CN111043210A - Shrink-ring type eddy current tuned mass damper - Google Patents
Shrink-ring type eddy current tuned mass damper Download PDFInfo
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- CN111043210A CN111043210A CN201911201247.9A CN201911201247A CN111043210A CN 111043210 A CN111043210 A CN 111043210A CN 201911201247 A CN201911201247 A CN 201911201247A CN 111043210 A CN111043210 A CN 111043210A
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- mass
- lightning rod
- eddy current
- type frame
- current tuned
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
- F16F7/00—Vibration-dampers; Shock-absorbers
- F16F7/10—Vibration-dampers; Shock-absorbers using inertia effect
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
- F16F15/00—Suppression of vibrations in systems; Means or arrangements for avoiding or reducing out-of-balance forces, e.g. due to motion
- F16F15/02—Suppression of vibrations of non-rotating, e.g. reciprocating systems; Suppression of vibrations of rotating systems by use of members not moving with the rotating systems
- F16F15/022—Suppression of vibrations of non-rotating, e.g. reciprocating systems; Suppression of vibrations of rotating systems by use of members not moving with the rotating systems using dampers and springs in combination
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
- F16F15/00—Suppression of vibrations in systems; Means or arrangements for avoiding or reducing out-of-balance forces, e.g. due to motion
- F16F15/02—Suppression of vibrations of non-rotating, e.g. reciprocating systems; Suppression of vibrations of rotating systems by use of members not moving with the rotating systems
- F16F15/03—Suppression of vibrations of non-rotating, e.g. reciprocating systems; Suppression of vibrations of rotating systems by use of members not moving with the rotating systems using magnetic or electromagnetic means
- F16F15/035—Suppression of vibrations of non-rotating, e.g. reciprocating systems; Suppression of vibrations of rotating systems by use of members not moving with the rotating systems using magnetic or electromagnetic means by use of eddy or induced-current damping
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
- F16F15/00—Suppression of vibrations in systems; Means or arrangements for avoiding or reducing out-of-balance forces, e.g. due to motion
- F16F15/02—Suppression of vibrations of non-rotating, e.g. reciprocating systems; Suppression of vibrations of rotating systems by use of members not moving with the rotating systems
- F16F15/04—Suppression of vibrations of non-rotating, e.g. reciprocating systems; Suppression of vibrations of rotating systems by use of members not moving with the rotating systems using elastic means
- F16F15/08—Suppression of vibrations of non-rotating, e.g. reciprocating systems; Suppression of vibrations of rotating systems by use of members not moving with the rotating systems using elastic means with rubber springs ; with springs made of rubber and metal
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
- F16F6/00—Magnetic springs; Fluid magnetic springs, i.e. magnetic spring combined with a fluid
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01T—SPARK GAPS; OVERVOLTAGE ARRESTERS USING SPARK GAPS; SPARKING PLUGS; CORONA DEVICES; GENERATING IONS TO BE INTRODUCED INTO NON-ENCLOSED GASES
- H01T19/00—Devices providing for corona discharge
- H01T19/04—Devices providing for corona discharge having pointed electrodes
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
- F16F2230/00—Purpose; Design features
- F16F2230/0005—Attachment, e.g. to facilitate mounting onto confer adjustability
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- Engineering & Computer Science (AREA)
- General Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Mechanical Engineering (AREA)
- Acoustics & Sound (AREA)
- Aviation & Aerospace Engineering (AREA)
- Electromagnetism (AREA)
- Plasma & Fusion (AREA)
- Chemical & Material Sciences (AREA)
- Combustion & Propulsion (AREA)
- Buildings Adapted To Withstand Abnormal External Influences (AREA)
Abstract
The invention provides a lantern ring type eddy current tuned mass damper, which comprises a hollow sleeve type frame (1), a mass block (3) arranged in the sleeve type frame (1), a copper plate (5) and a plurality of suspenders (2); the plurality of suspension rods (2) are uniformly and symmetrically arranged around the steel tube lightning rod (9), the upper end of each suspension rod (2) is fixed with the top of the sleeve type frame (1), the lower end of each suspension rod is fixed with the mass block (3), the copper plate (5) is positioned at the bottom of the sleeve type frame (1), the lightning rod with larger specification and quality can be damped, the damping effect is good, the sleeve type frame is fixed with the steel tube lightning rod through bolts, the welding process is avoided, and the installation and construction are convenient; the suspender has no initial friction, the inertia moment of the section is the same in all directions of 360 degrees, the vibration of the steel pipe lightning rod generated by wind can be controlled in all directions, the external energy supply is not needed, the elastic modulus is small, the section size is large, the length size is small, and the damper is convenient to design, manufacture and install.
Description
Technical Field
The invention relates to the technical field of wind vibration control in electric power engineering, in particular to a lantern ring type eddy current tuned mass damper.
Background
Lightning stroke can cause direct or indirect casualties and property loss, the consequences are very disastrous, and in electric power engineering, a lightning rod is used as an important component of a transformer substation and plays an important role in lightning protection of the transformer substation. The lightning rod is usually in a structural form of an independent steel pipe and is formed by sleeving a plurality of steel pipes, so that the lightning rod is convenient to design, process and install, has the advantages of light dead weight, attractive appearance, small occupied area, easiness in equipment maintenance and the like, and is widely applied at home and abroad. However, the steel pipe member may vibrate in a cross-wind direction at a relatively low wind speed, which is generally called vortex vibration or breeze vibration. This is because the vortex which falls off alternately is generated at the rear part of the steel pipe lightning rod under the action of the incoming wind, the vortex generates a vortex-shedding force transverse to the wind direction, and when the frequency of the vortex-shedding force is close to the frequency of the structure, vortex-induced resonance occurs. Such high frequency reciprocating loads generally cause breakage and collapse of the lightning rod.
The collapse accident of the steel tube lightning rod occurs from a transformer substation with 220 kV-750 kV lines, so the wind vibration control problem of the steel tube lightning rod becomes a key problem to be solved urgently in power transmission and transformation projects. The lightning rod vibration damper of the transformer substation in the prior art comprises a hoop sleeved on the outer wall surface of the top of a lightning rod body along the circumference, an annular mass block is horizontally sleeved outside the hoop, a spring and a damper are connected between the outer wall of the hoop and the inner wall of the annular mass block, a support is fixed on the lightning rod body above the hoop in a mode of extending outwards, and the support is connected with the upper end face of the annular mass block through a suspension cable. The support adopts a plurality of bracing pieces of welding on the lightning rod needle body, and the bracing piece outwards extends and evenly distributed is at the lightning rod needle body periphery. The disadvantages of the above-described damping device are as follows: 1) when the lightning rod is connected, a large amount of welding processes are used, so that the lightning rod is inconvenient to install and construct; 2) a large number of springs are used for providing elastic force, so that the size of the vibration damping device is limited, and the vibration damping device is usually large in size and inconvenient to develop in a miniaturized mode; 3) the suspension cable is used for supporting the mass block, the strength of the suspension cable is limited, the mass of the mass block is limited, and the lightning rod with large specification and large mass cannot be damped.
Disclosure of Invention
In order to overcome the defect that the lightning rod with larger specification and mass can not be damped in the prior art, the invention provides a lantern ring type eddy current tuned mass damper, which comprises a hollow sleeve type frame (1), a mass block (3) arranged in the sleeve type frame (1), a copper plate (5) and a plurality of suspenders (2); sleeve-type frame (1) cup joints outside steel pipe lightning rod (9), many jib (2) set up around steel pipe lightning rod (9), and even, symmetrical arrangement, every jib (2) upper end is fixed with sleeve-type frame (1) top, its lower extreme is fixed with quality piece (3), copper (5) are located sleeve-type frame (1) bottom, provide the support of quality piece through many jibs, the jib is along with the quality piece swing, the mass range of quality piece is great, can carry out the damping to the great lightning rod of specification and quality, and the damping is effectual.
In order to achieve the purpose of the invention, the invention adopts the following technical scheme:
the invention provides a lantern ring type eddy current tuned mass damper, which comprises a hollow and sleeve type frame (1), a mass block (3) arranged in the sleeve type frame (1), a copper plate (5) and a plurality of suspenders (2);
the telescopic frame (1) is sleeved outside the steel tube lightning rod (9), the plurality of suspension rods (2) are arranged around the steel tube lightning rod (9) and are uniformly and symmetrically arranged, the upper end of each suspension rod (2) is fixed with the top of the telescopic frame (1), the lower end of each suspension rod is fixed with the mass block (3), and the copper plate (5) is positioned at the bottom of the telescopic frame (1).
The mass block (3) is a circular permanent magnet and is axially magnetized;
the inner diameter of the mass block (3) is larger than the outer diameter of the steel tube lightning rod (9);
the mass of the mass block (3) is determined according to the mass of the steel tube lightning rod (9).
The mass block (3) is provided with through holes (7) which have the same number as the suspenders (2) and are matched with the suspenders in position along the circumferential direction;
the lower end of the suspender (2) passes through the through hole (7) and is fixed with the mass block (3) through a bolt.
The copper plate (5) is round or square; the inner diameter of the lightning rod is equal to the outer diameter of the steel tube lightning rod (9), and the thickness of the lightning rod is 2-5 cm.
The lifting device is characterized by further comprising iron blocks (4) with the same number as the lifting rods (2), wherein the iron blocks (4) are adsorbed at the bottom of the mass block (3), and a certain distance exists between the iron blocks (4) adsorbed at the bottom of the mass block (3) and the bottom copper plate (5) of the sleeve-type frame (1);
the mass of the iron block (4) is determined according to the mass of the mass block (3).
The suspender (2) is a solid cylinder;
the length and the diameter of the plurality of suspension rods (2) are equal.
The distance is 3-5 mm.
The horizontal distance between the mass block (3) and the sleeve type frame (1) and the horizontal distance between the mass block (3) and the steel tube lightning rod (9) are both larger than the maximum horizontal design amplitude;
the maximum horizontal design amplitude is determined based on wind speed.
The hanger rod (2) is made of stainless steel or aluminum;
the diameter of the hanger rod (2) is 3-10 mm, and the number of the hanger rods is 3-5.
The sleeve type frame (1) is made of metal;
and a rubber pad is arranged between the sleeve type frame (1) and the steel tube lightning rod (9).
Compared with the closest prior art, the technical scheme provided by the invention has the following beneficial effects:
the invention provides a lantern ring type eddy current tuned mass damper, which comprises a hollow sleeve type frame (1), a mass block (3) arranged in the sleeve type frame (1), a copper plate (5) and a plurality of suspenders (2); the sleeve type frame (1) is sleeved outside the steel tube lightning rod (9); the plurality of suspension rods (2) are arranged around the steel tube lightning rod (9) and are uniformly and symmetrically arranged, the upper end of each suspension rod (2) is fixed with the top of the sleeve type frame (1), the lower end of each suspension rod is fixed with the mass block (3), the copper plate (5) is positioned at the bottom of the sleeve type frame (1), the mass blocks are supported by the plurality of suspension rods, the suspension rods swing along with the mass blocks, the mass range of the mass blocks is large, the lightning rod with large specification and mass can be damped, and the damping effect is good;
according to the invention, the sleeve type frame is sleeved on the steel tube lightning rod and is fixed with the steel tube lightning rod through the bolt, so that a welding process is avoided, and the installation and construction are convenient;
according to the invention, the mass block is suspended inside the sleeve type frame through the plurality of suspension rods, so that the size of the vibration damper is not limited, and the vibration damper can be suitable for steel tube lightning rods with various specifications;
the suspender has no initial friction, provides an extremely low lower limit value for the damping of the damper, improves the wind vibration control sensitivity of the damper, can play a role in inhibiting vibration when the steel pipe lightning rod has small vibration, has the same section inertia moment in all directions of 360 degrees, can control the vibration of the steel pipe lightning rod generated by wind in all directions, does not need to provide energy from the outside, has smaller elastic modulus, larger section size and smaller length size, and is convenient for the design, manufacture and installation of the damper;
the mass block is a circular permanent magnet which generates a magnetic field, when the circular permanent magnet moves relative to the copper plate, eddy current can be generated in the copper plate, vibration energy is dissipated into heat energy generated by the eddy current, external energy is not needed, a large damping ratio can be realized, in the swinging process of the mass block, the copper plate can cut magnetic induction lines around the mass block to form magnetic damping, the size of the magnetic damping can be flexibly adjusted by adjusting the mass of the iron block, the thickness of the copper plate and the distance (namely air gap) between the iron block and the copper plate, and the adjusting range is large;
the invention changes the rigidity of the damper by changing the section size and the length of the hanging rod, so that the rigidity of the damper is zero-activity adjustable, the mechanical friction problem and the sealing problem are avoided, and the reliability and the durability are good.
Drawings
FIG. 1 is a diagram of a collar-type eddy current tuned mass damper according to an embodiment of the present invention;
FIG. 2 is a top view of a collar eddy current tuned mass damper in accordance with an embodiment of the present invention;
FIG. 3 is a mass block diagram in an embodiment of the invention;
FIG. 4 is a schematic view of a collar-type eddy current tuned mass damper installation in accordance with an embodiment of the present invention;
in the figure, the lightning arrester comprises a sleeve type frame 1, a sleeve type frame 2, a suspender 3, a mass block 4, an iron block 5, a copper plate 6, a bolt 7, a through hole arranged on the mass block 8, a damper 9 and a steel pipe lightning rod.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
The embodiment of the invention provides a collar type eddy current tuned mass damper, which comprises a collar type frame 1, a mass block 3 arranged in the collar type frame 1, a copper plate 5 and a plurality of suspenders 2, wherein the mass block 3 is arranged in the collar type frame 1;
the sleeve type frame 1 is sleeved outside the steel tube lightning rod 9; the plurality of suspension rods 2 are arranged around the steel tube lightning rod 9 and are uniformly and symmetrically arranged, the upper end of each suspension rod 2 is fixed with the top of the sleeve type frame 1, the lower end of each suspension rod is fixed with the mass block 3, and the copper plate 5 is positioned at the bottom of the sleeve type frame 1.
As shown in fig. 3, the mass block 3 is a circular permanent magnet, which is magnetized in the axial direction;
the inner diameter of the mass block 3 is larger than the outer diameter of the steel tube lightning rod 9;
the mass of the mass block 3 is determined according to the mass of the steel tube lightning rod 9.
The mass block 3 is provided with through holes 7 which have the same number as the suspenders 2 and are matched with the suspenders in position along the circumferential direction;
the lower end of the suspender 2 passes through the through hole 7 and is fixed with the mass block 3 through a bolt.
The copper plate 5 is round or square; the inner diameter of the lightning rod is equal to the outer diameter of the steel pipe lightning rod 9, and the thickness of the lightning rod is 2-5 cm.
The lantern ring type eddy current tuned mass damper provided by the embodiment of the invention further comprises iron blocks 4 with the same number as the hanger rods 2, wherein the iron blocks 4 are adsorbed at the bottom of the mass block 3, and a certain distance exists between the iron blocks 4 adsorbed at the bottom of the mass block 3 and the bottom copper plate 5 of the sleeve type frame 1, and the distance is 3-5 mm.
The mass of the iron block 4 is determined according to the mass of the mass block 3.
The suspender 2 is a solid cylinder;
the plurality of hanger rods 2 are equal in length and diameter. The horizontal distance between the mass block 3 and the sleeve type frame 1 and the horizontal distance between the mass block 3 and the steel tube lightning rod 9 are both larger than the maximum horizontal design amplitude;
the maximum horizontal design amplitude is determined based on wind speed.
The hanger rod 2 is made of stainless steel or aluminum;
the diameter of the hanger rod 2 is 3-10 mm, and the number is 3-5.
The sleeve frame 1 is made of metal, and the metal can ensure enough strength.
As shown in fig. 4, the telescopic frame 1 is fixed outside the steel pipe lightning rod 9 by bolts, and a rubber pad is arranged between the telescopic frame 1 and the steel pipe lightning rod 9.
The working principle of the lantern ring type eddy current tuned mass damper provided by the embodiment of the invention is as follows:
when the steel tube lightning rod vibrates, the eddy current tuned mass damper provided by the embodiment of the invention absorbs vibration energy, reduces the amplitude of the steel tube lightning rod and plays a role in protecting the steel tube lightning rod. When the steel tube lightning rod vibrates, the mass block 3 at the lower part of the suspender 2 vibrates, the mass block 3 moves relative to the copper plate 5, the copper plate 5 cuts a magnetic induction line generated by the mass block 3, eddy current is generated in the copper plate 5, the eddy current further generates heat energy, and the heat energy is dissipated along with air consumption, so that the main structure steel tube lightning rod is protected.
Finally, it should be noted that: the above embodiments are only intended to illustrate the technical solution of the present invention and not to limit the same, and a person of ordinary skill in the art can make modifications or equivalents to the specific embodiments of the present invention with reference to the above embodiments, and such modifications or equivalents without departing from the spirit and scope of the present invention are within the scope of the claims of the present invention as set forth in the claims.
Claims (12)
1. A lantern ring type eddy current tuned mass damper is characterized by comprising a hollow sleeve type frame (1), a mass block (3) arranged in the sleeve type frame (1), a copper plate (5) and a plurality of suspenders (2);
the sleeve type frame (1) is sleeved outside the steel tube lightning rod (9);
the plurality of suspension rods (2) are arranged around the steel tube lightning rod (9) and are uniformly and symmetrically arranged, the upper end of each suspension rod (2) is fixed with the top of the sleeve-type frame (1), the lower end of each suspension rod is fixed with the mass block (3), and the copper plate (5) is positioned at the bottom of the sleeve-type frame (1).
2. The collar eddy current tuned mass damper according to claim 1, characterized in that the mass (3) is a circular permanent magnet, which is axially magnetized.
3. The ferrule-based eddy current tuned mass damper according to claim 2, characterized in that the inner diameter of the mass block (3) is larger than the outer diameter of the steel tube lightning rod (9);
the mass of the mass block (3) is determined according to the mass of the steel tube lightning rod (9).
4. The collar type eddy current tuned mass damper according to claim 1, wherein the mass (3) is provided with through holes (7) in the same number and matching positions with the hanger rods (2) along the circumferential direction;
the lower end of the suspender (2) passes through the through hole (7) and is fixed with the mass block (3) through a bolt.
5. The ferrule-based eddy current tuned mass damper according to claim 1, characterized in that the copper plate (5) is circular or square; the inner diameter of the lightning rod is equal to the outer diameter of the steel tube lightning rod (9), and the thickness of the lightning rod is 2-5 cm.
6. The collar type eddy current tuned mass damper according to claim 1 or 2, further comprising iron blocks (4) in the same number as the hanger rods (2), wherein the iron blocks (4) are adsorbed at the bottom of the mass block (3), and the iron blocks (4) are adsorbed at the bottom of the mass block (3) and have a certain distance from the bottom copper plate (5) of the collar type frame (1);
the mass of the iron block (4) is determined according to the mass of the mass block (3).
7. The ferrule based eddy current tuned mass damper according to claim 1, characterized in that the suspension rod (2) is a solid cylinder;
the length and the diameter of the plurality of suspension rods (2) are equal.
8. The ferrule-based eddy current tuned mass damper according to claim 6, wherein said distance is 3-5 mm.
9. The thimble type eddy current tuned mass damper according to claim 1, characterized in that the horizontal distance between the mass (3) and the thimble frame (1), the horizontal distance between the mass (3) and the steel tube lightning rod (9) are larger than the maximum horizontal design amplitude;
the maximum horizontal design amplitude is determined based on wind speed.
10. The collar-type eddy current tuned mass damper according to claim 1, wherein the material of the suspension rod (2) is stainless steel or aluminum;
the diameter of the hanger rod (2) is 3-10 mm, and the number of the hanger rods is 3-5.
11. The ferrule based eddy current tuned mass damper according to claim 1, characterized in that the material of the ferrule based frame (1) is metal.
12. The ferrule-based eddy current tuned mass damper according to claim 1, characterized in that a rubber pad is arranged between the ferrule-based frame (1) and the steel tube lightning rod (9).
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911201247.9A CN111043210A (en) | 2019-11-29 | 2019-11-29 | Shrink-ring type eddy current tuned mass damper |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911201247.9A CN111043210A (en) | 2019-11-29 | 2019-11-29 | Shrink-ring type eddy current tuned mass damper |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN111043210A true CN111043210A (en) | 2020-04-21 |
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Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201911201247.9A Pending CN111043210A (en) | 2019-11-29 | 2019-11-29 | Shrink-ring type eddy current tuned mass damper |
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| CN (1) | CN111043210A (en) |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2022099717A1 (en) * | 2020-11-11 | 2022-05-19 | 中国电力科学研究院有限公司 | Eddy-current tuned mass damper for vibration control of steel-tube lightning rod |
| CN115030016A (en) * | 2022-06-23 | 2022-09-09 | 河海大学 | Double-tuned mass damper for vibration reduction of suspension cable of suspension bridge |
-
2019
- 2019-11-29 CN CN201911201247.9A patent/CN111043210A/en active Pending
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2022099717A1 (en) * | 2020-11-11 | 2022-05-19 | 中国电力科学研究院有限公司 | Eddy-current tuned mass damper for vibration control of steel-tube lightning rod |
| CN115030016A (en) * | 2022-06-23 | 2022-09-09 | 河海大学 | Double-tuned mass damper for vibration reduction of suspension cable of suspension bridge |
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