CN109492260A - A kind of dynamic absorber type high-pier coping pier-beam connects the determination method of optimal level rigidity and damping value - Google Patents
A kind of dynamic absorber type high-pier coping pier-beam connects the determination method of optimal level rigidity and damping value Download PDFInfo
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Abstract
A kind of method that can accurately calculate dynamic absorber type high-pier coping pier-beam connection optimal level coupling stiffness and damping provides the theoretical foundation and specific practical guidance of science with the calculating of support stiffness and damping value for dynamic absorber type high-pier coping.Method includes the following steps: 1. establishing dynamic absorber type high-pier coping Fem Analysis of Anti-seismic model;2. primarily determining pier-beam elastic connecting device horizontal connection rigidity k and damping c;3. applying harmonic responding analysis load at pier top node, pier displacement or the corresponding amplitude frequency curve of acceleration power result are drawn;4. judging whether there is two vertex (P point and Q point) in pier displacement or acceleration amplitude frequency curve, then appropriate adjustment pier-beam coupling stiffness carries out tentative calculation repeatedly to no obvious Double Tops point;5. judging whether P and Q two o'clock is contour, if P and Q point is not contour, constantly adjustment pier-beam coupling stiffness carries out tentative calculation repeatedly, until P and Q point is contour, the coupling stiffness is optimal level coupling stiffness at this time;6. adjusting pier-beam connection damping carries out tentative calculation repeatedly, P and Q two o'clock is made to become the peaking on amplitude frequency curve, the damping of the connection at this time is optimal level connection damping.
Description
Technical field
The present invention relates to science of bridge building anti-seismic technology field, in particular to a kind of dynamic absorber type high-pier coping pier-Liang Lian
Connect the determination method of optimal level rigidity and damping.
Background technique:
106120545 A of patent CN proposes " a method of utilize beam body improve anti-seismic performance of beam bridge ", i.e., power is inhaled
Vibration shape high-pier coping design method, basic principle are as follows: being tested by numerical value model analysis or experimental modal, obtain bridge pier vertical
To the natural frequency of vibration f with transverse directioni, equivalent modalities mass MiAnd modal stiffness Ki;Determine the quality m of beam bodyi;Calculate beam body with
Coupling stiffness k between bridge pieri;Calculate the connection damping c between beam body and bridge pieri;Selection has above-mentioned coupling stiffness kiWith
Connection damping ciThe support system of value can improve bridge pier anti-seismic performance as dynamic vibration absorber by beam body.Its beam body and
Coupling stiffness between pier body is obtained by following formula:
Damping is obtained by following formula:
Although the rigidity and Damping calculating formula realize purpose of the beam body as pier body dynamic vibration absorber, when bridge is adopted
When the horizontal rigidity and damping value that are calculated with the formula, anti seismic efficiency is simultaneously non-optimal, this is because the formula is only in matter
Amount is than μ=mi/MiThe difference between rigidity and damping value and optimal value being calculated when generally less than 0.1 is extremely faint, still
For high-pier coping, with the ratio between pier weight typically much deeper than 0.1 between beam body, passes through the formula and obtain rigidity and damping
Difference between value and optimal value is larger, therefore, very big to antidetonation influential effect and non-optimal.
Dynamic absorber type high-pier coping is mainly made of pier body, pier-beam elastic connecting device (such as support) and beam body.
By setting pier-beam elastic connecting device laterally or longitudinally coupling stiffness and damping value, fill beam body and pier-beam elastic connection
It sets to form the spring-damper-quality system for being attached to pier top, it is rigid using beam body quality and pier-beam elastic connecting device
The earthquake vibration energy that bridge pier main body is subject to can be absorbed in the subsystem that degree is constituted, while utilizing pier-beam elastic connecting device
Damping characteristic consumes system vibration energy.Dynamic absorber type high-pier coping is by rationally designing the company between beam body and pier body
Rigidity and damping are connect, can reach the vibration phase of beam body and pier body in the design intrinsic frequency of pier body on the contrary, to realize beam
Body eliminates the nuisance vibration at bridge pier intrinsic frequency as dynamic vibration absorber, therefore there are an optimal coupling stiffness and resistances
Buddhist nun, excessive or too small pier-beam elastic connecting device coupling stiffness and damping value will affect its anti seismic efficiency.
From the thirties in last century, related scholar has started a lot of research work for the optimal design of dynamic vibration absorber, and
Achieve the research achievement of plentiful and substantial brilliance.Damping and rigidity value for routine (mass ratio μ is less than 0.1) dynamic vibration absorber are really
It is fixed, it can be based on extension fixed point theory, using optimal with reconciliation optimal damper condition, can be derived using mass ratio μ as parameter
The design formula of dynamic vibration absorber essential element, specific as follows shown:
1) quality of dynamic vibration absorber
M=μM (kg)
2) the optimal spring rate of dynamic vibration absorber
3) optimum damping coefficient of dynamic vibration absorber
But it pays particular attention to and, it is emphasized that carrying on the back family one by the scholar in the famous mechanical kinetics field of Japan steps on Mr. institute
Point out that the optimum damping coefficient in above-mentioned dynamic vibration absorber essential element only has in " the dynamic vibration absorber and its application " book write
It could be set up when mass ratio μ is much smaller than 1.However, beam body is relative to pier body conduct for dynamic absorber type high-pier coping structure
Additional mass body, mass ratio μ have been unsatisfactory for the design condition.Therefore, the optimal level of dynamic absorber type high-pier coping structure
Coupling stiffness and damping can not be carried out calculating by above-mentioned classical formulas and directly determined.
Summary of the invention
Dynamic absorber type high-pier coping pier-Liang Lian can be accurately calculated technical problem to be solved by the invention is to provide a kind of
The method for connecing optimal level coupling stiffness and damping, with the calculating of support stiffness and damping value for dynamic absorber type high-pier coping
The theoretical foundation and specific practical guidance of science are provided.
It is as follows that the present invention solves the technical solution that above-mentioned technical problem is taken:
The determination side of a kind of dynamic absorber type high-pier coping pier of the invention-beam connection optimal level rigidity and damping value
Method, dynamic absorber type high-pier coping include pier body, beam body and the elastic connecting device being placed between beam body and pier body (1), are somebody's turn to do
Method the following steps are included:
1. establish dynamic absorber type high-pier coping Fem Analysis of Anti-seismic model, pier-beam elastic connecting device rigidity and
Damping characteristic is simulated by spring force member;
2. primarily determining that pier-beam elastic connecting device is horizontal than dynamic vibration absorber Classic couture formula according to conventional small quality
Coupling stiffness k and damping c, shown in following formula:
Wherein, it is bridge pier in horizontally equivalent modalities quality that m, which is 1/2, M of beam body quality, and K is bridge pier horizontally
Modal stiffness, K=M (2 π f)2, f is bridge pier in the horizontally natural frequency of vibration, mass ratio μ=m/M;
3. apply harmonic responding analysis load at pier top node, obtain the dynamic response of pier displacement or acceleration as a result,
And draw pier displacement or the corresponding amplitude frequency curve of acceleration power result;
4. two vertex, i.e. P point and Q point are judged whether there is, if without bright in pier displacement or acceleration amplitude frequency curve
Aobvious Double Tops point, appropriate adjustment pier-beam coupling stiffness carry out tentative calculation repeatedly, until there are two vertex P and Q in amplitude frequency curve;
5. judging whether P and Q two o'clock is contour, if P and Q point is not contour, constantly adjustment pier-beam coupling stiffness is tried repeatedly
It calculates, until P and Q point is contour, the coupling stiffness is optimal level coupling stiffness at this time;
6. adjusting pier-beam connection damping carries out tentative calculation repeatedly, P and Q two o'clock is set to become the peaking on amplitude frequency curve, at this time
Connection damping is optimal level connection damping.
The invention has the advantages that by applying simple harmonic quantity external force to dynamic absorber type high-pier coping finite element model, and
Repeatedly tentative calculation rigidity and damping value compare and analyze draw amplitude frequency curve P, Q two o'clock position, it may be determined that meet the optimal people having the same aspiration and interest and
The parameter value of optimal damper condition.The design method of dynamic vibration absorber essential element relative to traditional classical, it is attached can to break through its
Add mass block mass ratio need to limitation less than 0.1, method proposed by the present invention is more adaptive to mass ratio μ much larger than 0.1, very
To the case where being near or above 1.0.Connect especially suitable for this utilization beam body of dynamic absorber type high-pier coping and pier-beam elasticity
Connection device system forms the dynamic vibration absorber for being attached to pier top.In addition, for the complicated continuous shaking with infinite degrees of freedom
System, this method are not required to complicated cumbersome theoretical formula and derive calculating.Meanwhile it can voluntarily be selected according to engineering actual demand is calculated
Dynamic response of interest, and then pointedly determine optimal horizontal connection rigidity and damping value, it can be high for dynamic absorber type
The theoretical foundation that the calculating of the support stiffness and damping value of pier beam bridge provides science is instructed with specifically practical.
Detailed description of the invention
This specification includes following nine width attached drawing altogether:
Fig. 1 is calculation flow chart of the invention.
Fig. 2 a, Fig. 2 b are dynamic absorber type high-pier coping structure principle chart.
Fig. 3 is dynamic absorber type high-pier coping finite element model figure.
Fig. 4 is ball-type pier-beam elastic connecting device pier displacement amplitude frequency curve
Fig. 5 is non-optimal dynamic absorber type pier-beam elastic connecting device pier displacement amplitude frequency curve
Fig. 6 is optimal dynamic absorber type pier-beam elastic connecting device pier displacement amplitude frequency curve
Fig. 7 a, Fig. 7 b are the pier top lateral vibration acceleration comparing result that seismic (seismal motivates lower high-pier coping.
Structure title corresponding to each label is respectively as follows: pier body 1, pier-beam elastic connecting device 2, beam body 3 in attached drawing.
Specific embodiment
Below in conjunction with attached drawing, detailed description of the preferred embodiments, it should be appreciated that retouches in this place
The specific embodiment stated is merely to illustrate and explain the present invention, and is not intended to restrict the invention.
The determination method of a kind of dynamic absorber type high-pier coping pier of the present invention-beam connection optimal level rigidity and damping value,
Dynamic absorber type high-pier coping includes pier body 1, beam body 3 and the elastic connecting device 2 being placed between beam body 3 and pier body 1, the party
Method the following steps are included:
1. establishing dynamic absorber type high-pier coping Fem Analysis of Anti-seismic model, pier-beam elastic connecting device (2) rigidity
And damping characteristic is simulated by spring force member;
2. primarily determining pier -2 water of beam elastic connecting device than dynamic vibration absorber Classic couture formula according to conventional small quality
Flushconnection rigidity k and damping c, shown in following formula:
Wherein, it is bridge pier 3 in horizontally equivalent modalities quality that m, which is 1/2, M of beam body quality, and K is bridge pier 3 in horizontal direction
Modal stiffness, K=M (2 π f)2, f is bridge pier 3 in the horizontally natural frequency of vibration, mass ratio μ=m/M;
3. apply harmonic responding analysis load at pier top node, obtain the dynamic response of pier displacement or acceleration as a result,
And draw pier displacement or the corresponding amplitude frequency curve of acceleration power result;
4. two vertex, i.e. P point and Q point are judged whether there is, if without bright in pier displacement or acceleration amplitude frequency curve
Aobvious Double Tops point, appropriate adjustment pier-beam coupling stiffness carry out tentative calculation repeatedly, until there are two vertex P and Q in amplitude frequency curve;
5. judging whether P and Q two o'clock is contour, if P and Q point is not contour, constantly adjustment pier-beam coupling stiffness is tried repeatedly
It calculates, until P and Q point is contour, the coupling stiffness is optimal level coupling stiffness at this time;
6. adjusting pier-beam connection damping carries out tentative calculation repeatedly, P and Q two o'clock is set to become the peaking on amplitude frequency curve, at this time
Connection damping is optimal level connection damping.
The step 1. in, established dynamic absorber type high-pier coping Fem Analysis of Anti-seismic model across number three across or
Three across above, and simple harmonic quantity external force application position is at the pier top node of middle span.
Optimal level rigidity and damping value include lateral, longitudinal or horizontal and vertical three kinds of situations, specifically design antidetonation
Direction is determined according to engineering actual demand.
The step 3. in, the amplitude of harmonic responding analysis load can arbitrarily be set, different-stiffness and damping tentative calculation operating condition under
Amplitude be consistent, frequency range of choice include fixed point extension theory in P with Q two fixed point where frequency.
The node for extracting dynamic response need to be consistent with the node for applying load, be can extract the displacement at the node or added
The dynamic responses such as speed, concrete analysis object can be determined according to the focus of engineering actual demand or analysis and research.
Embodiment:
The variable cross-section nose circle shape hollow pier 1 and common 32.6m two-wire four generallyd use with railway double-track high-pier coping
Chip Simple T-Girders 3 are research object.Wherein, pier top rounded-end section apparent size is 10.6m × 5.4m, long from pier top to pier bottom
Spend linearly increasing, change rate 1:40.Establish dynamic absorber type high-pier coping finite element analysis model, pier-beam elastic connection dress
The rigidity and damping characteristic for setting 2 are simulated by spring force member, bridge model be equipped with altogether 3 across.The finite element model of bridge pier uses beam list
Member is simulated, and bridge pier 1 is C30 concrete, pier a height of 60m.The plastic deformation of bridge is not considered, it is assumed that in entire seismic stimulation mistake
Cheng Zhong, bridge deformation remain in elastic range, and springform measures 3.2 × 104MPa, Poisson's ratio take 0.2, and density is taken as
2500kg/m3.Pier bottom presses consolidation process, does not consider influence of the place basis to bridge pier intrinsic frequency, seismic (seismal is as global
Acceleration is applied.Beam body 3 is made of two panels side bar and two panels central sill altogether, beam piece cross-section center line height 2.7m, adjacent
Beam piece centreline space is coupled by diaphragm plate with lateral concrete muscle between piece and piece away from 2.2m.Girder is simulated using beam element,
Bridge floor secondary dead load is assigned on girder, and beam body uses C55 concrete, and springform measures 3.6 × 104MPa, Poisson's ratio take 0.2,
Density is taken as 2500kg/m3, secondary dead load takes 208.26kN/m, and beam body always weighs about 995t.The mass ratio of beam body 3 and pier body 1 is about
It is 0.583, therefore has been unsatisfactory for the condition of compatibility of bump leveller traditional counting formula powered by conventional energy.The dynamic absorber type high-pier coping
Respectively as shown in Fig. 2 a, Fig. 2 b and Fig. 3, the horizontal curved frequency of 1 rank is respectively 2.27Hz for structure principle chart and finite element model figure.
Pier-beam elasticity is primarily determined according to conventional small mass ratio (generally less than 0.1) dynamic vibration absorber Classic couture formula
2 horizontal connection rigidity k of attachment device and damping value c, calculation formula are as follows:
Wherein, it is bridge pier (3) in horizontally equivalent modalities quality that m, which is 1/2, M of beam body quality, and K is bridge pier (3) in water
Put down to modal stiffness, K=M (2 π f)2, f is bridge pier (3) in the horizontally natural frequency of vibration, mass ratio μ=m/M.
Optimal level rigidity and damping value include transverse direction and longitudinal direction both direction altogether, and the application direction of simple harmonic quantity external force is also the same
It needs to be divided into transverse direction and longitudinal direction.This application example carries out the calculating of Optimal Stiffness and damping, lateral connection rigidity by taking transverse direction as an example
And damping value initial value is respectively set as 1.10E+07N/m and 8.32E+05Ns/m.
Apply harmonic responding analysis load at pier top node, extracts the dynamic response of pier displacement or acceleration as a result, and drawing
The amplitude frequency curve of pier displacement or acceleration dynamic response processed.The application position of harmonic responding analysis load need to be the pier top of middle span
At node, amplitude can arbitrarily be set, but the amplitude under different-stiffness and damping tentative calculation operating condition need to be consistent.Meanwhile it mentioning
Taking the node of dynamic response need to be consistent with the node for applying load, can extract the power such as displacement or the acceleration at the node
Response.Concrete analysis object can be determined according to the focus of engineering actual demand or analysis and research.
Unit harmonic responding analysis load is chosen, i.e., the simple harmonic quantity power amplitude under each frequency is 1N.Rule of thumb Analysis on Selecting carries
The swept frequency range of lotus is 0.1~20Hz, and frequency interval is taken as 0.1Hz, while choosing the vibration displacement response results at pier top and being
Object is analyzed, pier displacement amplitude frequency curve is drawn.
In pier displacement or acceleration amplitude frequency curve, two vertex, i.e. P point and Q point are judged whether there is, if without obvious
Double Tops point, appropriate adjustment (increasing or reducing) pier-beam coupling stiffness carry out tentative calculation repeatedly, until there is P and Q two in amplitude frequency curve
A vertex.By Fig. 4 and Fig. 5 it is found that pier-beam elastic connecting device is using traditional spherical bearing and non-optimal dynamic absorber type branch
Apparent two peak values are not present in pier displacement amplitude frequency curve when seat.Adjustment pier-beam coupling stiffness is needed, then at this time to guarantee
There are two vertex for amplitude frequency curve.
Judge whether P and Q two o'clock is contour, if P and Q point is not contour, constantly adjustment pier-beam coupling stiffness is tried repeatedly
It calculates, until P and Q point is contour, the coupling stiffness is optimal level coupling stiffness at this time.
It adjusts (increasing or reducing) pier-beam connection damping and carries out tentative calculation repeatedly, become P and Q two o'clock on amplitude frequency curve
Peaking, the damping of the connection at this time are optimal level connection damping.
By the above method, constantly adjustment pier-beam connection horizontal rigidity and damping value, repeatedly tentative calculation is finally obtained each
The lateral Optimal Stiffness of pier-beam elastic connecting device and damping are 5.36 × 106N/m and 1.10 × 106Ns/m, at this time most
Excellent dynamic absorber type pier-beam elastic connecting device pier displacement amplitude frequency curve is as shown in fig. 6, left in the horizontal curved frequency of 1 rank of 50m bridge pier
Respectively there is a peak value in right adjacent locations, and the two peak values are substantially contour, and the highest point in amplitude curve of double curvature is shown
The optimality of the parameter.
Dynamic excitation of the Wenchuan earthquake actual measurement seismic wave as high-pier coping system is randomly selected, seismic wave is most
High acceleration value is in 0.037g or so, and principal earthquake frequency is within the scope of 1~4Hz.By the resulting beam body of above-mentioned calculating and pier body it
Between lateral stiffness and damping value, beam body is set to be attached to the dynamic vibration absorber of pier top.
As known to Fig. 7 a, Fig. 7 b, relative to the high pier bridge using conventional pier-beam joint device, dynamic absorber type bridge
The maximum value of pier top transverse vibrational displacement have and significantly reduce, pier top lateral displacement maximum value is reduced to by 13.09mm
6.74mm, aseismic ratio 48.51%.Meanwhile under the action of principal earthquake frequency is the seismic wave of 2~4Hz, the 1 of the high bridge of 60m pier
The horizontal curved mode of rank is excited first, and the master oscillator frequenc of pier top is at 1.70Hz, and dynamic absorber type bridge is by being set to beam
Lateral stiffness and damping system between body and pier body is to effectively inhibit the vibration of pier top and span centre near 1.70Hz.By
This explanation, the rigidity of above-mentioned calculating and damping value can effectively eliminate the nuisance vibration at bridge pier intrinsic frequency, shown in the present invention
Dynamic absorber type high-pier coping optimal level coupling stiffness and the determination method of damping are rationally effective, can provide reason for engineering design
By foundation and practical reference.
Claims (5)
1. the determination method of a kind of dynamic absorber type high-pier coping pier-beam connection optimal level rigidity and damping value, dynamic absorber
Type high-pier coping includes pier body (1), beam body (3) and the elastic connecting device (2) being placed between beam body (3) and pier body (1), is somebody's turn to do
Method the following steps are included:
1. establishing dynamic absorber type high-pier coping Fem Analysis of Anti-seismic model, pier-beam elastic connecting device (2) rigidity and resistance
Damping characteristics are simulated by spring force member;
2. primarily determining that pier-beam elastic connecting device (2) is horizontal than dynamic vibration absorber Classic couture formula according to conventional small quality
Coupling stiffness k and damping c, shown in following formula:
Wherein, it is bridge pier (3) in horizontally equivalent modalities quality that m, which is 1/2, M of beam body quality, and K is bridge pier (3) in horizontal direction
Modal stiffness, K=M (2 π f)2, f is bridge pier (3) in the horizontally natural frequency of vibration, mass ratio μ=m/M;
3. applying harmonic responding analysis load at pier top node, the dynamic response of pier displacement or acceleration is obtained as a result, and drawing
The corresponding amplitude frequency curve of pier displacement or acceleration power result processed;
4. two vertex, i.e. P point and Q point are judged whether there is in pier displacement or acceleration amplitude frequency curve, if without obvious double
Vertex, appropriate adjustment pier-beam coupling stiffness carry out tentative calculation repeatedly, until there are two vertex P and Q in amplitude frequency curve;
5. judging whether P and Q two o'clock is contour, if P and Q point is not contour, constantly adjustment pier-beam coupling stiffness carries out tentative calculation repeatedly,
Until P and Q point is contour, the coupling stiffness is optimal level coupling stiffness at this time;
6. adjusting pier-beam connection damping carries out tentative calculation repeatedly, P and Q two o'clock is set to become the peaking on amplitude frequency curve, at this time the company
Connecing damping is optimal level connection damping.
2. the determination of dynamic absorber type high-pier coping pier as described in claim 1-beam connection optimal level rigidity and damping value
Method, it is characterized in that: the step 1. in, established dynamic absorber type high-pier coping Fem Analysis of Anti-seismic model across number exist
Three across or three across above, simple harmonic quantity external force application position is at the pier top node of middle span.
3. the determination of dynamic absorber type high-pier coping pier as described in claim 1-beam connection optimal level rigidity and damping value
Method is specifically set it is characterized in that: optimal level rigidity and damping value include lateral, longitudinal or horizontal and vertical three kinds of situations
Meter antidetonation direction is determined according to engineering actual demand.
4. the determination of dynamic absorber type high-pier coping pier as described in claim 1-beam connection optimal level rigidity and damping value
Method, it is characterized in that: the step 3. in, the amplitude of harmonic responding analysis load can arbitrarily be set, different-stiffness and damping tentative calculation
Amplitude under operating condition is consistent, and frequency range of choice includes frequency of the P where with Q two fixed points in fixed point extension theory.
5. the determination of dynamic absorber type high-pier coping pier as described in claim 1-beam connection optimal level rigidity and damping value
Method can extract the position at the node it is characterized in that: extracting the node of dynamic response need to be consistent with the node for applying load
It moves or the dynamic responses such as acceleration, concrete analysis object can carry out true according to the focus of engineering actual demand or analysis and research
It is fixed.
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