CN100555294C - The whole-course numerical modeling method of main beam section pneumatic self excitation force - Google Patents

Abstract

The whole-course numerical modeling method of main beam section pneumatic self excitation force is to be the difficult point of bridge buffeting time-domain analysis for the time domainization that solves main beam section pneumatic self excitation force, realize the feasibility and the validity of pneumatic self excitation force time domain method, on the basis that existing kinetic equation is derived, create a kind of unit---Aero-dyn18 unit that is exclusively used in pneumatic rigidity of simulation and air damping, and provided correlation parameter, characteristic and the organigram of unit.By this Aero-dyn18 unit of interpolation on the basis of bridge structure finite element initial model, and adopt the CFD technology to determine the correlation parameter of Aero-dyn18 unit, just can realize whole-course numerical modeling main beam section pneumatic self excitation force.Obviously compare with existing pneumatic self excitation force time domain method, this method is simple and practical, has improved the efficient of analyzing greatly, has saved cost simultaneously, is convenient to apply among the numerous engineering staffs.

Description

The whole-course numerical modeling method of main beam section pneumatic self excitation force

Technical field

The present invention relates to a kind of whole-course numerical modeling method of main beam section pneumatic self excitation force, be particularly useful for the suffered pneumatic self excitation force of simulation main beam section when carrying out the time-domain analysis of bridge buffeting response.

Background technology

Along with bridge structure is striden continuous increase directly, bridge is buffeted to analyze and is seemed more and more important.Buffeting response is calculated frequency domain and the time domain two alanysis methods of mainly containing.Early stage domestic and abroad bridge is buffeted to analyze and is mainly carried out in frequency domain, but because frequency domain method can only count the mode of some in analytic process, what draw is the statistical nature of structural response value, and can only carry out linear analysis, can not be advantageously applied to nonlinear organization systems such as large span stayed-cable bridge, suspension bridge.

The Longspan Bridge buffeting response time-domain analysis method that is based upon on the numerical integration basis is converted into time series with excitation, obtains the time-histories of structure buffeting response by the dynamic finite element method, can count all kinds of effect of non-linear easily.Because Consideration is more comprehensive, the time-domain analysis method is to buffet the developing direction of calculating.But buffeting response time-domain analysis calculated amount is very big, and still remains further research on the problems such as time domain discrete processes of the simulation of three-dimensional random pulsation wind field and self excitation force.

Present many scholars begin to wait the buffeting time-domain analysis of carrying out Longspan Bridge by means of existing large-scale general finite element software such as ANSYS, ABAQUS, ADINA and MSC/NASTRAN, according to the pneumatic rigidity and the air damping matrix of the girder unit of deriving, the influence of the self excitation force form with unit air damping matrix and the pneumatic stiffness matrix in unit is taken in based on certainly normal Aerodynamic Model.This method has made full use of existing common finite element analysis software strong non-linear time-domain analysis function, but wherein has two subject matters:

(1) because existing common finite element software not necessarily has special pneumatic self excitation force unit, usually adopt other matrix unit to replace when buffet analyzing, cause that amount of calculation increases, error probability strengthens, precise decreasing and use inconvenience etc. as a result to carry out the simulation of self excitation force with similar characteristics;

(2) usually adopt in the wind tunnel test gained aerodynamic derivative as parameter in the pneumatic rigidity of girder unit and the air damping matrix, process of the test complexity not only, and spend big, as to cause cast material waste, existing Fluid Mechanics Computation (Computational Fluid Dynamics, CFD) fully do not used in the newest research results in identification aerodynamic derivative field by technology.

Summary of the invention

Technical matters: the objective of the invention is to create a kind of whole-course numerical modeling method that is used for the main beam section main beam section pneumatic self excitation force, comprise and invented a kind of unit that is exclusively used in the main beam section pneumatic self excitation force simulation, and with its called after Aero-dyn18 unit, when the determining unit parameter, utilize simultaneously the newest research results of CFD technology in the identification aerodynamic derivative, realize the robotization and the time domainization of pneumatic self excitation force numerical simulation overall process, finished the Longspan Bridge buffeting response time-domain analysis of considering the pneumatic self excitation force influence quickly and easily.

Technical scheme: at the problems referred to above, the present invention has developed a kind of matrix unit that is exclusively used in the simulation of Longspan Bridge main beam section pneumatic self excitation force, has accurately realized the time domainization of pneumatic self excitation force easily.Unit form is simple, each parameter physical significance is simple and clear, is convenient to apply in vast bridge Wind Engineering technician.In order to realize the time domainization of pneumatic self excitation force, according to based on certainly normal Aerodynamic Model and nonlinear dynamics theory that derive with pneumatic stiffness matrix in unit and air damping the matrix suffered pneumatic self excitation force equivalence of girder, develop a kind of Aero-dyn18 unit that is exclusively used in the pneumatic self excitation force simulation, and provided synoptic diagram, cell matrix constructing variable and the meaning thereof of unit.It is as follows to address the above problem the technical scheme flow process that is adopted:

The first step:, adopt the programmable parameter design language to set up the FEM (finite element) calculation initial model of Longspan Bridge according to the structural design drawing;

Second step: identify the aerodynamic derivative of Longspan Bridge main beam section based on the Fluid Mechanics Computation technology, and it is stored can call the array mode;

The 3rd step: determine pneumatic self excitation force unit---the parameter of Aero-dyn18 unit created according to the aerodynamic derivative that is used for buffeting the air speed data of analysis and identify;

The 4th step: the Aero-dyn18 unit of determining parameter is added in the first step gained FEM (finite element) calculation initial model, obtain to have counted the limited element calculation model of pneumatic self excitation force;

The 5th step: on the limited element calculation model that counts pneumatic self excitation force, add static(al) wind load and the power of buffeting time-histories, carry out the buffeting response Nonlinear time-history analysis.

The 3rd step described pneumatic self excitation force unit---stiffness matrix K and damping matrix C can be determined by the mode of importing 9 real constants in the Aero-dyn18 unit, to simulate the pneumatic rigidity and the air damping matrix of main beam section; This unit has two nodes, and each node has 6 degree of freedom; The Aero-dyn18 unit does not have fixing geometric configuration, can arbitrarily conversion profile between two node i and j; Under the asymmetric situation, the Aero-dyn18 cell matrix is 12 * 12 matrixes, has 9 different coefficients:

$\left[\begin{array}{cccccccccccc}0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& C_1& C_2& C_3& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& C_4& C_5& C_6& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& C_7& C_8& C_9& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& C_1& C_2& C_3& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& C_4& C_5& C_6& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& C_7& C_8& C_9& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\end{array}\right]$

The 4th step, described Aero-dyn18 unit with definite parameter added in the process of first step gained FEM (finite element) calculation initial model, and each bridge floor girder node place need add two Aero-dyn18 unit E, comprises a rigidity unit and a damping unit; The node of unit E is girder node i or j, and another node can be fixed on the optional position.

Beneficial effect: at present,, buffet and adopt other matrix unit to replace when analyzing usually, cause amount of calculation to increase, use a series of problems such as inconvenience to carry out the simulation of self excitation force with similar characteristics owing to there is not special pneumatic self excitation force unit.This patent is being carried out on the improved basis existing similar matrix unit, created a kind of matrix unit that is exclusively used in the self excitation force simulation, realize the time domain simulation of pneumatic self excitation force comparatively simply and easily, solved a key issue in the Wind-Induced Buffeting response time-domain analysis of Longspan Bridge.Simultaneously when carrying out aerodynamic parameter identification, adopted advanced CFD technology but not the wind tunnel test that expends a large amount of manpower, material resources and financial resources, realized the whole-course numerical modeling of main beam section pneumatic self excitation force.Because time-domain analysis and CFD technology are the directions of bridge Wind Engineering development, this paper method is on the basis that guarantees computational accuracy, greatly reduce the difficulty of long span bridge beam buffeting response time-domain analysis, improved the efficient of analyzing, valuable social resources have been saved, therefore be with a wide range of applications in the bridge Wind Engineering field in future, will produce significant social and economic benefit.

Description of drawings

Fig. 1 main beam section pneumatic self excitation force whole-course numerical modeling process flow diagram

The pneumatic self excitation force synoptic diagram of bridge main beam section under Fig. 2 wind action,

Fig. 3 Aero-dyn18 cell schematics,

The matrix of coefficients of Fig. 4 Aero-dyn18 unit,

Fig. 5 adopts the Aero-dyn18 unit to carry out pneumatic self excitation force finite element analogy synoptic diagram.

Embodiment

According to technique scheme, when calculating the non-linear buffeting response of Longspan Bridge, the time domain simulation of main beam section pneumatic self excitation force can realize by add the Aero-dyn18 unit at two ends, girder unit, wherein the required aerodynamic parameter in Aero-dyn18 unit adopts the CFD technology to discern, and the implementation procedure that this method specifically is applied in the Longspan Bridge buffeting analysis comprises following 5 steps:

1) sets up the initial limited element calculation model of Longspan Bridge according to design drawing;

2) adopt the CFD technology to discern the aerodynamic derivative of main beam section;

3), be identified for simulating the parameter of the Aero-dyn18 unit of stiffness matrix and damping matrix jointly according to formula (3), (4) and (5) according to the aerodynamic derivative of air speed data and main beam section;

4) on the basis of initial finite element model, add the Aero-dyn18 unit, obtained considering the finite element model that is used to buffet analysis of pneumatic self excitation force;

5), add the static(al) wind load and carry out the buffeting response analysis and solution with the power of buffeting time-histories on the finite element model basis that is used to buffet analysis.

Specific as follows:

The pneumatic self excitation force expression formula that proposes according to professor Scanlan, suffered aerodynamic lift L on the girder unit length _Se, aerodynamic drag D _SeWith aerodynamic moment M _SeCan be expressed as the function of vertical displacement h, horizontal shift p and torsional displacement α respectively, adopt dimensionless aerodynamic derivative H _i ^*, P _i ^*, A _i ^*(i=1,2 ..., 6) express:

$L_{\mathrm{ae}}=\frac{1}{2}{\mathrm{\&rho;U}}^2\left(2B\right)[{\mathrm{KH}}_1^{*}\frac{\stackrel{\&CenterDot;}{h}}{U}+{\mathrm{<figure-callout\; id="2"\; label="KH"\; filenames="C20081002342000112.png"\; state="\{\{state\}\}">KH</figure-callout>}}_2^{*}\frac{B\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}{U}+K^2{\mathrm{<figure-callout\; id="3"\; label="H"\; filenames="C20081002342000112.png"\; state="\{\{state\}\}">H</figure-callout>}}_3^{*}\mathrm{\&alpha;}+K^2{H}_4^{*}\frac{h}{B}+{\mathrm{KH}}_5^{*}\frac{\stackrel{\&CenterDot;}{p}}{U}+K^2{H}_6^{*}\frac{p}{B}]---\left(1a\right)$

$D_{\mathrm{ae}}=\frac{1}{2}{\mathrm{\&rho;U}}^2\left(2B\right)[{\mathrm{KP}}_1^{*}\frac{\stackrel{\&CenterDot;}{p}}{U}+{\mathrm{KP}}_2^{*}\frac{B\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}{U}+K^2{\mathrm{<figure-callout\; id="3"\; label="P"\; filenames="C20081002342000112.png"\; state="\{\{state\}\}">P</figure-callout>}}_3^{*}\mathrm{\&alpha;}+K^2{\mathrm{<figure-callout\; id="4"\; label="P"\; filenames="C20081002342000112.png"\; state="\{\{state\}\}">P</figure-callout>}}_4^{*}\frac{p}{B}+{\mathrm{KP}}_5^{*}\frac{\stackrel{\&CenterDot;}{h}}{U}+K^2{P}_6^{*}\frac{h}{B}]---\left(1b\right)$

$M_{\mathrm{ae}}=\frac{1}{2}{\mathrm{\&rho;U}}^2\left(2B^2\right)[{\mathrm{KA}}_1^{*}\frac{\stackrel{\&CenterDot;}{h}}{U}+{\mathrm{KA}}_2^{*}\frac{B\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}}{U}+K^2{A}_3^{*}\mathrm{\&alpha;}+K^2{A}_4^{*}\frac{h}{B}+{\mathrm{KA}}_5^{*}\frac{\stackrel{\&CenterDot;}{p}}{U}+K^2{A}_6^{*}\frac{p}{B}]---\left(1c\right)$

In the formula (1), ρ is an atmospheric density; U is a mean wind speed; B is a bridge deck width; K=B ω/U is a dimensionless frequency; ω is the vibration circular frequency; Aerodynamic derivative H _i ^*, P _i ^*, A _i ^*(i=1,2 ..., 6) and be the dimensionless wind speed $\tilde{U}=U/\left(\mathrm{fB}\right)$ Or the function of dimensionless frequency, their value is relevant with the geometric configuration in bridge cross section.L _Se, D _SeAnd M _SeDirection and the isoparametric signal of B, α see accompanying drawing 2.

Obviously, the aerodynamic force that is subjected on the girder unit length is distributed load, is the load that acts on two nodes in unit with these distributed load equivalences:

$\left\{\begin{array}{c}{\left(F_{\mathrm{ae}}^e\right)}_i\\ {\left(F_{\mathrm{ae}}^e\right)}_j\end{array}\right\}=\left[\begin{array}{cc}{\left(K_{\mathrm{ae}}^e\right)}_{\mathrm{ii}}& {\left(K_{\mathrm{ae}}^e\right)}_{\mathrm{ij}}\\ {\left(K_{\mathrm{ae}}^e\right)}_{\mathrm{ji}}& {\left(K_{\mathrm{ae}}^e\right)}_{\mathrm{jj}}\end{array}\right]\left\{\begin{array}{c}{X}_i^e\\ X_j^e\end{array}\right\}+\left[\begin{array}{cc}{\left(C_{\mathrm{ae}}^e\right)}_{\mathrm{ii}}& {\left(C_{\mathrm{ae}}^e\right)}_{\mathrm{ij}}\\ {\left(C_{\mathrm{ae}}^e\right)}_{\mathrm{ji}}& {\left(C_{\mathrm{ae}}^e\right)}_{\mathrm{jj}}\end{array}\right]\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{X}}_i^e\\ {\stackrel{\&CenterDot;}{X}}_j^e\end{array}\right\}---\left(2\right)$

In the formula (2), X _i ^eAnd X _j ^eBe respectively the motion vector of unit e at i and j node;

With

Be respectively the velocity vector of unit e at i and j node; K _Ae ^eAnd C _Ae ^eBe respectively pneumatic rigidity and the air damping matrix of unit e.When the aerodynamic force matrix was concentrated in employing, pneumatic stiffness matrix and air damping matrix were respectively:

$K_{\mathrm{ae}}^e=\left[\begin{array}{cc}{K}_{\mathrm{ae}1}^e& 0\\ 0& K_{\mathrm{ae}1}^e\end{array}\right]---\left(3a\right)$

Wherein, $K_{\mathrm{ae}1}^e=\frac{{\mathrm{\&rho;U}}^2{K}^2{\mathrm{<figure-callout\; id="2"\; label="L\; e"\; filenames="C20081002342000112.png"\; state="\{\{state\}\}">L</figure-callout>}}_e}{2}\left[\begin{array}{cccccc}0& 0& 0& 0& 0& 0\\ 0& P_6^{*}& {\mathrm{<figure-callout\; id="4"\; label="P"\; filenames="C20081002342000112.png"\; state="\{\{state\}\}">P</figure-callout>}}_4^{*}& {\mathrm{<figure-callout\; id="3"\; label="BP"\; filenames="C20081002342000112.png"\; state="\{\{state\}\}">BP</figure-callout>}}_3^{*}& 0& 0\\ 0& H_6^{*}& {\mathrm{<figure-callout\; id="4"\; label="H"\; filenames="C20081002342000112.png"\; state="\{\{state\}\}">H</figure-callout>}}_4^{*}& {\mathrm{BH}}_3^{*}& 0& 0\\ 0& {\mathrm{BA}}_6^{*}& {\mathrm{BA}}_4^{*}& B^2{A}_3^{*}& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\end{array}\right]---\left(3b\right)$

$C_{\mathrm{ae}}^e=\left[\begin{array}{cc}{C}_{\mathrm{ae}1}^e& 0\\ 0& C_{\mathrm{ae}1}^e\end{array}\right]---\left(4a\right)$

Wherein, $C_{\mathrm{ae}1}^e=\frac{\mathrm{\&rho;UBK}{\mathrm{<figure-callout\; id="2"\; label="L\; e"\; filenames="C20081002342000112.png"\; state="\{\{state\}\}">L</figure-callout>}}_e}{2}\left[\begin{array}{cccccc}0& 0& 0& 0& 0& 0\\ 0& P_5^{*}& P_1^{*}& {\mathrm{<figure-callout\; id="2"\; label="BP"\; filenames="C20081002342000112.png"\; state="\{\{state\}\}">BP</figure-callout>}}_2^{*}& 0& 0\\ 0& H_5^{*}& H_1^{*}& {\mathrm{BH}}_2^{*}& 0& 0\\ 0& {\mathrm{BA}}_5^{*}& {\mathrm{BA}}_1^{*}& B^2{A}_2^{*}& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\end{array}\right]---\left(4b\right)$

In formula (3) and (4), L _eLength for girder unit e.The form that it is pointed out that above two formulas is relevant with the direction of global coordinate.By above two formulas as can be known, pneumatic rigidity and air damping matrix can be definite fully by the geometric configuration in bridge cross section, therefore as can be known according to formula (1), when the wide B of bridge and all aerodynamic derivative be when known, suffered self excitation force can be determined by the displacement of node separately on two nodes of unit e, but prerequisite is to create the unit that can be used for pneumatic rigidity shown in formula (3) and (4) and air damping chess matrix analogue.

Special cell---the Aero-dyn18 unit has two nodes for pneumatic rigidity that the present invention created and air damping simulation, and each node has 6 degree of freedom, and it shows that sincere figure sees Fig. 3.Among the figure, X, Y, Z axle and X _e, Y _e, Z _eAxle is represented global coordinate system and the local coordinate system of unit e respectively; I and j represent two nodes of unit e.This unit does not have fixing geometric configuration, and it can import stiffness matrix K and damping matrix C by the mode of real constant, with the pneumatic rigidity and the air damping matrix of model configuration system.

The Aero-dyn18 cell matrix is 12 * 12 matrixes, has 9 different coefficients, the matrix coefficient in the difference corresponding (3) or (4), and its matrix construction synoptic diagram is seen Fig. 4.With pneumatic stiffness matrix coefficient or the air damping matrix coefficient substitution Aero-dyn18 cell matrix that has defined, this unit just can be used for simulating the pneumatic self excitation force that bridge floor is subjected to.

Because one of in pneumatic rigidity or the air damping matrix the two can only be simulated in Aero-dyn18 unit, and can not simulate the two simultaneously, therefore add two Aero-dyn18 unit E at each bridge floor girder node place, comprising a rigidity unit and a damping unit, as shown in Figure 5.In Fig. 5, the node of unit E is girder node i or j, and another node is fixed, because element length can be appointed and be got, therefore can set the position of stationary nodes arbitrarily.For example, at the node i place, unit E1 is used to simulate pneumatic rigidity and single E3 is used to simulate the equivalent air damping that girder node i place is subjected to, shared two nodes of unit E1 and E3.The function of unit E2 and E4 is identical with E3 with analogy method and unit E1.

As seen from the above analysis, when the equal in length of each BEAM4 unit of simulation girder, the Aero-dyn18 matrix that is used to simulate pneumatic rigidity and air damping can be obtained by formula (5):

$K^{E_1}=-{2K}_{\mathrm{ae}}^e,$ ${\mathrm{<figure-callout\; id="3"\; label="C\; E"\; filenames="C20081002342000112.png"\; state="\{\{state\}\}">C</figure-callout>}}^{E_{}}=-2C_{\mathrm{ae}}^e---\left(5a\right)$

$K^{{\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="C20081002342000112.png"\; state="\{\{state\}\}">E</figure-callout>}}_2}=-{2K}_{\mathrm{ae}}^e,$ ${\mathrm{<figure-callout\; id="4"\; label="C\; E"\; filenames="C20081002342000112.png"\; state="\{\{state\}\}">C</figure-callout>}}^{E_{}}=-2C_{\mathrm{ae}}^e---\left(5b\right)$

In the formula (5),

With

Be respectively the stiffness matrix of unit E1 and E2;

With

With the damping matrix that is respectively unit E3 and E4; K _Ae ^eAnd C _Ae ^eBe respectively pneumatic stiffness matrix and the air damping matrix of unit e.Therefore, with the stiffness matrix of formula (5) with damping matrix is transformed under the global coordinate and group integrated morphology total aerodynamic force matrix, and superpose with the stiffness matrix and the damping matrix of original structure respectively, just can obtain being used to buffeting the system stiffness matrix and the damping matrix of the finite element model of analysis.Simultaneously, in order to avoid the wind tunnel test of the sections model that aerodynamic parameter identification institute must carry out in the existing analytical approach, the aerodynamic parameter employing CFD technology in pneumatic stiffness matrix and the air damping matrix is discerned.

Claims (2)

1. the whole-course numerical modeling method of a main beam section pneumatic self excitation force is characterized in that this method may further comprise the steps:

The first step:, adopt the programmable parameter design language to set up the FEM (finite element) calculation initial model of Longspan Bridge according to the structural design drawing;

Second step: identify the aerodynamic derivative of Longspan Bridge main beam section based on the Fluid Mechanics Computation technology, and it is stored to call the array mode;

The 3rd step: determine pneumatic self excitation force unit---the parameter of Aero-dyn18 unit created according to the aerodynamic derivative that is used for buffeting the air speed data of analysis and identify;

The 4th step: the Aero-dyn18 unit of determining parameter is added in the first step gained FEM (finite element) calculation initial model, obtain to have counted the limited element calculation model of pneumatic self excitation force;

The 5th step: on the limited element calculation model that counts pneumatic self excitation force, add static(al) wind load and the power of buffeting time-histories, carry out the buffeting response Nonlinear time-history analysis;

The 3rd step described pneumatic self excitation force unit---stiffness matrix K and damping matrix C are determined by the mode of importing 9 real constants in the Aero-dyn18 unit, to simulate the pneumatic rigidity and the air damping matrix of main beam section; This unit has two nodes, and each node has 6 degree of freedom; The Aero-dyn18 unit does not have fixing geometric configuration, can arbitrarily conversion profile between two node i and j; Under the asymmetric situation, the Aero-dyn18 cell matrix is 12 * 12 matrixes, has 9 different coefficients:

$\left[\begin{array}{cccccccccccc}0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& C_1& C_2& C_3& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& C_4& C_5& C_6& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& C_7& C_8& C_9& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& C_1& C_2& C_3& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& C_4& C_5& C_6& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& C_7& C_8& C_9& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\end{array}\right]$

2. the whole-course numerical modeling method of main beam section pneumatic self excitation force according to claim 1, it is characterized in that described Aero-dyn18 unit with definite parameter of the 4th step adds in the process of first step gained FEM (finite element) calculation initial model, each bridge floor girder node place need add two Aero-dyn18 unit E, comprises a rigidity unit and a damping unit; The node of unit E is girder node i or j, and another node can be fixed on the optional position.

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