CN102682168A - Method for determining dimension of rectangular beam section of low-speed flutter main beam model of airplane - Google Patents

Abstract

The invention belongs to the field of structural mechanics and relates to a method for determining the dimension of a rectangular beam section of a low-speed flutter main beam model of an airplane. The method is characterized by adapting to the situation that the half width a of a rectangular section is smaller than the half height b of the rectangular section or the situation that J/Ix<1.69, wherein Ix refers to vertical inertia moment and J refers to polar inertia moment. The method for determining the dimension of the rectangular beam section with a lug piece comprises the following steps of: calculating the half width ar and the half height br of the rectangular section when the rectangular beam without the lug piece has the vertical inertia moment Ix of a preset value and the polar inertia moment J of a preset value; adjusting the polar inertia moment J with the preset value; calculating the half width a and the half height b; and calculating the half width 1 of the rectangular beam section with the lug piece when the rectangular beam with the lug piece has lateral inertia moment Iy of a preset value and the thickness of the lug piece is t. The method disclosed by the invention has the advantages of increasing the rigidity precision of the section of the model, reducing the uncertainty of model design, shortening the time for determining the dimension of the section, and increasing the design efficiency of the flutter model.

Description

A kind of aircraft low speed flutter girder model rectangular beam sectional dimension is confirmed method

Technical field

The invention belongs to the structural mechanics field, relate to a kind of aircraft low speed flutter girder model rectangular beam sectional dimension and confirm method.

Background technology

For the airplane flutter modelling of high aspect ratio wing, single-beam structure of models form is widely used in structures such as wing, fuselage, empennage.In order to satisfy the designing requirement of three-way rigidity, the square-section of band auricle is an ideal designs form.

Usually need obtain the sectional dimension that meets the demands through the method that examination is gathered in the past.The method that examination is gathered has following shortcoming: the first, the adjustment sectional dimension data needs designer's experience; The dimensional data that provides by rule of thumb often error is very big; Even the situation of the size that meets design requirement can appear being difficult to adjust; Influence the precision of model section rigidity, increased the uncertainty of modelling.The second, to confirm sectional dimension through method of trial and error, need carry out the manual work adjustment of many rounds and judge that the time is long that efficient is low, has a strong impact on the modelling cycle.

Referring to Chinese patent " band auricle rectangular beam sectional dimension confirm method " (application number 201110232655.8), need not examination and gather, only need provide and comprise the auricle thickness t, vertically to moment of inertia I _x, side direction moment of inertia I _yWith polar moment of inertia J in interior input data, can obtain sectional dimension data, comprise width 2a, height 2b and the cross-sectional width 2l of rectangle, but the applicable elements of this method is J/I _x>=1.69.Work as J/I _x＜1.69, design error can increase.

Summary of the invention

The objective of the invention is: propose a kind of aircraft low speed flutter girder model rectangular beam sectional dimension and confirm method; To improve the precision of model section rigidity, reduce the uncertainty of modelling, shorten the time of confirming sectional dimension; Improve the design efficiency of flutter model, and be applicable to cross section J/I _x＜1.69 o'clock requirement.

Technical solution of the present invention is: aircraft low speed flutter girder model rectangular beam cross section is the rectangular beam of band auricle, guarantee band auricle rectangular beam have predetermined value vertically to moment of inertia I _x, side direction moment of inertia I _yWith polar moment of inertia J and auricle thickness be under the situation of t, confirm width 2a, height 2b and the cross-sectional width 2l of its rectangle, it is characterized in that, confirm that the step of band auricle rectangular beam sectional dimension is following:

1, calculate not with the auricle rectangular beam have predetermined value vertically to moment of inertia I _xSquare-section half width a during with polar moment of inertia J _rWith cross section half height b _r:

1.1, set the initial value α of iteration variable α ₀=0.93 ~ 0.99:

1.2, according to computes intermediate variable β and iteration variable α ₁:

$\left\{\begin{array}{c}24{\left(\frac{2}{\mathrm{\&pi;}}\right)}^5{\mathrm{\&alpha;}}_0{\mathrm{\&beta;}}^3-4{\mathrm{\&beta;}}^2+\frac{J}{I_x}=0\\ {\mathrm{\&alpha;}}_1=\tanh \frac{\mathrm{\&pi;}}{2\mathrm{\&beta;}}+\frac{1}{243}\tanh \frac{3\mathrm{\&pi;}}{2\mathrm{\&beta;}}\end{array}\right....\left[1\right]$

Attention: when finding the solution β, relate to finding the solution of simple cubic equation, the flat-sawn method is adopted in suggestion, and β ∈ (0,1);

1.3, calculate iterative value α ₁With initial value α ₀Scale error e ₁:

$e_1=\frac{{\mathrm{\&alpha;}}_1-{\mathrm{\&alpha;}}_0}{{\mathrm{\&alpha;}}_0}...\left[2\right]$

If | e ₁|＜0.000001, square-section half width a then _rWith cross section half height b _rFor:

$\left\{\begin{array}{c}{a}_r=\sqrt[4]{\frac{{3I}_x{\mathrm{\&beta;}}^3}{4}}\\ b_r=\sqrt[4]{\frac{3I_x}{4\mathrm{\&beta;}}}\end{array}\right....\left[3\right]$

Step 1.1 finishes; Otherwise, carry out step 1.4;

1.4, make α ₀=α ₁, the method for repeating step 1.2～step 1.3, through iterative computation, up to | e ₁|＜0.000001, and obtain square-section half width a at this moment _rWith cross section half height b _r, step 1 finishes;

2, predetermined polar moment of inertia J is adjusted: go out the adjusted value J of polar moment of inertia J according to computes ₁,

Note answering guaranteed conditions: t＜a _r;

3, calculate half width a and half height b: change the J in the formula [1] into J ₁, calculate half width a and half height b according to the described method of step 1 then;

4, calculate band auricle rectangular beam cross section half-breadth l:

4.1, according to computes intermediate variable δ:

$\mathrm{\&delta;}=\frac{{3I}_y-{4a}^{3}b}{2t}...\left[5\right]$

4.2, calculate band auricle rectangular beam cross section half-breadth l:

$l=\sqrt[3]{\mathrm{\&delta;}+a^3}...\left[6\right]$

So far, obtain half width a, half height b and cross section half-breadth l, and then obtain width 2a, height 2b and the cross-sectional width 2l of corresponding rectangular beam with the auricle rectangular beam.

Advantage of the present invention is: improved the precision of model section rigidity, reduced the uncertainty of modelling, shortened the time of definite sectional dimension, improved the design efficiency of flutter model, and satisfied J/I _x＜1.69 requirement.One embodiment of the present of invention are compared with the present examination method of gathering, and the present invention confirms that the time of sectional dimension is merely 3 minutes, and the present examination method of gathering needs 4 hours, and the time spent of the present invention is merely examination and gathers 1/80th of method.

Description of drawings

Fig. 1 is a schematic cross section of not being with the rectangular beam of auricle.A among the figure _rBe the half width of the rectangle that calculates of step 1 of the present invention, b _rIt is half height of the rectangle that calculates of step 1 of the present invention.The initial point 0 of the two-dimensional coordinate system among Fig. 1 is the center of rectangle, and the x axle is parallel to the Width of rectangle, and positive dirction is towards the right side, and the positive dirction of y axle up.

Fig. 2 is the schematic cross section of the rectangular beam of band auricle.Two-dimensional coordinate system among Fig. 2 is identical with Fig. 1.

Embodiment

Explain further details in the face of the present invention down.Referring to Fig. 1,2, band auricle rectangular beam sectional dimension is confirmed method, guarantee band auricle rectangular beam have predetermined value vertically to moment of inertia I _x, side direction moment of inertia I _yWith polar moment of inertia J and auricle thickness be under the situation of t, confirm width 2a, height 2b and the cross-sectional width 2l of its rectangle, it is characterized in that, confirm that the step of band auricle rectangular beam sectional dimension is following:

1, calculate not with the auricle rectangular beam have predetermined value vertically to moment of inertia I _xSquare-section half width a during with polar moment of inertia J _rWith cross section half height b _r:

1.1, set the initial value α of iteration variable α ₀=0.93 ~ 0.99:

1.2, according to computes intermediate variable β and iteration variable α ₁:

$\left\{\begin{array}{c}24{\left(\frac{2}{\mathrm{\&pi;}}\right)}^5{\mathrm{\&alpha;}}_0{\mathrm{\&beta;}}^3-4{\mathrm{\&beta;}}^2+\frac{J}{I_x}=0\\ {\mathrm{\&alpha;}}_1=\tanh \frac{\mathrm{\&pi;}}{2\mathrm{\&beta;}}+\frac{1}{243}\tanh \frac{3\mathrm{\&pi;}}{2\mathrm{\&beta;}}\end{array}\right....\left[1\right]$

Attention: when finding the solution β, relate to finding the solution of simple cubic equation, the flat-sawn method is adopted in suggestion, and β ∈ (0,1);

1.3, calculate iterative value α ₁With initial value α ₀Scale error e ₁:

$e_1=\frac{{\mathrm{\&alpha;}}_1-{\mathrm{\&alpha;}}_0}{{\mathrm{\&alpha;}}_0}...\left[2\right]$

If | e ₁|＜0.000001, square-section half width a then _rWith cross section half height b _rFor:

$\left\{\begin{array}{c}{a}_r=\sqrt[4]{\frac{{3I}_x{\mathrm{\&beta;}}^3}{4}}\\ b_r=\sqrt[4]{\frac{3I_x}{4\mathrm{\&beta;}}}\end{array}\right....\left[3\right]$

Step 1 finishes; Otherwise, carry out step 1.4;

1.4, make α ₀=α ₁, the method for repeating step 1.2～step 1.3, through iterative computation, up to | e ₁|＜0.000001, and obtain square-section half width a at this moment _rWith cross section half height b _r, step 1 finishes;

2, predetermined polar moment of inertia J is adjusted: go out the adjusted value J of polar moment of inertia J according to computes ₁,

Note answering guaranteed conditions: t＜a _r;

3, calculate half width a and half height b: change the J in the formula [1] into J ₁, calculate half width a and half height b according to the described method of step 1 then;

4, calculate band auricle rectangular beam cross section half-breadth l:

4.1, according to computes intermediate variable δ:

$\mathrm{\&delta;}=\frac{{3I}_y-{4a}^{3}b}{2t}...\left[5\right]$

4.2, calculate band auricle rectangular beam cross section half-breadth l:

$l=\sqrt[3]{\mathrm{\&delta;}+a^3}...\left[6\right]$

So far, obtain half width a, half height b and cross section half-breadth l, and then obtain width 2a, height 2b and the cross-sectional width 2l of corresponding rectangular beam with the auricle rectangular beam.

Principle of work of the present invention is: derive and the parameter correction through the mechanics of materials and Elasticity fundamental formular; (seeing the logical Higher Education Publishing House 1997 of " Elasticity " Yang Gui and " mechanics of materials " single brightness ancestral Higher Education Publishing House 1999) obtained a kind ofly directly to obtain the method with auricle rectangular beam sectional dimension from cross section property; For definite sectional dimension, this is a kind of reverse mentality of designing and method, therefore; Than need try to gather the method that obtains sectional dimension through manual work in the past; Efficient and precision have obtained improving greatly, and than the reverse engineer method that proposes before, this method more is applicable to J/I _x＜1.69 conditions.

Embodiment

To the method for the invention, calculate checking.

Provide three groups of aircraft low speed flutter girder model band auricle rectangular beam cross sections, P1～P3 cross section is respectively embodiment 1～embodiment 3.Table 1 has provided the geometrical property predetermined value of three embodiment, i.e. desired value, and desired value J/I _x＜1.69.For P1, make t=2.0mm, for P2 and P3, make t=1.0mm, carry out the sectional dimension design.Table 1 has also provided the geometrical property of using the design section that the inventive method obtains, the i.e. error of design load, and design load.Table 2 has provided the size design value of three embodiment.

The design load of the cross section geometric characteristic of table 1 is the sectional dimension corresponding according to table 2, is calculated by FEMAP v9.31.The desired value of comparing, the error of design section characteristic value all is not more than 2%, says from engineering viewpoint, and this is a kind of high-precision result of calculation.

Table 1 cross section geometric characteristic, unit: mm ⁴

	I x	I y	J
				The P1 desired value	227635.2	213104.0	18696.0
The P1 design load	227761.0	213117.0	18535.4
				The P1 error amount	0.06%	0.01%	-0.86%
The P2 desired value	3528.3	52734.5	5835.9
				The P2 design load	3531.3	52745.6	5892.3
The P2 error amount	0.09%	0.02%	0.97%
				The P3 desired value	2276.35	2131.04	236.96
The P3 design load	2282.3	2132.4	232.7
				The P3 error amount	0.26%	0.06%	-1.82%

Table 2 cross section geometry design load, unit: mm.

	t	2a	2b	2l
					P1	2.00	9.67	65.62	107.72
P2	1.00	14.08	14.43	84.12
					P3	1.00	3.30	20.24	29.19

Claims (1)

1. an aircraft low speed flutter girder model rectangular beam sectional dimension is confirmed method, and aircraft low speed flutter girder model rectangular beam cross section is the rectangular beam of band auricle, guarantee band auricle rectangular beam have predetermined value vertically to moment of inertia I _x, side direction moment of inertia I _yWith polar moment of inertia J and auricle thickness be under the situation of t, and satisfy J/I _x＜1.69, confirm to it is characterized in that width 2a, height 2b and the cross-sectional width 2l of its rectangle, confirm that the step of band auricle rectangular beam sectional dimension is following:

1.1, calculate not with the auricle rectangular beam have predetermined value vertically to moment of inertia I _xSquare-section half width a during with polar moment of inertia J _rWith cross section half height b _r:

1.1.1, set the initial value α of iteration variable α ₀=0.93 ~ 0.99:

1.1.2, according to computes intermediate variable β and iteration variable α ₁:

$\left\{\begin{array}{c}24{\left(\frac{2}{\mathrm{\&pi;}}\right)}^5{\mathrm{\&alpha;}}_0{\mathrm{\&beta;}}^3-4{\mathrm{\&beta;}}^2+\frac{J}{I_x}=0\\ {\mathrm{\&alpha;}}_1=\tanh \frac{\mathrm{\&pi;}}{2\mathrm{\&beta;}}+\frac{1}{243}\tanh \frac{3\mathrm{\&pi;}}{2\mathrm{\&beta;}}\end{array}\right....\left[1\right]$

Attention: when finding the solution β, relate to finding the solution of simple cubic equation, the flat-sawn method is adopted in suggestion, and β ∈ (0,1);

1.1.3, calculate iterative value α ₁With initial value α ₀Scale error e ₁:

$e_1=\frac{{\mathrm{\&alpha;}}_1-{\mathrm{\&alpha;}}_0}{{\mathrm{\&alpha;}}_0}...\left[2\right]$

If | e ₁|＜0.000001, square-section half width a then _rWith cross section half height b _rFor:

$\left\{\begin{array}{c}{a}_r=\sqrt[4]{\frac{{3I}_x{\mathrm{\&beta;}}^3}{4}}\\ b_r=\sqrt[4]{\frac{3I_x}{4\mathrm{\&beta;}}}\end{array}\right....\left[3\right]$

Step 1.1 finishes; Otherwise, carry out step 1.1.4;

1.1.4, make α ₀=α ₁, the method for repeating step 1.1.2～step 1.1.3, through iterative computation, up to | e ₁|＜0.000001, and obtain square-section half width a at this moment _rWith cross section half height b _r, step 1.1 finishes;

1.2, predetermined polar moment of inertia J is adjusted: go out the adjusted value J of polar moment of inertia J according to computes ₁,

Note answering guaranteed conditions: t＜a _r;

1.3, calculate half width a and half height b: change the J in the formula [1] into J ₁, calculate half width a and half height b according to the described method of step 1.1 then;

1.4, calculate band auricle rectangular beam cross section half-breadth l:

1.4.1, according to computes intermediate variable δ:

$\mathrm{\&delta;}=\frac{{3I}_y-{4a}^{3}b}{2t}...\left[5\right]$

1.4.2, calculate band auricle rectangular beam cross section half-breadth l:

$l=\sqrt[3]{\mathrm{\&delta;}+a^3}...\left[6\right]$

So far, obtain half width a, half height b and cross section half-breadth l, and then obtain width 2a, height 2b and the cross-sectional width 2l of corresponding rectangular beam with the auricle rectangular beam.

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