JP2019192003A - Structure amplitude evaluation method - Google Patents

Abstract

To provide a structure amplitude evaluation method which precisely evaluates an amplitude of a structure acted with load.SOLUTION: The structure amplitude evaluation method includes: a step ST1 of setting a model of a structure; a step ST2 of setting analysis region and analysis matrix for the model of the structure; a step ST3 of setting excitation amplitude, excitation frequency and wind speed; a step ST4 of performing numerical fluid analysis on the model of the structure for each analysis matrix, using the excitation amplitude, the excitation frequency and the wind speed; a step ST5 of calculating unsteady aerodynamic force coefficient acting on the model of the structure; a step ST8 of calculating relationship of unsteady aerodynamic force coefficient with respect to dimensionless wind speed and excitation amplitude; and a step ST10 of evaluating excited amplitude using the unsteady aerodynamic force coefficient.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a structure amplitude evaluation method for evaluating the amplitude of a structure to which a load is applied.

  Conventionally, a vibration experiment using a partial model has been performed as a method for evaluating the influence when a load is applied to a structure. For example, a direction for conducting a wind tunnel experiment using a partial model is disclosed as a method for evaluating the influence of wind on a suspension bridge (see Patent Document 1).

JP-A-1-240835

  However, in experiments using partial models, a large amount of labor is required for appropriate reproduction of real conditions, such as the evaluation of complex shapes and small parts of structures or reproduction of the natural environment. It was difficult.

  An object of the present invention is to provide a structure amplitude evaluation method for accurately evaluating the amplitude of a structure to which a load is applied.

An amplitude evaluation method for a structure according to an embodiment of the present invention includes:
Setting the model of the structure;
Setting an analysis region and an analysis grid for the model of the structure;
Setting excitation amplitude, excitation frequency and wind speed for the model of the structure;
Performing a numerical fluid analysis on the model of the structure from the excitation amplitude, excitation frequency and wind speed for each analysis grid;
Calculating an unsteady aerodynamic coefficient acting on the model of the structure from the analysis result of the numerical fluid analysis;
Calculating the relationship of the unsteady aerodynamic coefficient to the non-dimensionalized wind speed and excitation amplitude;
Evaluating the excited amplitude from the unsteady aerodynamic coefficient;
It is characterized by having.

An amplitude evaluation method for a structure according to an embodiment of the present invention includes:
After the step of calculating the relationship of the non-steady aerodynamic coefficient to the non-dimensionalized wind speed and the vibration amplitude, there is a step of removing the effect of structural damping from the aerodynamic damping term of the unsteady aerodynamic coefficient. .

ここで、u_i：流速のi(i＝1〜3)成分、U^k：反変流速のk(k＝1〜3)成分、x_i：デカルト座標のi(i＝1〜3)成分、ξ^k：一般座標のk(k＝1〜3)成分、P＝p/ρ、ただし、p：圧力、ρ：空気密度、Re：レイノルズ数（＝UD/ν、U：代表風速、D：代表長（桁高）、ν：動粘性係数）、t：時間である。
また、Jは座標変換のヤコビアンで、以下の式（３）で表される。

An amplitude evaluation method for a structure according to an embodiment of the present invention includes:
In the step of performing the numerical fluid analysis on the model of the structure, the incompressible Navier-Stokes equation of the general coordinate system represented by the following equation (1) and the continuous equation represented by the equation (2) are analyzed as governing equations. It is characterized by that.

Where u _i : i (i = 1 to 3) component of flow velocity, U ^k : k (k = 1 to 3) component of contravariant flow velocity, x _i : i (i = 1 to 3) component of Cartesian coordinates , Ξ ^k : k (k = 1 to 3) component of general coordinates, P = p / ρ, where p: pressure, ρ: air density, Re: Reynolds number (= UD / ν, U: representative wind speed, D : Representative length (digit height), ν: kinematic viscosity coefficient), t: time.
J is a Jacobian for coordinate transformation and is represented by the following equation (3).

ここで、K＝Bω/U、B：幅員、ω：角振動数、L：奥行き方向長さ、η₀：鉛直たわみ振幅、H₁ ^*，H₄ ^*：非定常空気力係数、t：時間である。 An amplitude evaluation method for a structure according to an embodiment of the present invention includes:
In the step of calculating an unsteady aerodynamic coefficient acting on the model of the structure,
The unsteady aerodynamic coefficient H ₁ ^* , which is the coefficient of the attenuation term represented by the following equation (8), is obtained.

Where K = Bω / U, B: width, ω: angular frequency, L: depth length, η ₀ : vertical deflection amplitude, H ₁ ^* , H ₄ ^* : unsteady aerodynamic coefficient, t: time It is.

ここで、δ：対数減衰率、m：質量である。 An amplitude evaluation method for a structure according to an embodiment of the present invention includes:
In the step of removing the effect of structural damping from the aerodynamic damping term of the unsteady aerodynamic coefficient,
The following expression (9) is used.

Here, δ: logarithmic decay rate, m: mass.

  According to the amplitude evaluation method for a structure according to the present invention, it is possible to accurately evaluate the amplitude of a structure to which a load is applied.

The flowchart of the structure vibration analysis method of this embodiment is shown. The model of the structure used with the structure vibration analysis method of this embodiment is shown. The analysis area | region and analysis grid with respect to the model of the structure used with the structure aerodynamic evaluation analysis method of this embodiment are shown. The numerical fluid analysis result with respect to the model of the structure by the structure aerodynamic force evaluation analysis method of this embodiment is shown. The relationship between the non-dimensional excitation amplitude, the non-dimensional wind speed, and the unsteady aerodynamic coefficient of the model of the structure by the structural aerodynamic evaluation analysis method of the present embodiment is shown. The relationship between the non-dimensional excitation amplitude, the non-dimensional wind speed, and the unsteady aerodynamic coefficient from which the structural damping term has been removed is shown for the structural model by the structural aerodynamic evaluation analysis method of the present embodiment. FIG. 7 shows a modified display format of FIG.

  The structure aerodynamic force evaluation analysis method of this embodiment will be described below with reference to the drawings.

  FIG. 1 shows a flowchart of a structural aerodynamic evaluation analysis method of the present embodiment.

  First, in the structural aerodynamic evaluation analysis of the present embodiment, a structural model 1 is set in step 1 (ST1).

  FIG. 2 shows a model 1 of the structure used in the structure aerodynamic force evaluation analysis method of the present embodiment. In this embodiment, a box girder cross section of a bridge having a rotation center O as shown in FIG. In FIG. 2, Df represents drag, Lf represents lift, Mf represents moment, and D represents height. In the present embodiment, a bridge is used as the model 1 of the structure, but other structures may be used. In the present embodiment, the lift force Lf is analyzed as an example, but the drag force Df or the moment Mf may be analyzed.

  Next, in step 2, an analysis region and an analysis grid for the model 1 of the structure are set (ST2). The analysis is performed on the space around the model 1 of the structure. However, since it is a finite value that can be calculated by the computer, it is preferable to analyze by cutting out the space at an appropriate place. This cut out area is called an analysis area. In order to perform analysis, it is necessary to divide the analysis region into a plurality of small lattice elements and discretize the equations to obtain the relationship between adjacent lattice elements. This set of divided lattice elements is called an analysis lattice.

  FIG. 3 shows an analysis region and an analysis grid for the model 1 of the structure used in the structure aerodynamic evaluation analysis method of the present embodiment. The analysis area is preferably determined to be circular with reference to the height D of the model 1 shown in FIG.

  The size of the elements constituting the lattice in the orthogonal direction with respect to the model 1 is small near the wall surface of the model 1 and increases as the distance from the model 1 increases. It is preferable that each element in the vicinity of the wall surface of the model 1 is adjusted to be orthogonal.

  Next, in step 3, the excitation amplitude, the excitation frequency, and the wind speed for the model 1 of the structure are set (ST3). The range to be analyzed may be set for the setting of the excitation amplitude, the excitation frequency, and the wind speed.

ここで、u_i：流速のi(i＝1〜3)成分、U^k：反変流速のk(k＝1〜3)成分、x_i：デカルト座標のi(i＝1〜3)成分、ξ^k：一般座標のk(k＝1〜3)成分、P＝p/ρ、ただし、p：圧力、ρ：空気密度、Re：レイノルズ数（＝UD/ν、U：代表風速、D：代表長（桁高）、ν：動粘性係数）、t：時間である。 Next, in step 4, a numerical fluid analysis is performed on the structure model 1 (ST4). In this embodiment, as an example, the incompressible Navier-Stokes equation of the general coordinate system represented by the following equation (1) and the continuous equation represented by equation (2) were analyzed as governing equations.

Where u _i : i (i = 1 to 3) component of flow velocity, U ^k : k (k = 1 to 3) component of contravariant flow velocity, x _i : i (i = 1 to 3) component of Cartesian coordinates , Ξ ^k : k (k = 1 to 3) component of general coordinates, P = p / ρ, where p: pressure, ρ: air density, Re: Reynolds number (= UD / ν, U: representative wind speed, D : Representative length (digit height), ν: kinematic viscosity coefficient), t: time.

J is a Jacobian for coordinate transformation and is represented by the following equation (3).

  When vibration of the structure accompanies, by performing coordinate transformation on the four-dimensional coordinates (x, y, z, t) including time, general coordinates (ξ, η fixed with respect to time) , ζ, τ) (where τ = t).

ここで、U_g ^k：格子の反変速度のk(k＝1〜3)成分である。 At this time, the Navier-Stokes equation in a general coordinate system fixed with respect to time is expressed by the following equation (4).

Here, U _g ^{k is} the k (k = 1 to 3) component of the lattice invariant velocity.

Furthermore, the continuous formula can also be expressed by the following formula by using Geometric Conservation Law.

  FIG. 4 shows a numerical fluid analysis result for a structure model by the structure aerodynamic evaluation analysis method of the present embodiment. This result is the pressure distribution of the time-averaged flow field made dimensionless with the dynamic pressure and the representative length D, and the absolute value of the wind speed. What is shown by shading is the pressure distribution, and what is shown by a line is the straight line of the absolute value of the wind speed. The pressure is high at the upstream end, and the pressure drops low in the dark part slightly downstream.

ここで、η：鉛直たわみ変位、η₀：鉛直たわみ振幅、ω：角振動数、t：時間である。 Next, in step 5, the unsteady aerodynamic force acting on the model 1 of the structure is calculated (ST5). In the present embodiment, sinusoidal excitation is performed on the model 1 with one degree of freedom in the vertical deflection or torsional direction. The vertical deflection vibration as the excitation vibration in this case can be expressed by the following equation (6).

Here, η: vertical deflection displacement, η ₀ : vertical deflection amplitude, ω: angular frequency, t: time.

ここで、B：幅員、L：奥行き方向長さ、K＝Bω/U、H₁ ^*，H₄ ^*：非定常空気力係数、 The unsteady aerodynamic force acting on the structure by the vertical deflection vibration can be expressed by the following equation (7) using Scanlan's unsteady aerodynamic coefficient.

Where B: width, L: length in the depth direction, K = Bω / U, H ₁ ^* , H ₄ ^* : unsteady aerodynamic coefficient,

Next, in step 6, an unsteady aerodynamic coefficient acting on the model 1 of the structure is calculated (ST6). Substituting equation (7) into equation (6) and using the definition of dimensionless frequency: K = Bω / U, the unsteady aerodynamic force can be expressed by the following equation (8). Here, B is a width.

Therefore, it is possible to calculate the two unsteady aerodynamic coefficients H ₁ ^* and H ₄ ^* from the amplitude ratio and phase difference between the vertical deflection displacement and the unsteady aerodynamic force. Here, in the present embodiment, the unsteady aerodynamic coefficient H ₁ ^* , which is the coefficient of the attenuation term, is obtained.

ここで、B：幅員、L：奥行き方向長さ、K＝Bω/U、φ：ねじれ角度、A₂ ^*，A₃ ^*：非定常空気力係数である。 The unsteady aerodynamic force Mae acting on the structure related to torsional vibration can be expressed by the following equation (9). As the unsteady aerodynamic coefficient of torsional vibration, the coefficient A ₂ ^* of the aerodynamic damping term may be obtained.

Here, B: width, L: depth direction length, K = Bω / U, φ: twist angle, A ₂ ^* , A ₃ ^* : unsteady aerodynamic coefficient.

  Next, in step 7, it is determined whether or not an unsteady aerodynamic coefficient has been determined (ST7). The unsteady aerodynamic coefficient is determined when the vibration amplitude, vibration frequency and wind speed are changed within the range set in Step 3 and all the vibration amplitude, vibration frequency and wind speed within the range are analyzed. Is done.

  If the unsteady aerodynamic coefficient is not determined in step 7, the process returns to step 3. When the unsteady aerodynamic coefficient is determined in step 7, the process proceeds to step 8.

  In step 8, the relationship between the non-dimensionalized wind speed and excitation amplitude and the unsteady aerodynamic coefficient is calculated (ST8).

  FIG. 5 shows the relationship between the non-dimensional excitation amplitude, the non-dimensional wind speed, and the unsteady aerodynamic coefficient of the structure model according to the structural aerodynamic evaluation analysis method of the present embodiment.

As shown in FIG. 5, the amplitude dependence of the unsteady aerodynamic coefficient was confirmed in the range of wind speed and excitation amplitude for the purpose of checking vortex excitation. In particular, in the range of U / fD = 8.0 to 12.0, which is the wind speed region where overexcitation occurs, there is a significant amplitude dependence, and there are excitation amplitude regions and wind velocity regions where the unsteady aerodynamic coefficient H ₁ ^* is positive. It was confirmed.

  Next, in step 9, the effect of structural damping is removed from the aerodynamic damping term of the unsteady aerodynamic coefficient (ST9).

  FIG. 6 shows the relationship between the non-dimensional excitation amplitude, the non-dimensional wind speed, and the unsteady aerodynamic coefficient from which the structural damping term is removed in the structure model according to the structural aerodynamic evaluation analysis method of this embodiment. .

ここで、δ：対数減衰率、m：質量である。 The increase and decrease in the amplitude of overexcitation can be evaluated using the relationship between aerodynamic damping and structural damping. When the following equation (10) is positive, vibration is excited, and when negative, it is attenuated.

Here, δ: logarithmic decay rate, m: mass.

ここで、I：質量慣性モーメントである。 In the case of torsional vibration, the following equation (11) may be used.

Here, I is the mass moment of inertia.

  Next, in step 10, the non-stationary aerodynamic coefficient from which the effect of structural damping is removed becomes zero or more, and the amplitude excited from the non-dimensional wind speed and excitation amplitude is evaluated (ST10).

  Overexcitation can be evaluated by obtaining a non-dimensional wind speed and excitation amplitude at which Equation (10) becomes zero. As shown in FIG. 6, in the wind speed region of U / fD = 9.0 to 12.0, expression (10) is positive with some excitation amplitude, and it can be evaluated that overexcitation occurs.

  FIG. 7 shows a modification of the display format of FIG.

  In FIG. 7, the unsteady aerodynamic coefficient from which the effect of structural damping according to the non-dimensional wind speed and the excitation amplitude is removed can be confirmed at a glance. In the wind velocity region of U / fD = 9.0 to 12.0 and the excitation amplitude of η / D = 0.025 to 0.15, Equation (10) is positive, and it can be evaluated that overexcitation occurs.

  As described above, the amplitude evaluation method for a structure according to the present embodiment includes the steps of setting the model 1 of the structure, setting the analysis region and analysis grid for the model 1 of the structure, and exciting the model 1 of the structure. A step for setting the amplitude, excitation frequency and wind speed, a step for performing the numerical fluid analysis on the model 1 of the structure from the excitation amplitude, the excitation frequency and the wind speed for each analysis grid, and the structure from the analysis result of the numerical fluid analysis Excited from the unsteady aerodynamic coefficient, the step of calculating the unsteady aerodynamic coefficient acting on the model 1 of the object, the step of calculating the relationship of the unsteady aerodynamic coefficient to the non-dimensionalized wind speed and excitation amplitude Evaluating the amplitude. Therefore, it is possible to accurately evaluate the amplitude of the structure on which the load is applied. In addition, the calculation load can be reduced.

  In addition, the amplitude evaluation method for the structure according to the present embodiment is configured to calculate the structural damping from the aerodynamic damping term of the unsteady aerodynamic coefficient after the step of calculating the relationship between the non-dimensional wind speed and the vibration amplitude. There is a step of removing the effect. Therefore, the amplitude of the structure can be more accurately evaluated.

ここで、u_i：流速のi(i＝1〜3)成分、U^k：反変流速のk(k＝1〜3)成分、x_i：デカルト座標のi(i＝1〜3)成分、ξ^k：一般座標のk(k＝1〜3)成分、P＝p/ρ、ただし、p：圧力、ρ：空気密度、Re：レイノルズ数（＝UD/ν、U：代表風速、D：代表長（桁高）、ν：動粘性係数）、t：時間である。
また、Jは座標変換のヤコビアンで、以下の式（３）で表される。

したがって、構造物の振幅をより的確に評価することが可能となる。 In the structure amplitude evaluation method of the present embodiment, in the step of performing the numerical fluid analysis on the model of the structure, the incompressible Navier-Stokes equation of the general coordinate system represented by the following expression (1) and the expression ( The continuous equation shown in 2) is analyzed as the governing equation.

Where u _i : i (i = 1 to 3) component of flow velocity, U ^k : k (k = 1 to 3) component of contravariant flow velocity, x _i : i (i = 1 to 3) component of Cartesian coordinates , Ξ ^k : k (k = 1 to 3) component of general coordinates, P = p / ρ, where p: pressure, ρ: air density, Re: Reynolds number (= UD / ν, U: representative wind speed, D : Representative length (digit height), ν: kinematic viscosity coefficient), t: time.
J is a Jacobian for coordinate transformation and is represented by the following equation (3).

Therefore, the amplitude of the structure can be more accurately evaluated.

ここで、K＝Bω/U、B：幅員、ω：角振動数、L：奥行き方向長さ、η₀：鉛直たわみ振幅、H₁ ^*，H₄ ^*：非定常空気力係数、t：時間である。
したがって、構造物の振幅をより的確に評価することが可能となる。 In the structure amplitude evaluation method according to the embodiment of the present invention, in the step of calculating the unsteady aerodynamic coefficient acting on the structure model, unsteady air that is a coefficient of an attenuation term represented by the following equation (8): Find the force coefficient H ₁ ^* .

Where K = Bω / U, B: width, ω: angular frequency, L: depth length, η ₀ : vertical deflection amplitude, H ₁ ^* , H ₄ ^* : unsteady aerodynamic coefficient, t: time It is.
Therefore, the amplitude of the structure can be more accurately evaluated.

ここで、δ：対数減衰率、m：質量である。
したがって、構造物の振幅をより的確に評価することが可能となる。 The amplitude evaluation method for a structure according to the embodiment of the present invention uses the following equation (10) in the step of removing the effect of structural damping from the aerodynamic damping term of the unsteady aerodynamic coefficient.

Here, δ: logarithmic decay rate, m: mass.
Therefore, the amplitude of the structure can be more accurately evaluated.

  In addition, this invention is not limited by this embodiment. That is, in describing the embodiment, many specific details are included for illustration, but those skilled in the art may add various variations and changes to these details.

1. Model of structure

Claims (5)

Setting the model of the structure;
Setting an analysis region and an analysis grid for the model of the structure;
Setting excitation amplitude, excitation frequency and wind speed for the model of the structure;
Performing a numerical fluid analysis on the model of the structure from the excitation amplitude, excitation frequency and wind speed for each analysis grid;
Calculating an unsteady aerodynamic coefficient acting on the model of the structure from the analysis result of the numerical fluid analysis;
Calculating the relationship of the unsteady aerodynamic coefficient to the non-dimensionalized wind speed and excitation amplitude;
Evaluating the excited amplitude from the unsteady aerodynamic coefficient;
A method for evaluating an amplitude of a structure, comprising: After the step of calculating the relationship of the non-steady aerodynamic coefficient to the non-dimensionalized wind speed and the vibration amplitude, there is a step of removing the effect of structural damping from the aerodynamic damping term of the unsteady aerodynamic coefficient. The amplitude evaluation method for a structure according to claim 1. In the step of performing the numerical fluid analysis on the model of the structure, the incompressible Navier-Stokes equation of the general coordinate system represented by the following equation (1) and the continuous equation represented by the equation (2) are analyzed as governing equations. The amplitude evaluation method for a structure according to claim 2, wherein:

Where u _i : i (i = 1 to 3) component of flow velocity, U ^k : k (k = 1 to 3) component of contravariant flow velocity, x _i : i (i = 1 to 3) component of Cartesian coordinates , Ξ ^k : k (k = 1 to 3) component of general coordinates, P = p / ρ, where p: pressure, ρ: air density, Re: Reynolds number (= UD / ν, U: representative wind speed, D : Representative length (digit height), ν: kinematic viscosity coefficient), t: time.
J is a Jacobian for coordinate transformation and is represented by the following equation (3).

In the step of calculating an unsteady aerodynamic coefficient acting on the model of the structure,
The method for evaluating an amplitude of a structure according to claim 3, wherein the unsteady aerodynamic coefficient H ₁ ^* , which is a coefficient of an attenuation term expressed by the following equation (8), is obtained.

Where K = Bω / U, B: width, ω: angular frequency, L: depth length, η ₀ : vertical deflection amplitude, H ₁ ^* , H ₄ ^* : unsteady aerodynamic coefficient, t: time It is. In the step of removing the effect of structural damping from the aerodynamic damping term of the unsteady aerodynamic coefficient,
The amplitude evaluation method for a structure according to claim 4, wherein the following equation (9) is used.

Here, δ: logarithmic decay rate, m: mass.

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