damping and the rigidity at the node k, and obtaining a TMD system balance equation according to the formula (1-2):
Figure GDA0001552389850000044
wherein M isT,CT,KTSubstituting the formulas (1-1) and (1-4) into the following formulas (1-4) for the designed TMD mass, damping and stiffness respectively to derive a new state space equation standard form.
The dynamic balance equation of the inhaul cable under the load action is as follows:
Figure GDA0001552389850000045
wherein L is a load vector
u (t) -dynamic load time course
By example analysis, the designed dual TMD damping system can be further effectively damped
Dynamic response of small guy cables.
Analysis by calculation example: TABLE 1TMD basic parameters and ranges thereof
Figure GDA0001552389850000046
The table 1 lists TMD basic parameters selected based on the actual engineering situation, and lists the value ranges of the parameters based on the TMD basic parameters, so as to analyze the influence of the parameters on the modal damping of the system.
Selecting inhaul cable parameters according to the TMD basic parameter value range selected based on the actual engineering situation listed in the table 1 as follows: 0.00808 square meter in cross section area, 180.94m in length, 7482.38KN in tension, 3.0 in safety coefficient, 0.6712HZ in fundamental frequency of the stay cable, 200GPa in elastic modulus and 7849.08kg/m in density3. According to the parameters, dynamic response time course analysis of the stay cable additional tuned mass damper considering bridge deck movement is carried out and compared with a single TMD vibration attenuation effect, because vibration attenuation analysis mainly aims at the front two-order mode of the stay cable, firstly, the TMD installation position is assumed to be a three-point position of the stay cable with the optimal vibration attenuation effect, and design parameters can be respectively determined according to the influence rule of each TMD parameter on system mode damping obtained by analysis:
quality parameter MT＝1.5％×m×L≈320kg
The stiffness parameters at this time are:
KT＝MT(ωd2)2≈2470N·m-1
corresponding TMD damping systemThe number as a single influencing parameter is determined here mainly by the dichotomy in the program as CT＝1333N·s·m-1. The reasonability of the optimization result of the damper parameters based on the analytic model is verified, and the dynamic response of the stay cable under the excitation of the vertical end part caused by the earthquake action shown in figure 3 is further analyzed.
Referring to fig. 3, 4, and 5, the seismic data: a class 4.1 Richter earthquake of 37 minutes 32 seconds (UTC) occurred at 12 days 1/5/2005 in Arkansas, Manila, 175km from the Cape Girardeau bridge for a duration of about 78 seconds and a source depth of about 10 km. Acceleration response time interval of 120 seconds from the application of the IRIS Data Management Center (DMC) to 12 hours 37.
The dynamic balance equation of the guy cable at the installation TMD position (assuming the node number is k, two damping devices with the same design parameters are adopted here) is as follows:
Figure GDA0001552389850000061
wherein m isk,ck,kkRespectively, concentrated mass, damping and stiffness at node k
TMD system equilibrium equation:
Figure GDA0001552389850000062
wherein M isT,CT,KTRespectively the designed TMD mass, damping and stiffness. Assuming the cable initial speed is zero, the controlled and uncontrolled dynamic response displacement time course at the cable midpoint under end excitation is shown in fig. 4 and 5. Compared with a single TMD, the designed double TMD damping system can further effectively reduce the dynamic response of the cable.

Claims (2)

1. A vibration reduction design method for a suspension type cable-stayed bridge inhaul cable is characterized by comprising the following steps:
firstly, establishing a stay cable double TMD vibration reduction model by using a numerical analysis model;
secondly, analyzing a dynamic balance equation of a mounting TMD position and a TMD system balance equation by using a double TMD vibration reduction model of the stay cables; according to the established vibration reduction model, analyzing a dynamic balance equation and a TMD system balance equation of the stay cable at the position where the TMD is installed, wherein the node number is k, and the dynamic balance equation of the stay cable at the position where the TMD is installed (the node number is k) is as follows:
Figure FDA0002765720320000011
the vertical equilibrium equation of the TMD mounting point is:
Figure FDA0002765720320000012
wherein v isdFor damper vertical displacement, at the same time, the TMD system equilibrium equation is:
Figure FDA0002765720320000013
wherein m isk,ck,kkRespectively, the concentrated mass, the damping and the rigidity at the node k, and obtaining a TMD system balance equation according to the formula (1-2):
Figure FDA0002765720320000014
wherein M isT,CT,KTSubstituting the formulas (1-1) and (1-4) into the following formulas (1-4) to derive a new state space equation standard form for the designed TMD mass, damping and rigidity respectively;
the dynamic balance equation of the inhaul cable under the load action is as follows:
Figure FDA0002765720320000015
wherein L is a load vector
u (t) -dynamic load time course;
and thirdly, verifying that the designed double TMD damping system can further effectively reduce the dynamic response of the inhaul cable through example analysis.
2. The method for designing the vibration reduction of the suspension type cable-stayed bridge cable according to claim 1, wherein the method comprises the following steps: establishing a stay cable double TMD vibration reduction model by using a numerical analysis model; the cable force is T, the linear density of the cables is m, the inclination angle is theta, the total length of the cables is L, and the TMD is arranged at an anchoring end L away from the cable bridge deck1And l1+l2The position of (a).
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CN108873685A (en) * 2018-07-03 2018-11-23 武汉理工大学 A kind of drag-line additional bending moment vibration insulating system based on macro fibrous composite
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CN116577996B (en) * 2023-07-06 2023-10-20 华南理工大学 Movable active control method for vibration of flexible civil structure

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101016758A (en) * 2007-01-22 2007-08-15 哈尔滨工业大学 Novel mixing quality driving variable damping control device for structure vibration control
CN101302995A (en) * 2008-05-21 2008-11-12 三一电气有限责任公司 Tuning quality damper vibration damping control device for blower fan
CN106951668A (en) * 2017-05-04 2017-07-14 中铁二院工程集团有限责任公司 The stiffness reliability method and cable-stayed bridge of a kind of Long Span Railway cable-stayed bridge
CN107145664A (en) * 2017-05-04 2017-09-08 中铁二院工程集团有限责任公司 A kind of method that Long Span Railway cable-stayed bridge rigidity is controlled by suspension cable

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101016758A (en) * 2007-01-22 2007-08-15 哈尔滨工业大学 Novel mixing quality driving variable damping control device for structure vibration control
CN101302995A (en) * 2008-05-21 2008-11-12 三一电气有限责任公司 Tuning quality damper vibration damping control device for blower fan
CN106951668A (en) * 2017-05-04 2017-07-14 中铁二院工程集团有限责任公司 The stiffness reliability method and cable-stayed bridge of a kind of Long Span Railway cable-stayed bridge
CN107145664A (en) * 2017-05-04 2017-09-08 中铁二院工程集团有限责任公司 A kind of method that Long Span Railway cable-stayed bridge rigidity is controlled by suspension cable

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
"地震作用下填充墙MTMD 减震结构频域响应分析";卢俊龙等;《振动与冲击》;20131231;第32卷(第18期);第136-140页 *
"基于MATLAB 的车桥耦合动力学分析";李沣;《中国优秀硕士学位论文全文数据库（电子期刊）工程科技Ⅱ辑》;20170615;第C034-112页 *
"简支梁桥车桥耦合振动及MTMD振动控制研究";涂勇;《中国优秀硕士学位论文全文数据库（电子期刊）工程科技Ⅱ辑》;20130215;第C034-112页 *

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