CN102364477A - Aircraft flutter characteristic analysis method with no additional aerodynamic damping - Google Patents

Abstract

The invention provides an aircraft flutter characteristic analysis method with no additional aerodynamic damping, which comprises: building an aircraft aeroelastic model at first, calculating the sub-critical damping and frequency in each mode at each flying speed point within the flying speed scope containing an aircraft flutter critical speed, drawing a change curve of the sub-critical damping and frequency along with the flying speed, and determining the aircraft flutter critical speed. The aircraft flutter analysis equation with no additional aerodynamic damping is introduced, and the damping iteration method is adopted for analysis of sub-critical damping characteristics according to the corresponding nonlinear characteristic value of the equation. Compared with the conventional flutter analysis method with the additional aerodynamic damping, no additional aerodynamic damping needs to be introduced, the obtained sub-critical damping characteristics of aircrafts are more accurate, the determination of the aircraft flutter characteristics can be facilitated, and a reliable basis can be provided for trial flutter flights.

Description

A kind of aircraft buffet characteristic analytical approach of not having the Additional Gas dynamic damping

Technical field

The present invention relates to aircraft fatigue resistance and stability techniques field, be specially a kind of aircraft buffet characteristic analytical approach of not having the Additional Gas dynamic damping, be used to analyze aircraft underdamping and frequency characteristic.

Background technology

In the aircraft flight process; Its airfoil structure can receive the coupling of non-permanent aerodynamic force, inertial force and elastic force; Make aircraft under certain critical flying speed, unattenuated vibration---flutter can take place in structure, causes aircaft configuration to destroy; Therefore the tragedy that leads to the fatal crass need be analyzed the aircraft buffet characteristic.

The method of analyzing the aircraft buffet characteristic at present is that the non-permanent aerodynamic force in the flutter analysis equation is separated into pneumatic stiffness term and air damping item; Find the solution eigenwert then and then obtain aircraft underdamping and frequency characteristic, confirm the flutter critical velocity by the condition that negative becomes positive number according to underdamping.Compare with realistic model; This method has been introduced an Additional Gas dynamic damping item, though this Additional Gas dynamic damping item under the flutter critical velocity, be tending towards disappearing, under undercritical conditions; Because the existence of this additive term is unfavorable for trying to achieve accurate aircraft underdamping characteristic and frequency characteristic.

In the flutter flight test process of at present the aircraft buffet characteristic being verified; From security consideration; Can not make flying speed be tending towards the flutter critical velocity; Be reference mainly, formulate plan that flutter takes a flight test and the guidance decision-making of taking a flight test in view of the above, so need Accurate Analysis aircraft underdamping characteristic and frequency characteristic with the underdamping characteristic of calculating gained.

Summary of the invention

The technical matters that solves

For Accurate Analysis aircraft underdamping characteristic and frequency characteristic, the present invention proposes a kind of aircraft buffet characteristic analytical approach of not having the Additional Gas dynamic damping.

Technical scheme

Technical scheme of the present invention is:

Said a kind of aircraft buffet characteristic analytical approach of not having the Additional Gas dynamic damping is characterized in that: may further comprise the steps:

Step 1: set up the aircraft aeroelastic model, and the generalized mass battle array M of definite aircraft aeroelastic model, broad sense damping battle array B, broad sense Stiffness Matrix K, the non-permanent aerodynamic influence matrix of coefficients Q of broad sense (ik), reference length b; The non-permanent aerodynamic influence matrix of coefficients Q of broad sense (ik) is separated into real part Q ^R(k) and imaginary part Q ^I(k);

Step 2: confirm to comprise the flying speed scope of aircraft flutter critical velocity, calculate underdamping g and frequency f each rank mode of each flying speed point in should velocity range, g=2 γ wherein, f=ω/2 π, γ are attenuation rate, ω is a circular frequency; Wherein calculate and be the underdamping g of the j rank mode of certain speed point V in should velocity range and the step of frequency f:

Step 2.1: the initial value k that selects reduced frequency k ₀=ω ₀V/b, the initial value γ of attenuation rate γ ₀=0, ω wherein ₀Be the Flight Vehicle Structure natural frequency;

Step 2.2: iterative computation reduced frequency k and attenuation rate γ: wherein by reduced frequency n step iterative value k _nWith attenuation rate n step iterative value γ _nCalculate n+1 step iterative value k _N+1And γ _N+1Process be: with k _nAnd γ _nBring the aircraft flutter analysis equation of no Additional Gas dynamic damping into

$[{\mathrm{Ms}}^2+(B-\frac{1}{2}\mathrm{\ρVb}{Q}^I\left(k\right)/k)s+K-\frac{1}{2}\mathrm{\ρ}{V}^2(Q^R\left(k\right)-\mathrm{\γ}{Q}^I\left(k\right))]\left\{q\right\}=0$

In, s is Laplce's variable in the formula, and q is a generalized coordinate, and ρ is an atmospheric density, and V is an aircraft flight speed, calculates the n+1 step iterative value of the equational j of aircraft flutter analysis rank eigenwert

By

Obtain γ _N+1And ω _N+1, again by k _N+1=ω _N+1V/b obtains k _N+1When iterative computation extremely | k _M+1-k _m|≤ε ₁And | γ _M+1-γ _m|≤ε ₂The time, iterative computation stops, and obtains the underdamping g=2 γ of corresponding flying speed V _m, frequency f=ω _m/ 2 π, wherein ε ₁≤0.001, ε ₂≤0.001;

Step 3: each flying speed point that obtains according to step 2 and the corresponding result of underdamping g and frequency f, draw underdamping g and frequency f change curve respectively with flying speed, and definite aircraft flutter critical velocity.

Beneficial effect

The present invention has introduced the aircraft flutter analysis equation of no Additional Gas dynamic damping item; And, adopt the damping alternative manner to carry out the underdamping specificity analysis to the corresponding NONLINEAR EIGENVALUE PROBLEMS of this equation, the contrast flutter analysis method that has Additional Gas dynamic damping item in the past; The present invention need not to introduce Additional Gas dynamic damping item; So the aircraft underdamping characteristic that obtains is more accurate, help to confirm the aircraft buffet characteristic that taking a flight test for flutter provides reliable foundation.

Description of drawings

Fig. 1: the wind tunnel test binary wing profile model synoptic diagram that adopts among the embodiment;

Fig. 2: the subcritical frequency characteristic comparison diagram of the model among the embodiment;

Fig. 3: the model underdamping characteristic comparison diagram among the embodiment;

Embodiment

Below in conjunction with specific embodiment the present invention is described:

Embodiment:

Object model such as Fig. 1 that present embodiment is analyzed are said, are a wind tunnel test binary wing model.

Step 1: according to the raw data of wing model, confirm the generalized mass battle array M of model, broad sense damping battle array B, broad sense Stiffness Matrix K is respectively:

$M=\left[\begin{array}{cc}3.2930& 0.0859\\ 0.0859& 0.0135\end{array}\right],$ $B=\left[\begin{array}{cc}3.2962& 0.03517\\ 0.03517& 0.03042\end{array}\right],$ $K=\left[\begin{array}{cc}2818.8& 0\\ 0& 37.3\end{array}\right]$

Atmospheric density ρ=1.225kg/m ³, reference length b=0.127m, elastic shaft are positioned on 1/4 string of a musical instrument.The non-permanent aerodynamic influence matrix of coefficients Q of broad sense (ik) adopts Theodorsen; T. the document of showing " General Theory of Aerodynamic Instability and the Mechanism of Flutter " NACA Rept.496; 1935. in method calculate, the non-permanent aerodynamic influence matrix of coefficients Q of the broad sense that calculates (ik) further is separated into real part Q ^R(k) and imaginary part Q ^I(k).

Step 2: the aircraft flutter analysis equation of confirming no Additional Gas dynamic damping.

Basic aircraft flutter analysis equation does at present

$[{\mathrm{Ms}}^2+\mathrm{Bs}+K-\frac{1}{2}\mathrm{\ρ}{V}^{2}Q\left(\mathrm{ik}\right)]\left\{q\right\}=0---\left(1\right)$

S is that Laplce's variable, q are that generalized coordinate, V are aircraft flight speed in the formula, is in the present embodiment incoming flow wind speed of wind tunnel test Q (ik) to be separated into real part Q ^R(k) and imaginary part Q ^I(k) back substitution formula (1) obtains

$[{\mathrm{Ms}}^2+\mathrm{Bs}+K-\frac{1}{2}\mathrm{\ρ}{V}^2{Q}^R\left(k\right)-\frac{1}{2}\mathrm{\ρ}{V}^{2}i{Q}^I\left(k\right)]\left\{q\right\}=0---\left(2\right)$

Directly make s=i ω=ikV/b in the method in the past, obtain i=sb/kV, the substitution formula obtains in (2)

$[{\mathrm{Ms}}^2+\mathrm{Bs}+K-\frac{1}{2}\mathrm{\ρ}{V}^2{Q}^R\left(k\right)-\frac{1}{2}\mathrm{\ρVsb}{Q}^I\left(k\right)/k]\left\{q\right\}=0---\left(3\right)$

(γ+i) ω=(γ+i) kV/b, and substitution formula (3) obtains and according to the definition of Laplace variable s=is arranged

$[{\mathrm{Ms}}^2+\mathrm{Bs}+K-\frac{1}{2}\mathrm{\ρ}{V}^{2}Q\left(k\right)-\frac{1}{2}\mathrm{\ρ}{V}^2\mathrm{\γ}{Q}^I\left(k\right)]\left\{q\right\}=0---\left(4\right)$

Formula (4) and original formula (1) contrast; In the left end item many Additional Gas dynamic damping items

this cause aircraft being lower than under the subcritical flying condition of flutter speed, the underdamping precision that calculates is affected.

In the present invention, (ω of γ+i)=(kV/b of γ+i) obtains i=sb/kV-γ, is updated to the aircraft flutter analysis equation that can obtain not having the Additional Gas dynamic damping in the formula (2) Laplce's variable to be expanded into the array configuration s=of attenuation rate and reduced frequency

$[{\mathrm{Ms}}^2+(B-\frac{1}{2}\mathrm{\ρVb}{Q}^I\left(k\right)/k)s+K-\frac{1}{2}\mathrm{\ρ}{V}^2(Q^R\left(k\right)-\mathrm{\γ}{Q}^I\left(k\right))]\left\{q\right\}=0---\left(5\right)$

Formula (5) is not introduced Additional Gas dynamic damping item, and all matrixes are real number in the formula (5), are suitable for Eigenvalue Analysis.

Step 3: after obtaining not having the aircraft flutter analysis equation of Additional Gas dynamic damping; Can confirm the buffet characteristic of aircraft through the method for Eigenvalue Analysis: at first confirm a flying speed scope that comprises aircraft flutter critical velocity roughly, calculate the underdamping g and the frequency f of each rank mode of each speed point in this velocity range then; G=2 γ wherein; F=ω/2 π, γ are attenuation rate, and ω is a circular frequency.In the present embodiment, selected velocity range is 10m/s-30m/s, gets speed point with the interval of 0.2m/s; Wing model has two degree of freedom, and corresponding two natural mode of vibration: mode of flexural vibration and torsion mode, the undamped natural frequency of a mechanical system of two mode is respectively 28.3128rad/s, 59.4775rad/s.

Underdamping g and the step of frequency f of calculating the j rank mode of certain speed point V are:

Step 3.1: the initial value k that selects reduced frequency k ₀=ω ₀V/b, the initial value γ of attenuation rate γ ₀=0, ω wherein ₀Be the Flight Vehicle Structure undamped natural frequency of a mechanical system;

Step 3.2: iterative computation reduced frequency k and attenuation rate γ: wherein by reduced frequency n step iterative value k _nWith attenuation rate n step iterative value γ _nCalculate n+1 step iterative value k _N+1And γ _N+1Process be: with k _nAnd γ _nBring in the aircraft flutter analysis equation of no Additional Gas dynamic damping, calculate the n+1 step iterative value of the equational j of aircraft flutter analysis rank eigenwert

By

Obtain γ _N+1And ω _N+1, again by k _N+1=ω _N+1V/b obtains k _N+1When iterative computation extremely | k _M+1-k _m|≤ε ₁And | γ _M+1-γ _m|≤ε ₂The time, iterative computation stops, and obtains the underdamping g=2 γ of corresponding flying speed V _m, frequency f=ω _m/ 2 π, wherein ε ₁≤0.001, ε ₂≤0.001.

In the present embodiment, get ε ₁=0.001, ε ₂=0.001, mode of flexural vibration (V-γ-ω) result of calculation is:

Torsion mode (V-γ-ω) result of calculation is:

What provide in table 1 and the table 2 is 2m/s result of calculation at interval; But the subcritical frequency that draws after speed point calculates and the damping change curve with speed is got at the interval that has provided 0.2m/s in accompanying drawing 2 and the accompanying drawing 3; The corresponding gained result of the present invention of solid line among the figure, the corresponding previous methods gained of dotted line result.It is thus clear that because the influence of Additional Gas dynamic damping item make previous methods can't obtain comparatively accurate underdamping and frequency characteristic, and the present invention can not introduce Additional Gas dynamic damping item, more meets the actual physics model, gained precision as a result is higher.

Claims (1)

1. aircraft buffet characteristic analytical approach of not having the Additional Gas dynamic damping is characterized in that: may further comprise the steps:

Step 1: set up the aircraft aeroelastic model, and the generalized mass battle array M of definite aircraft aeroelastic model, broad sense damping battle array B, broad sense Stiffness Matrix K, the non-permanent aerodynamic influence matrix of coefficients Q of broad sense (ik), reference length b; The non-permanent aerodynamic influence matrix of coefficients Q of broad sense (ik) is separated into real part Q ^R(k) and imaginary part Q ^I(k);

Step 2: confirm to comprise the flying speed scope of aircraft flutter critical velocity, calculate underdamping g and frequency f each rank mode of each flying speed point in should velocity range, g=2 γ wherein, f=ω/2 π, γ are attenuation rate, ω is a circular frequency; Wherein calculate and be the underdamping g of the j rank mode of certain speed point V in should velocity range and the step of frequency f:

Step 2.1: the initial value k that selects reduced frequency k ₀=ω ₀V/b, the initial value γ of attenuation rate γ ₀=0, ω wherein ₀Be the Flight Vehicle Structure undamped natural frequency of a mechanical system;

Step 2.2: iterative computation reduced frequency k and attenuation rate γ: wherein by reduced frequency n step iterative value k _nWith attenuation rate n step iterative value γ _nCalculate n+1 step iterative value k _N+1And γ _N+1Process be: with k _nAnd γ _nBring the aircraft flutter analysis equation of no Additional Gas dynamic damping into

$[{\mathrm{Ms}}^2+(B-\frac{1}{2}\mathrm{\ρVb}{Q}^I\left(k\right)/k)s+K-\frac{1}{2}\mathrm{\ρ}{V}^2(Q^R\left(k\right)-\mathrm{\γ}{Q}^I\left(k\right))]\left\{q\right\}=0$

In, s is Laplce's variable in the formula, and q is a generalized coordinate, and ρ is an atmospheric density, and V is an aircraft flight speed, calculates the n+1 step iterative value of the equational j of aircraft flutter analysis rank eigenwert

By

Obtain γ _N+1And ω _N+1, again by k _N+1=ω _N+1V/b obtains k _N+1When iterative computation extremely | k _M+1-k _m|≤ε ₁And | γ _M+1-γ _m|≤ε ₂The time, iterative computation stops, and obtains the underdamping g=2 γ of corresponding flying speed V _m, frequency f=ω _m/ 2 π, wherein ε ₁≤0.001, ε ₂≤0.001;

Step 3: each flying speed point that obtains according to step 2 and the corresponding result of underdamping g and frequency f, draw underdamping g and frequency f change curve respectively with flying speed, and definite aircraft flutter critical velocity.