CN109930472B - Pendulum bob vibration reduction design method for bridge and building structure - Google Patents
Pendulum bob vibration reduction design method for bridge and building structure Download PDFInfo
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Abstract
The invention discloses a pendulum bob vibration damping design method for bridges and building structures, which is characterized in that a pendulum bob is suspended on a bridge to solve the problems of wind-induced flutter and pedestrian excitation of the bridge, the pendulum bob arranged on the bridge is regarded as a substructure from the structural dynamics, and the swinging of the pendulum bob can generate a reaction force on the movement of the bridge structure, so that the vibration of a bridge deck is inhibited. The pendulum bob is arranged on the bridge, and aims to improve the performance of dynamic load on the pedestrian bridge, particularly the wind load and pedestrian induced load, has a certain stabilizing effect on the wind-induced flutter instability of the prolate bridge, particularly has a certain stabilizing effect on the wind-induced flutter instability of the prolate bridge under the condition of zero attack angle when the wind is at a positive wind attack angle and a negative wind attack angle, can change the flutter mode from quick dispersion into gradual dispersion, can be used for inhibiting vertical and lateral vibration generated by pedestrian load, can well solve the problems of the wind-induced flutter instability and the lateral vibration of the bridge, and is favorable for people to use.
Description
Technical Field
The invention relates to the technical field of design of bridges or building structures, in particular to a pendulum bob vibration damping design method for bridges and building structures.
Background
Compared with a large-span highway bridge, the modern pedestrian bridge faces different challenges in design, and aesthetic satisfaction based on cultural value is an important factor of pedestrian bridge design, so the design of the pedestrian bridge is often slimmer and lighter, however, an unexpected consequence is that the vertical rigidity and the lateral rigidity of some light and slender bridges are usually smaller and are very easily influenced by dynamic loads, particularly wind loads and pedestrian induced loads, and through preliminary research, the main design problems include: (1) the critical flutter wind speed exceeds the required design value especially for a flat and flexible bridge structure in a typhoon-prone area, and (2) the problem of bridge vibration caused by pedestrian excitation must be controlled, so that pedestrians are possibly alarmed, and the situation similar to the lateral shaking of London millennium bridges occurs.
In order to improve aerodynamic stability and inhibit bridge vibration caused by pedestrians, the conventional method is to optimize the aerodynamic appearance of the bridge or relieve the transverse motion caused by the pedestrians through the shape of a sidewalk, but the methods can limit the architectural design of the bridge and influence the aesthetic effect.
Disclosure of Invention
The invention aims to provide a pendulum bob vibration damping design method for bridges and building structures, which has the advantages of improving the performance of pedestrian bridge flutter and lateral vibration and solves the problems of wind-induced flutter instability and lateral vibration of bridges.
In order to achieve the purpose, the invention provides the following technical scheme: a pendulum bob vibration damping design method for a bridge and a building structure is characterized in that the pendulum bob is hung on the bridge to solve the problems of wind-induced flutter and pedestrian excitation of the bridge, the pendulum bob arranged on the bridge is taken as a substructure from the structural dynamics, and the swinging of the pendulum bob can generate a reaction force on the movement of the bridge structure so as to inhibit the vibration of a bridge deck;
the pendulum mass and the rigidity of a suspension spring are adjusted, and the pendulum system can play a role of a vertical tuned mass damper to obtain a vertical vibration reduction effect;
the pendulum mass and the gravity center position of the pendulum are adjusted, and the pendulum system can play a role of a transverse tuned mass damper to obtain a lateral vibration reduction effect;
the position and the shape of the pendulum bob are adjusted, and vortex shedding of airflow can be influenced from the aerodynamic perspective, so that the aerodynamic stability of the bridge is improved, and the wind-induced vibration is reduced;
solving the optimum design parameters of the suspended pendulum through the mechanical relationship among the mass, the swing length and the swing damping level of the suspended pendulum
Compared with the prior art, the invention has the following beneficial effects: the pendulum bob is arranged on the bridge, and aims to improve the performance of dynamic load on the pedestrian bridge, particularly the wind load and pedestrian induced load, has a certain stabilizing effect on the wind-induced flutter instability of the prolate bridge, particularly has a certain stabilizing effect on the wind-induced flutter instability of the prolate bridge under the condition of zero attack angle when the wind is at a positive wind attack angle and a negative wind attack angle, can change the flutter mode from quick dispersion into gradual dispersion, can be used for inhibiting vertical and lateral vibration generated by pedestrian load, can well solve the problems of the wind-induced flutter instability and the lateral vibration of the bridge, and is favorable for people to use.
Drawings
FIG. 1 is a schematic view of the pendulum calculation of the present invention;
FIG. 2 is a graph of the equivalent damping ratio as a function of frequency ratio of the present invention;
FIG. 3 is a plot of the equivalent damping ratio as a function of mass ratio for the present invention;
FIG. 4 is a graph of the equivalent damping ratio versus the roll damping function of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1-4, in the design method for pendulum vibration damping of a bridge and a building structure, the pendulum is suspended on the bridge to solve the problems of wind-induced flutter and pedestrian excitation of the bridge, and the pendulum arranged on the bridge can be regarded as a substructure from the viewpoint of structural dynamics, and the swinging of the pendulum generates a reaction force on the movement of the bridge structure, so as to suppress the vibration of the bridge deck.
In order to obtain the optimal transverse tuning effect, the invention provides a practical calculation method for parameter design of a pendulum: using the coordinate system shown in fig. 1, for the study of the bridge, the objective is to suppress the transverse vibration of the fundamental mode, where the kinetic and potential energy of the bridge are expressed as:
in the formula
= generalized mass of deck;
= vibration mode of bridge deck;x= generalized deflection;k= generalized steel given by formulaDegree K = ω2 BMB，ωBIs the natural frequency of the bridge without pendulums, the kinetic and potential energy of each pendulum in oscillation is expressed as:
in the formula
= vibration pattern of aeolian bells;
= mass of wind bell;Lthe sum of all pendulum equations (2) yields the total energy, and the motion equation of the bridge-pendulum system is written as follows according to the principle of the lagrange equation:
in the formula
= generalized mass of total pendulum mass;
；
(ii) a F = generalized force on bridge, for fundamental mode
By normalizing equation (3) with the generalized mass and introducing a damping term in the equation, the equation of motion is written as:
in the formula
= pendulum to bridge mass ratio;
= natural frequency of pendulum;
thus, the transfer function of the bridge vibration and pendulum oscillation is determined by the following equation:
in the formula
in the performance evaluation, acceleration is taken as an index, and in the case of a severe vibration of the bridge, the acceleration is determined by its resonance component, and therefore, the acceleration is estimated by the following simplified expression:
the relationship between acceleration and structural damping shown in equation (7) is used to estimate the effect of the bob on the suppression of vibration, where
Is a pedestrian load spectrum, we define the equivalent damping ratio of a bridge-pendulum system as follows:
the numerator on the right side of the formula (8) represents the acceleration variance of a bridge without a pendulum bob, and the denominator gives the acceleration variance of the bridge with the pendulum bob;
the optimization objective is to maximize the equivalent damping ratio by adjusting the mechanical properties of the pendulum, which can be described by three parameters: length L of each pendulum, mass mc of each pendulum and pendulum damping ζ C In order to perform a parametric analysis to optimize the pendulum performance and thus reduce the bridge vibration, the parameter L can be expressed using a frequency ratio λ, since the natural frequency of the pendulum is determined only by the length and the mass of the pendulum is expressed by the mass ratio μ.
Fig. 2 shows the equivalent damping ratio of the whole system (bridge structure plus pendulum) as a function of the frequency ratio, and the results show that in order to reduce the vibration of the bridge with the pendulum, the swing frequency of the pendulum should be approximately the same as the swing frequency of the bridge, so as to obtain the optimal length:
fig. 3 gives the equivalent damping ratio as a function of the mass ratio, and the results show that although the equivalent damping increases with increasing mass ratio, its efficiency depends strongly on the oscillation damping, e.g. if the oscillation damping is small, only 0.5%, the mass ratio increases from 1% to 6%, the equivalent damping ratio increases only from 1.4% to 1.5%, whereas if the oscillation damping is 5%, the mass ratio increases from 1% to 6% resulting in an increase of the equivalent damping ratio from 2.7% to 4.4%.
Fig. 4 further illustrates the importance of the pendulum damping in pendulum design, the optimum value of the pendulum damping being dependent on the mass ratio, the maximum equivalent damping being 2.2% when the mass ratio is 0.5% and the optimum pendulum damping being about 3%, and the maximum equivalent damping being 4.9% when the pendulum damping ratio is 10% when the mass ratio is 5%.
Example 1
The pendulum bob arranged on the bridge can be regarded as a substructure from the structural dynamics, and the swinging of the pendulum bob can generate reaction force to the movement of the bridge structure, so that the vibration of the bridge deck is inhibited.
Example 2
In example 1, the following additional steps were added:
the pendulum mass and the rigidity of the suspension spring are adjusted, and the pendulum system can play a role of a vertical tuned mass damper to obtain a vertical vibration reduction effect.
The pendulum bob arranged on the bridge can be regarded as a substructure from the structural dynamics, and the swinging of the pendulum bob can generate reaction force to the movement of the bridge structure, so that the vibration of the bridge deck is inhibited.
Example 3
In example 2, the following steps were added:
the pendulum mass and the pendulum mass center position are adjusted, and the pendulum mass system can play a role of a transverse tuning mass damper, so that a lateral vibration reduction effect is obtained.
The pendulum bob arranged on the bridge can be regarded as a substructure from the structural dynamics, and the swinging of the pendulum bob can generate reaction force to the movement of the bridge structure, so that the vibration of the bridge deck is inhibited.
Example 4
In example 3, the following steps were added:
the position and the shape of the pendulum bob are adjusted, and vortex shedding of airflow can be influenced from the aerodynamic perspective, so that the aerodynamic stability of the bridge is improved, and the flutter caused by wind is reduced.
The pendulum bob arranged on the bridge can be regarded as a substructure from the structural dynamics, and the swinging of the pendulum bob can generate reaction force to the movement of the bridge structure, so that the vibration of the bridge deck is inhibited.
Example 5
In example 4, the following steps were added:
and solving the optimal design parameters of the suspended pendulum bob according to the mechanical relationship among the mass, the swing length and the swing damping level of the suspended pendulum bob.
The pendulum bob arranged on the bridge can be regarded as a substructure from the structural dynamics, and the swinging of the pendulum bob can generate reaction force to the movement of the bridge structure, so that the vibration of the bridge deck is inhibited.
When in use, the optimization process of the length and the weight of the pendulum bob arranged on the two sides of the bridge can be summarized into the following aspects: step 1: selecting the length of the pendulum by formula (9); step 2: if other designs allow, choose a slightly heavier pendulum; and step 3: increasing the damping of the pendulum swing, for example increasing the viscosity of the suspension point; step 2 and step 3 need multiple iterations to reach the theoretical optimal value; and 4, step 4: selecting the shape of the pendulum according to the building landscape effect and the mobility evaluation; and 5: performing a wind tunnel test to verify the improvement level of the pneumatic stability of the pendulum bob system to the bridge; step 6: according to the wind tunnel test result, the shape of the pendulum bob is further improved.
In summary, the following steps: the pendulum bob vibration reduction design method for the bridge and the building structure can improve the aerodynamic stability of the bridge and prevent flutter instability through the pendulum bob arranged on the bridge, particularly under the condition of positive and negative wind directions, the dispersion of flutter becomes more moderate along with the participation of the pendulum bob, the pendulum bob can be regarded as a seed structure from the view of structural dynamics, the swinging of the pendulum bob can generate reaction force to the movement of the bridge structure, thereby inhibiting the vibration of a bridge deck, the pendulum bob system is similar to a tuned mass damper, the pendulum bob system can play the role of a vertical tuned mass damper through adjusting the mass of the pendulum bob and the gravity center position of the pendulum bob, the pendulum bob system can play the role of a transverse tuned mass damper to obtain the lateral vibration reduction effect, the problems of wind-induced flutter instability and lateral vibration of the bridge are solved.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (1)
1. Bridge and building structure pendulum damping design method hangs the pendulum through on the bridge to improve the wind-induced flutter and the people's motion excitation problem of bridge, its characterized in that: the pendulum bob arranged on the bridge is regarded as a substructure from the viewpoint of structural dynamics, and the swinging of the pendulum bob can generate reaction force to the movement of the bridge structure so as to inhibit the vibration of the bridge deck;
a practical calculation method for parameter design of a pendulum bob comprises the following steps: for the study of bridges, the aim is to suppress the transverse vibration of the fundamental mode, and the kinetic energy and potential energy of the bridge in the fundamental mode are expressed as:
in the formula MBThe generalized mass of the bridge deck; phiBVibration mode of the bridge deck; x is generalized deflection; k is the generalized stiffness given by the formula K ω2 BMB，ωBIs the natural frequency of the bridge without pendulums, the kinetic and potential energy of each pendulum in oscillation is expressed as:
in the formula phiCThe vibration mode of the aeolian bells is defined; m iscMass of the aeolian bells; the sum of all pendulum equations (2) yields the total energy, and the motion equation of the bridge-pendulum system is written as follows according to the principle of the lagrange equation:
in the formula
F is the generalized force on the bridge, for the fundamental mode γ1≈γ21, by normalizing equation (3) with the generalized mass and introducing a damping term in the equation, the equation of motion is written as:
where mu is MC/MBThe mass ratio of the pendulum bob to the bridge;
fB＝F/MBthus, the transfer function of bridge vibration and pendulum oscillationDetermined by the following equation:
in the formula
λ＝ωB/ωCThe transfer function of a bridge without a pendulum is:
in the performance evaluation, acceleration is taken as an index, and in the case of a severe vibration of the bridge, the acceleration is determined by its resonance component, and therefore, the acceleration is estimated by the following simplified expression:
the relationship between acceleration and structural damping shown in equation (7) is used to estimate the effect of the bob on the suppression of vibration, where
Is a pedestrian load spectrum, we define the equivalent damping ratio of a bridge-pendulum system as follows:
the numerator on the right side of the formula (8) represents the acceleration variance of a bridge without a pendulum bob, and the denominator gives the acceleration variance of the bridge with the pendulum bob;
the pendulum mass and the rigidity of a suspension spring are adjusted, and the pendulum system can play a role of a vertical tuned mass damper to obtain a vertical vibration reduction effect;
the pendulum mass and the gravity center position of the pendulum are adjusted, and the pendulum system can play a role of a transverse tuned mass damper to obtain a lateral vibration reduction effect;
the position and the shape of the pendulum bob are adjusted, and vortex shedding of airflow can be influenced from the aerodynamic perspective, so that the aerodynamic stability of the bridge is improved, and the wind-induced vibration is reduced;
and solving the optimal design parameters of the suspended pendulum bob according to the mechanical relationship among the mass, the swing length and the swing damping level of the suspended pendulum bob.
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Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH11159191A (en) * | 1997-11-25 | 1999-06-15 | Toshiba Corp | Damper |
| CN203499048U (en) * | 2013-09-10 | 2014-03-26 | 隔而固(青岛)振动控制有限公司 | Frequency regulating device for swinging type turning mass damper |
| CN104372870A (en) * | 2014-11-13 | 2015-02-25 | 柳州东方工程橡胶制品有限公司 | Pendulous eddy current tuned mass damper vibration reduction control device |
| CN205639427U (en) * | 2016-03-17 | 2016-10-12 | 同济大学 | Harmonious mass damper of suspension type two freedoms current vortex |
| CN106988592A (en) * | 2017-04-06 | 2017-07-28 | 东南大学 | A kind of swing-type tuned mass damper device |
| CN107119959A (en) * | 2017-06-30 | 2017-09-01 | 安徽理工大学 | Combined type mono-pendulum type tuned mass damper structural system and construction method |
-
2019
- 2019-02-03 CN CN201910109100.0A patent/CN109930472B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH11159191A (en) * | 1997-11-25 | 1999-06-15 | Toshiba Corp | Damper |
| CN203499048U (en) * | 2013-09-10 | 2014-03-26 | 隔而固(青岛)振动控制有限公司 | Frequency regulating device for swinging type turning mass damper |
| CN104372870A (en) * | 2014-11-13 | 2015-02-25 | 柳州东方工程橡胶制品有限公司 | Pendulous eddy current tuned mass damper vibration reduction control device |
| CN205639427U (en) * | 2016-03-17 | 2016-10-12 | 同济大学 | Harmonious mass damper of suspension type two freedoms current vortex |
| CN106988592A (en) * | 2017-04-06 | 2017-07-28 | 东南大学 | A kind of swing-type tuned mass damper device |
| CN107119959A (en) * | 2017-06-30 | 2017-09-01 | 安徽理工大学 | Combined type mono-pendulum type tuned mass damper structural system and construction method |
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