CN101877038B - Method for acquiring cross-shaped structural section rigidity data of flutter model beam of aircraft - Google Patents

Abstract

The invention relates to a method for acquiring cross-shaped structural section rigidity data of an airplane flutter model bridge, belonging to the field of structural mechanics. The method comprises the following steps of: transforming the acquiring process of the cross-shaped structural section rigidity data into the solving process of cross-shaped structural membrane volume data by utilizing a membrane analogy method in elasticity mechanics; and then transforming the membrane volume data into the rigidity data which corresponds to a solved structure by utilizing basic assumptions and boundary value conditions corresponding to the structure in the elasticity mechanics. The invention can acquire the cross-shaped structural section rigidity data with higher accuracy by utilizing the solution of cross-shaped structural membrane volume, and provides reliable theory analysis means for the analysis and the application of the cross-shaped structure and an effective way for the accurate simulation of the rigidity of an airplane.

Description

Obtain the method for the cross-shaped structural section rigidity data of airplane flutter Model Beam

Technical field

The invention belongs to the structural mechanics field, relate to a kind of method of obtaining the cross-shaped structural section rigidity data of airplane flutter Model Beam.

Background technology

All the time; The design of the roof beam structure of flutter model all is confined to the square-section or with the square-section of auricle; Even if with the beam of band auricle, its torsional rigidity of section Data Acquisition also can only be considered the torsional rigidity data of its main rectangle, is difficult to obtain the torsional rigidity that auricle partly provides; So that our flutter model is difficult to the true stiffness of simulated aircraft, thus had a strong impact on flutter model can be with reference to property.

Summary of the invention

The objective of the invention is to provide a kind of method that can obtain " ten " font structural section data of airplane flutter Model Beam comparatively exactly.Technical solution of the present invention is: whether the range of application of judging this airplane flutter Model Beam structure is in elastic range; If satisfy the elastic condition requirement, carry out following step,

(1) utilizes " membrane analogy " method in the Elasticity; The acquisition process of the section rigidity data of " ten " font structure is converted into the solution procedure of the film volume data of " ten " font structure; Wherein, The horizontal outer boundary span of the film volume of corresponding " ten " font structure of main rectangle lateral length b; The vertical height H of main rectangle is corresponding to vertical outer boundary length of the film volume of " ten " font structure, and auricle length t1 is corresponding to the lower boundary length at the auricle position in the film volume of " ten " font structure, and the vertical height t 2 of auricle is corresponding to the longitudinal boundary at the film volume middle ear sheet position of " ten " font structure;

(2) utilize the boundary value condition of this structure, the volume integral method in the utilization mathematics is tried to achieve

The film volume of " ten " font structure;

(3) introduce basic assumption in the Elasticity; The film volume data that will be somebody's turn to do " ten " font structure is converted into the section rigidity data of " ten " font structure; Obtain the lateral cross section rigidity data I1 of " ten " font structure; The longitudinal cross-section rigidity data I2 of " ten " font structure and " ten " font structure reverse section rigidity data J

$I_1=\frac{(b-t_1)H^3+t_1(H+{2t}_2)}{12}---\left(1\right)$

$I_2=\frac{{\mathrm{bH}}^3+{2t}_2{t_1}^3}{12}---\left(2\right)$

$J=\frac{(b-t_1)H^3}{3}-\frac{H^4}{{\mathrm{\π}}^5}\underset{m\mathrm{1,3,5}\·\·\·}{\overset{\∞}{\mathrm{\Σ}}}\frac{\mathrm{th}\left(\frac{\mathrm{m\πb}}{2H}\right)-\mathrm{th}\left(\frac{\mathrm{m\π}{t}_1}{2H}\right)}{m^5}$

$+\frac{t_1(H+{2t}_2)}{3}-\frac{{(H+{2t}_2)}^4}{{\mathrm{\π}}^5}\underset{m=\mathrm{1,3,5}\·\·\·}{\overset{\∞}{\mathrm{\Σ}}}\frac{\mathrm{th}\left(\frac{\mathrm{m\π}{t}_1}{2(H+2t_2)}\right)}{m^5}---\left(3\right)$

The compare rigidity data of " ten " font structure of advantage that the present invention has and beneficial effect, the film volume of utilization of the present invention " ten " font structure makes that the solution procedure of rigidity data is visual in image, and is easier to realize.Through this technology, we can obtain the section rigidity data of " ten " font structure with higher accuracy.The appearance of this method; Reliable theoretical analysis means are provided for calculating, analysis and the practical applications of " ten " font structure; And " ten " font structure is easier to realize the simulation to three principal direction rigidity of aircraft, and this provides reliable theoretical foundation for the accurate emulation to aircraft rigidity.

Description of drawings

Fig. 1 is the characteristic cross-section synoptic diagram of the present invention " ten " font structure.

Embodiment

(1) because the differential equation that the elastic torsion problem is write out with stress function; In full accord in form with the deflection equation of the film that receives the surface pressing effect; Therefore; When finding the solution torsion problem, can compare " membrane analogy " method in the Elasticity that Here it is with the amount of deflection problem of the film of separating tensioning.Utilize this method; Can the acquisition process of the section rigidity data of " ten " font structure be converted into the solution procedure of the film volume data of " ten " font structure; Wherein, The horizontal outer boundary span of the film volume of corresponding " ten " font structure of the lateral length b of main rectangle; Vertical height H of main rectangle is corresponding to vertical outer boundary length of the film volume of " ten " font structure, and auricle length t1 is corresponding to the lower boundary length at the auricle position in the film volume of " ten " font structure, and the vertical height t 2 of auricle is corresponding to the longitudinal boundary at the film volume middle ear sheet position of " ten " font structure;

(2) utilize the boundary value condition of this structure, the method for finding the solution the differential equation in the utilization mathematics is tried to achieve the film volume function of " ten " font structure, again through the volume integral method, tries to achieve the film volume of " ten " font structure;

(3) basic assumption in the introducing Elasticity; The film volume data that will be somebody's turn to do " ten " font structure is converted into the section rigidity data of " ten " font structure; Obtain the lateral cross section rigidity data I1 of " ten " font structure, the longitudinal cross-section rigidity data I2 of " ten " font structure and " ten " font structure reverse section rigidity data J.

$I_1=\frac{(b-t_1)H^3+t_1(H+{2t}_2)}{12}---\left(1\right)$

$I_2=\frac{{\mathrm{bH}}^3+{2t}_2{t_1}^3}{12}---\left(2\right)$

$J=\frac{(b-t_1)H^3}{3}-\frac{H^4}{{\mathrm{\π}}^5}\underset{m\mathrm{1,3,5}\·\·\·}{\overset{\∞}{\mathrm{\Σ}}}\frac{\mathrm{th}\left(\frac{\mathrm{m\πb}}{2H}\right)-\mathrm{th}\left(\frac{\mathrm{m\π}{t}_1}{2H}\right)}{m^5}$

$+\frac{t_1(H+{2t}_2)}{3}-\frac{{(H+{2t}_2)}^4}{{\mathrm{\π}}^5}\underset{m=\mathrm{1,3,5}\·\·\·}{\overset{\∞}{\mathrm{\Σ}}}\frac{\mathrm{th}\left(\frac{\mathrm{m\π}{t}_1}{2(H+2t_2)}\right)}{m^5}---\left(3\right)$

Embodiment:

" ten " word structure with certain airplane flutter Model Beam is an example,

Whether the range of application of (1) judging this structure is in elastic range; If satisfy the elastic condition requirement, can carry out next step;

(2) measure the characteristic cross-section data of this structure; That is: main rectangle lateral length b, the vertical height H of main rectangle, auricle length t1, the vertical height t 2 of auricle;

(3) with these characteristic cross-section data; Bringing the method for obtaining " ten " font shaped structural section rigidity data by pin-point accuracy into derives and to obtain; Computing formula 1～3 is tried to achieve the lateral cross section rigidity data I1 of " ten " font structure, longitudinal cross-section rigidity data I2 with reverse section rigidity data J.

$I_1=\frac{(b-t_1)H^3+t_1(H+{2t}_2)}{12}---\left(1\right)$

$I_2=\frac{{\mathrm{bH}}^3+{2t}_2{t_1}^3}{12}---\left(2\right)$

$J=\frac{(b-t_1)H^3}{3}-\frac{H^4}{{\mathrm{\π}}^5}\underset{m\mathrm{1,3,5}\·\·\·}{\overset{\∞}{\mathrm{\Σ}}}\frac{\mathrm{th}\left(\frac{\mathrm{m\πb}}{2H}\right)-\mathrm{th}\left(\frac{\mathrm{m\π}{t}_1}{2H}\right)}{m^5}$

$+\frac{t_1(H+{2t}_2)}{3}-\frac{{(H+{2t}_2)}^4}{{\mathrm{\π}}^5}\underset{m=\mathrm{1,3,5}\·\·\·}{\overset{\∞}{\mathrm{\Σ}}}\frac{\mathrm{th}\left(\frac{\mathrm{m\π}{t}_1}{2(H+2t_2)}\right)}{m^5}---\left(3\right)$

The section feature dimensional data that measures this structure is: b=12.0mm, and H=10.0mm, t1=3.0mm, t2=2.0mm brings these data into formula 3, can obtain the torsional rigidity of section data of this structure: J=2052.316mm3.

Verification experimental verification: the testpieces material is 7075T6, and its E value is 72 * 10 ⁵N/mm ², the G value is: 27 * 10 ⁵N/mm ², axial length is 200mm, sectional dimension: b=12.0mm, H=10.0mm, t1=3.0mm, t2=2.0mm, test findings: moment M=9.67 * 10 ⁷Nmm, torsional angle θ=0.01745 radian by J=M/ (G θ), obtains this testpieces and gets torsional rigidity data J=2052.42mm ³This value is very approaching with the Theoretical Calculation result, and relative mistake is merely 0.01%, and the section rigidity data that this method of utilization is obtained is described, accuracy is very high.

Claims (1)

1. method of obtaining the cross-shaped structural section rigidity data of airplane flutter Model Beam is characterized in that: whether the range of application of judging this airplane flutter Model Beam structure is in elastic range; If satisfy the elastic condition requirement, carry out following step,

(1) utilizes " membrane analogy " method in the Elasticity; The acquisition process of the section rigidity data of " ten " font structure is converted into the solution procedure of the film volume data of " ten " font structure; Wherein, The horizontal outer boundary span of the film volume of corresponding " ten " font structure of main rectangle lateral length b; The vertical height H of main rectangle is corresponding to vertical outer boundary length of the film volume of " ten " font structure, and auricle length t1 is corresponding to the lower boundary length at the auricle position in the film volume of " ten " font structure, and the vertical height t 2 of auricle is corresponding to the longitudinal boundary at the film volume middle ear sheet position of " ten " font structure;

(2) utilize the boundary value condition of this structure, the volume integral method in the utilization mathematics is tried to achieve the film volume of " ten " font structure;

(3) introduce basic assumption in the Elasticity; The film volume data that will be somebody's turn to do " ten " font structure is converted into the section rigidity data of " ten " font structure; Obtain the lateral cross section rigidity data I1 of " ten " font structure; The longitudinal cross-section rigidity data I2 of " ten " font structure and " ten " font structure reverse section rigidity data J

$I_1=\frac{(b-t_1)H^3+t_1(H+{2t}_2)}{12}---\left(1\right)$

$I_2=\frac{{\mathrm{bH}}^3+{2t}_2{t_1}^3}{12}---\left(2\right)$

$J=\frac{(b-t_1)H^3}{3}-\frac{H^4}{{\mathrm{\π}}^5}\underset{m\mathrm{1,3,5}\·\·\·}{\overset{\∞}{\mathrm{\Σ}}}\frac{\mathrm{th}\left(\frac{\mathrm{m\πb}}{2H}\right)-\mathrm{th}\left(\frac{\mathrm{m\π}{t}_1}{2H}\right)}{m^5}$

$+\frac{t_1(H+{2t}_2)}{3}-\frac{{(H+{2t}_2)}^4}{{\mathrm{\π}}^5}\underset{m=\mathrm{1,3,5}\·\·\·}{\overset{\∞}{\mathrm{\Σ}}}\frac{\mathrm{th}\left(\frac{\mathrm{m\π}{t}_1}{2(H+2t_2)}\right)}{m^5}---\left(3\right).$

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