CN105760577A - Estimation method for sound vibration fatigue life containing uncertain metal structure - Google Patents

Abstract

The invention discloses an estimation method for a sound vibration fatigue life containing an uncertain metal structure.According to the method, firstly, a finite element analytical model of a metal structure is established, the uncertain effect of material and structure characteristic parameters under finite sample conditions is considered, and a systematic transfer function is obtained based on the frequency response analytical theory; secondly, according to the characteristics of random noise loads, a mean square root response and stress power spectral density function (PSD) of displacement and stress of all key nodes is obtained through an SRSS method for typical broadband steady ergodic random noise loads; thirdly, in combination with a Dirlik model, an interval uncertain propagation second-order Taylor series expansion method and an analytical method for vibration fatigue within a frequency domain, the relation between a rain flow amplitude probability density function and the power spectral density function is set up; finally, the Miner linear accumulative damage theory is used for obtaining an interval range of the sound vibration fatigue life containing the uncertain metal structure.Dispersity of the structure and material parameters is taken into full consideration during calculation of the structural life excited by typical random noise, and therefore the obtained fatigue life is more reasonable.

Description

A kind of evaluation method shaken fatigue life containing uncertain metal structure sound

Technical field

The present invention relates to metal structure noise and vibration fatigue technical field, particularly to considering that the uncertainty lower structure of effect is for the dynamic response of random noise load and acoustic fatigue life estimation method.Efficiently predict suitable in the acoustic fatigue life-span of various structure types under typical complex acoustic loads, offer help for Engineering Anti acoustic fatigue structural design.

Background technology

The effect essence of structure is a kind of spatial distribution by acoustic loads, has the dynamic random pressure loading of certain frequency distribution character.When sound pressure level magnitude is more than 140dB, it can structurally produce certain distributed stress response, and when the dynamic characteristic of the structure particularly acted on when the frequency distribution characteristic of noise and it is mutually coupled, structure will produce significant stress response.Acoustic fatigue belongs to high all low stress problems, under the long duration of action of this dynamic stress, the stress of structure is concentrated and rejected region will form fatigue crack, is taken in crack nucleation namely create the sound that namely Fatigue Crack Formation Life to study after expanding to the stage that can examine length and shake fatigue life in engineering.

Aircraft process under arms is in the complicated noise that electromotor jet, aerodynamic force and wall coupling, body self structure operational vibration etc. produce.Along with the improvement of the raising of vehicle flight speeds, the increase of power set thrust and war fighting requirement performance, the various noise values that aircraft produces in running constantly increase.Practice have shown that, whether in use all can usually there is various types of acoustic fatigue breakoff phenomenon in military aircraft or civil aircraft.Wherein great majority show themselves in that various aerofoil eyelid covering and fuselage side skin crackle, rib and fuselage ring frame crackle, air intake duct inside panel crackle, the tail various destructions under sedimentation exhalation.There is a lot of limitation in traditional acoustic fatigue life estimate, such as: only considered low order frequency when considering dynamic stress effect, what have only considered first natural frequency, and the effect that the load that frequency distribution width energy is high is caused has certain error；In Preliminary design, designer need to know the whether identical of material used by object and structural shape and existing curve, identical, the acoustic fatigue test curve of specific structural shape and material can be quoted after obtaining root-mean-square value stress to obtain the life-span, but differ, need to re-start design of Structural Parameters, coming equivalent conversion and result experiential modification according to existing curve, this measure workload is big and precision is low；The root-mean-square value life curve of ad hoc structure and material inherently lacks very much, and current existing quantity is few, it is necessary to obtain substantial amounts of test data support.

It addition, the initial imperfection that causes of manufacturing processing technic and material anisotropism and damage are inevitable, and in following long service process in inside configuration development, spread, propagate, drastically influence the mechanical behavior of structure and use safety.Set up uncertain characterization technique based on non-probability theory framework, uncertain metal structure sound estimation of fatigue life technology of shaking has significant realistic meaning.

Summary of the invention

The technical problem to be solved in the present invention is: overcome the deficiencies in the prior art, it is provided that a kind of for the evaluation method shaken fatigue life containing uncertain metal structure sound.The present invention takes into full account ubiquitous uncertain factor in Practical Project problem, characterizes Uncertainty with non-probability interval method, introduces indeterminacy section communication theory, and obtained design result more conforms to truth, and engineering adaptability is higher.

The technical solution used in the present invention is: a kind of evaluation method shaken fatigue life containing uncertain metal structure sound, it is achieved step is as follows:

The first step: according to flight mission profile time data and state acoustic load Measurement bandwidth sound pressure level, adoptsIt is converted into the frequency spectrum load of random noise, wherein L=L_b-10lg (Δ f), P₀=2 × 10^-5Pa is reference sound pressure, L_bFor bandwidth sound pressure level, Δ f is bandwidth, and G (f) is the noise power spectral density value after converting；

Second step: introduce interval vector x ∈ x^IThe uncertain parameter of the structure under the reasonable quantitative lean information of=[E, a, b], few data qualification, wherein E is metal material elastic modelling quantity, and a and b represents the geometric parameter of structure different parts respectively.Then the uncertainty containing structural parameters can be expressed as: $\stackrel{\‾}{x}=\[\stackrel{\‾}{E},\stackrel{\‾}{a},\stackrel{\‾}{b}\]=\[E^c+E^r,a^c+a^r,b^c+b^r\],$ Represent the value upper bound of parameter,x=[E,a,b]=[E^c-E^r,a^c-a^r,b^c-b^r],xRepresenting the value lower bound of parameter, wherein subscript c represents central value, and subscript r represents radius；

3rd step: set up the geometric model of interested structure, analyzes the type of attachment of component, and classifying rationally grid applies boundary condition and forms finite element analysis model.Loading unit uniform surface pressure loading in finite element analysis software, wherein the frequency range of load is identical with the frequency range of the acoustic loads of first step gained, extracts the Stress Transfer function of each node of structure after model carries out frequency response analysis；

4th step: application quadratic sum evolution (SRSS) method, MSC.Patran random vibration module reads the ssystem transfer function that the 4th step obtains, and the pectrum noise load applying first step gained obtains stress power spectrum density (PSD) curve of node, wherein random vibration analysis output file also includes the zero crossing number in the positive slope direction of the power spectral density of frequency response, auto-correlation function, time per unit and the RMS value of stress response；

5th step: the typical feature of random noise is pressure time course amplitude is change at random, the form that namely irregular non-decay can not be expressed with analytical function, the excursion width of this kind of noise frequency, its spectrum is until significantly high frequency is all continuous print.Dirlik model in conjunction with exemplary wideband stochastic process analyzes method with interval propagation, with stress PSD curve obtained in the previous step for input, apply the Taylor series expansion method in non-probability interval procedural theory and obtain stress rain stream amplitude probability density function (PDF) excursion of each key event after uncertain Variable Transmission；

6th step: for continuous distribution stress state, by time T inherent strain scope (S_i,S_i+ΔS_i) in stress-number of cycles be expressed as n_i=vTp (S_i)ΔS_i.The stress-number of cycles in the v representation unit time in formula, is determined by peak dot number E [P] per second, i.e. v=E [P], p (S_i) represent that stress level level is S_iTime amplitude probability density functional value, Δ S_iFor minimal stress level excursion；

7th step: selecting the S-N curve of corresponding metal material in MSC.Fatigue, its expression formula is N (S_i)=K/S^m, apply Miner linear progressive damage theory D=∑ D_i=∑ n_i/N_i, fatigue life time obtaining component generation fatigue rupture as overall impairment degree D=1 is:

$T=\frac{K}{E\[P\]\∫S^{m}P\left(S\right)dS}$

Wherein, K and m is material constant, and N is metal material cycle-index, and D is injury tolerance.The final time lifetime cloud charts calculated when obtaining component generation fatigue rupture.Propagate analysis theories according to non-probability interval and obtain the life time scale of component.

Further, in described second step, bounded-but-unknown uncertainty parameter vector x can be expressed as:

$\begin{array}{c}x=\[\underset{\‾}{x},\stackrel{\‾}{x}\]=\[x^c-x^r,x^c+x^r\]\\ =x^c+x^r\[-1,1\]\\ =x^c+x^r\×e\end{array}$

Wherein, x^c=(E^c,a^c,b^c), x^r=(E^r,a^r,b^r), e ∈ Ξ³, Ξ³Being defined as the 3 dimensional vector set that all elements is included in [-1,1], symbol "×" is defined as two each corresponding elements of vector, and product is still 3 dimensional vectors.

Further, in described 5th step, the Dirlik model of application is applicable to the simulation of exemplary wideband stochastic process, and its result accuracy of stochastic process for arrowband or with spike (i.e. pulse amplitude) characteristic is for reference.

Further, in described 5th step, non-probability interval is propagated analysis method and is used second order Taylor series expansion method, and the bound in its response interval is represented by:

$\underset{\‾}{{\mathrm{\Ψ}}_i}={\mathrm{\Ψ}}_i\left(x_c\right)-\underset{j=1}{\overset{m}{\Σ}}\left|\frac{\∂{\mathrm{\Ψ}}_i\left(x_c\right)}{\∂x_j}\right|{\mathrm{\Δx}}_j-\frac{1}{2}{\left(\underset{i=1}{\overset{m}{\Σ}}\underset{j=1}{\overset{m}{\Σ}}\right|\frac{\∂{\mathrm{\Ψ}}_i\left(x_c\right)}{\∂x_j}\left|{\mathrm{\Δx}}_i{\mathrm{\Δx}}_j\right)}^2$

$\stackrel{\‾}{{\mathrm{\Ψ}}_i}={\mathrm{\Ψ}}_i\left(x_c\right)+\underset{j=1}{\overset{m}{\Σ}}\left|\frac{\∂{\mathrm{\Ψ}}_i\left(x_c\right)}{\∂x_j}\right|{\mathrm{\Δb}}_j+\frac{1}{2}{\left(\underset{i=1}{\overset{m}{\Σ}}\underset{j=1}{\overset{m}{\Σ}}\right|\frac{\∂{\mathrm{\Ψ}}_i\left(x_c\right)}{\∂x_j}\left|{\mathrm{\Δx}}_i{\mathrm{\Δx}}_j\right)}^2$

Wherein,WithΨ _i Represent that i Uncertainty takes bound respectivelyWithx _iThe bound of response results, Ψ_i(x_c) represent that uncertain variables takes intermediate value x_cTime the interested amount response value of structure,Represent Ψ_i(x_c) first derivative expansion value at i-th uncertain parameter midpoint,Represent the second order expension at uncertain variables interval midpoint place, Δ x_iWith Δ x_jRepresent the interval radius of i-th and jth uncertain variables respectively.

Present invention advantage compared with prior art is in that: the invention provides the new approaches of acoustic fatigue life estimate, makes up and the perfect limitation of traditional theory.The method of tradition estimation acoustic fatigue can only for specific version, and the method can calculate arbitrary structures form；Traditional method needs a root-mean-square value stress-life, and the method has only to classic fatigue life curve.When considering material and structure disperses, the method requires no knowledge about the form of probability of uncertain parameter, have only to know that the boundary up and down of metal material and geometrical parameters just can solve the acoustic fatigue life-span interval range containing uncertain metal material arbitrary structures form easily, in Practical convenient reliably.

Accompanying drawing explanation

Fig. 1 the present invention is directed to the evaluation method flow chart shaken fatigue life containing uncertain metal structure sound；

Fig. 2 is the schematic flow sheet of the finite element analysis software that the present invention uses；

Fig. 3 the present invention is directed to aircraft cavity structure to carry out the FEM (finite element) model after simplifying and apply boundary condition；

Fig. 4 is the power spectral density function schematic diagram that the present invention calculates the key event obtaining model；

Fig. 5 the present invention is directed to the S-N curve that 7075-HV-T6 metal material is quoted；

Fig. 6 is that the calculated metal material sound of the present invention shakes FATIGUE LIFE DISTRIBUTION cloud atlas；

Fig. 7 is the node minimum life interval range that the structure containing uncertain parameter is obtained by the present invention.

Detailed description of the invention

The present invention is further illustrated below in conjunction with accompanying drawing and specific embodiment.

As it is shown in figure 1, the present invention proposes a kind of evaluation method shaken fatigue life containing uncertain metal structure sound, comprise the following steps:

(1) according to the regulation in general norm, acoustic fatigue problem is only considered when airplane structural parts bear the 130dB sound pressure level exceeding people's otalgia territory.According to flight mission profile time data and state acoustic load Measurement bandwidth sound pressure level (octave bandwidth or third-octave bandwidth etc.), adoptIt is converted into the frequency spectrum load of random noise, wherein L=L_b-10lg (Δ f), P₀=2 × 10^-5Pa is reference sound pressure, L_bFor bandwidth sound pressure level, Δ f is bandwidth, and G (f) is the noise power spectral density value after converting.

Table 1 is the International standardization octave frequency meter that the present invention is cited, illustrates the frequency meter of International Organization for Standardization's suggestion.The noise bandwidth of any mid frequency can be tabled look-up and be drawn, the bandwidth sound pressure level according to actual measurement, according to the power spectral density of above-mentioned conversion formula then its correspondence.Such as the sound field of 100Hz mid frequency, its bandwidth is 22.9Hz, if actual measurement bandwidth sound pressure level be 127dB, then sound field change after power spectral density be 87.544Pa²/Hz.If the measured value time-domain signal of noise field, it is changed into spectrum signal by welfare leaf transformation and is analyzed again.

Table 1

Lower frequency limit	Mid frequency	Upper limiting frequency	Lower frequency limit	Mid frequency	Upper limiting frequency
						22.4	25	28.2	707.9	800	891.3
28.2	31.5	35.5	891.3	1000	1122
						35.5	40	44.7	1122	1250	1413
44.7	50	56.2	1413	1600	1778
						56.2	63	70.8	1778	2000	2239
70.8	80	89.1	2239	2500	2818
						89.1	100	112.2	2818	3150	3548
112.2	125	141.3	3548	4000	4467
						141.3	160	177.8	4467	5000	5623
177.8	200	223.9	5623	6300	7079
						223.9	250	281.8	7079	8000	8913
281.8	315	354.8	8913	10000	11220
						354.8	400	446.7	11220	12500	14125
446.7	500	562.3	14125	16000	17783
						562.3	630	707.9	17783	20000	22387

(2) interval vector x ∈ x is introduced^IThe uncertain parameter of the structure under the reasonable quantitative lean information of=[E, a, b], few data qualification, wherein E is metal material elastic modelling quantity, and a and b represents the geometric parameter of structure different parts respectively.Then the uncertainty containing structural parameters can be expressed as: $\stackrel{\‾}{x}=\[\stackrel{\‾}{E},\stackrel{\‾}{a},\stackrel{\‾}{b}\]=\[E^c+E^r,a^c+a^r,b^c+b^r\],$ Represent the value upper bound of parameter,x=[E,a,b]=[E^c-E^r,a^c-a^r,b^c-b^r],xRepresenting the value lower bound of parameter, wherein subscript c represents central value, and subscript r represents radius；Bounded-but-unknown uncertainty parameter vector x can be expressed as:

$\begin{array}{c}x=\[\underset{\‾}{x},\stackrel{\‾}{x}\]=\[x^c-x^r,x^c+x^r\]\\ =x^c+x^r\[-1,1\]\\ =x^c+x^r\×e\end{array}$

Wherein, x^c=(E^c,a^c,b^c), x^r=(E^r,a^r,b^r), e ∈ Ξ³, Ξ³Being defined as the 3 dimensional vector set that all elements is included in [-1,1], symbol "×" is defined as two each corresponding elements of vector, and product is still 3 dimensional vectors.

(3) finite element analysis model is formed, MSC.Patran loads unit uniform surface pressure loading, wherein the frequency range of load is identical with the frequency range of the acoustic loads of first step gained, the frequency response function of each node of structure is extracted, herein referred to as Stress Transfer function after model is carried out frequency response analysis.

(4) application quadratic sum evolution (SRSS) method, random vibration module reads the ssystem transfer function that the 4th step obtains, and the pectrum noise load applying first step gained obtains stress power spectrum density (PSD) curve of node, wherein random vibration analysis output file also includes the zero crossing number in the positive slope direction of the auto-correlation function of frequency response, time per unit and the RMS value of stress response.The following is the theoretical procedure calculating stress response mean-square value and power spectral density.

Multiple degrees of freedom problem by single-point-excitation is had:

$M\stackrel{\·\·}{a}\left(t\right)+C\stackrel{\·}{a}\left(t\right)+Ka\left(t\right)=qg\left(t\right)$

Wherein M, C and K distinguish mass matrix damping matrix and stiffness matrix, the dynamic respond function that a (t) is system of representative system, and g (t) represents zero-mean stationary random process noise excitation, and its auto-correlation function is R_ggT (), power spectral density function are S_ggF (), q is load amplitude coefficient vector.Assuming that damping matrix is proportional damping, the available formation addition method obtains system response and is:

$a\left(t\right)=\underset{j=1}{\overset{n}{\Σ}}{\mathrm{\γ}}_j{\mathrm{\φ}}_j{\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}{h}_j\left(\mathrm{\τ}\right)g(t-\mathrm{\τ})d\mathrm{\τ}$

WhereinCoefficient is participated in for formation,For the jth rank formation of system, τ is tiny time interval, h_j(τ) it is the system transter obtained in the 3rd step.

Definition according to auto-correlation function has the autocorrelation matrix of system response function to be:

$\begin{array}{c}{R}_{aa}\left(\mathrm{\τ}\right)=E\[a\left(t\right)a^T(t+\mathrm{\τ})\]\\ ={\Σ}_{-\mathrm{\∞}}^{+\mathrm{\∞}}{\Σ}_{-\mathrm{\∞}}^{+\mathrm{\∞}}{\mathrm{\γ}}_j{\mathrm{\γ}}_k{\mathrm{\φ}}_j{\mathrm{\φ}}_k^T{\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}{\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}{h}_j\left({\mathrm{\τ}}_1\right)h_k\left({\mathrm{\τ}}_2\right)R_{gg}(\mathrm{\τ}+{\mathrm{\τ}}_1-{\mathrm{\τ}}_2){\mathrm{d\τ}}_1{\mathrm{\τ}}_2\end{array}$

R in formula_aa(τ) and R_gg(τ) representing the auto-correlation function of response and excitation respectively, E represents stochastic variable is taken average.Above formula shows that the autocorrelation matrix of response can be expressed as the double integral of the autocorrelation matrix of excitation.The autopower spectral density matrix constituting Fourier transform pairs with it is solved by Wiener relational expression:

$S_{aa}\left(f\right)={\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}{R}_{aa}\left(\mathrm{\τ}\right)\exp (-i2\mathrm{\π}f\mathrm{\τ})$

Exp (-i2 π f τ) in this formula is rewritten into exp (-i2 π f τ₁)·exp(-i2πfτ₂)·exp(-i2πf(τ+τ₁-τ₂)), then this triple integral can be rewritten into the company of following three integration types and takes advantage of:

$H_j^{*}\left(f\right)={\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}{h}_j\left({\mathrm{\τ}}_1\right)\exp \left(i2{\mathrm{\πf\τ}}_1\right){\mathrm{d\τ}}_1$

$S_{gg}\left(f\right)={\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}{R}_{gg}(\mathrm{\τ}+{\mathrm{\τ}}_1-{\mathrm{\τ}}_2)\exp \left(i2\mathrm{\π}f\right(\mathrm{\τ}+{\mathrm{\τ}}_1-{\mathrm{\τ}}_2\left)\right)d(\mathrm{\τ}+{\mathrm{\τ}}_1-{\mathrm{\τ}}_2)$

$H_k\left(f\right)={\∫}_{-\mathrm{\∞}}^{+\mathrm{\∞}}{h}_k\left({\mathrm{\τ}}_2\right)\exp \left(i2{\mathrm{\πf\τ}}_2\right){\mathrm{d\τ}}_2$

The conclusion of Fourier transform pairs is respectively constituted here with impulse response function and frequency response function, auto-correlation function and auto-power spectrum function.Then the autopower spectral density matrix that can meet with a response is:

$s_{aa}\left(f\right)=\underset{j=1}{\overset{n}{\Σ}}\underset{k=1}{\overset{n}{\Σ}}{\mathrm{\γ}}_j{\mathrm{\γ}}_k{\mathrm{\φ}}_j{\mathrm{\φ}}_k^T{H}_j^{*}\left(f\right)H_k\left(f\right)S_{gg}\left(f\right)$

Responding for the many-degrees of freedom system under general excitation, autopower spectral density matrix can by the autopower spectral density matrix S of load_qqF () and transfer function matrix H (f) are obtained by following formula:

S_aa(f)=H^*(f)S_qq(f)H^T(f)

Wherein, H^*F () takes the function that negative value obtains, H for frequency response function medium frequency^TF transposed matrix that () is frequency response function.Stress power spectral density function (PSD) curve of system can be obtained in sum after according to said method obtaining the displacement of system, stress response.

(5) method is analyzed in conjunction with the Dirlik model of exemplary wideband stochastic process with interval propagation, with stress PSD curve obtained in the previous step for input, apply the vertex scheme in non-probability interval procedural theory and obtain stress rain stream amplitude probability density function (PDF) excursion of each key event after uncertain Variable Transmission.Dirlik model representation is as follows:

$p\left(S\right)=\frac{\frac{D_1}{Q}\·e^{\frac{-Z}{Q}}+\frac{D_2}{R^2}\·e^{\frac{-Z^2}{2R^2}}+D_{3}Z\·e^{\frac{-Z^2}{2}}}{2\sqrt{m_0}},Z=\frac{S}{2\sqrt{m_0}},\mathrm{\γ}=\frac{m_2}{\sqrt{m_0\·m_4}},x_m=\frac{m_1}{m_0}\sqrt{\frac{m_2}{m_4}}$

$D_1=\frac{2(x_m-{\mathrm{\γ}}^2)}{1+{\mathrm{\γ}}^2},D_2=\frac{1-\mathrm{\γ}-D_1+D_1^2}{1-R},D_3=1-D_1-D_2$

$Q=\frac{1.25(\mathrm{\γ}-D_3-D_2\·R)}{D_1},R=\frac{\mathrm{\γ}-x_m-D_1^2}{1-\mathrm{\γ}-D_1+D_1^2}$

Wherein, p (S) represents stress probability density function, m₀～m₄For spectrum parameter byTrying to achieve, S represents stress level level, and above formula illustrates the method directly extracting the popular journey PDF of rain from stress PSD.

Interval propagation is analyzed method and is used second order Taylor series expansion method.The bound in its response interval is represented by:

$\underset{\‾}{{\mathrm{\Ψ}}_i}={\mathrm{\Ψ}}_i\left(x_c\right)-\underset{j=1}{\overset{m}{\Σ}}\left|\frac{\∂{\mathrm{\Ψ}}_i\left(x_c\right)}{\∂x_j}\right|{\mathrm{\Δx}}_j-\frac{1}{2}{\left(\underset{i=1}{\overset{m}{\Σ}}\underset{j=1}{\overset{m}{\Σ}}\right|\frac{\∂{\mathrm{\Ψ}}_i\left(x_c\right)}{\∂x_j}\left|{\mathrm{\Δx}}_i{\mathrm{\Δx}}_j\right)}^2$

$\stackrel{\‾}{{\mathrm{\Ψ}}_i}={\mathrm{\Ψ}}_i\left(x_c\right)+\underset{j=1}{\overset{m}{\Σ}}\left|\frac{\∂{\mathrm{\Ψ}}_i\left(x_c\right)}{\∂x_j}\right|{\mathrm{\Δb}}_j+\frac{1}{2}{\left(\underset{i=1}{\overset{m}{\Σ}}\underset{j=1}{\overset{m}{\Σ}}\right|\frac{\∂{\mathrm{\Ψ}}_i\left(x_c\right)}{\∂x_j}\left|{\mathrm{\Δx}}_i{\mathrm{\Δx}}_j\right)}^2$

Wherein,WithΨ _i Represent that i Uncertainty takes bound respectivelyWithx _iThe bound of response results, x_cRepresent the central value of uncertain variables, Ψ_i(x_c) represent that uncertain variables takes intermediate value x_cTime the interested amount response value of structure,Represent Ψ_i(x_c) first derivative expansion value at i-th uncertain parameter midpoint,Represent the second order expension at uncertain variables interval midpoint place, Δ x_iWith Δ x_jRepresent the interval radius of i-th and jth uncertain variables respectively.

(6) for continuous distribution stress state, time T inherent strain scope (S_i,S_i+ΔS_i) in stress-number of cycles can be expressed as n for (frequency equal to sum be multiplied by probability)_i=vTp (S_i)ΔS_i.The stress-number of cycles in the v representation unit time in formula, is determined by peak dot number E [P] per second, i.e. v=E [P], p (S_i) represent that stress level level is S_iTime amplitude probability density functional value, Δ S_iFor minimal stress level excursion；

(7) selecting the S-N curve of corresponding metal material in MSC.Fatigue, its expression formula is N (S_i)=K/S^m, apply Miner linear progressive damage theory D=∑ D_i=∑ n_i/N_i, obtain as overall impairment degree D=1 component fatigue of voice destroy fatigue life time be:

$T=\frac{K}{E\[P\]\∫S^{m}P\left(S\right)dS}$

Wherein, K and m is material constant, and N is metal material cycle-index, and D is injury tolerance.Be illustrated in figure 2 in MSC finite list meta software analyze flow chart.The final time lifetime cloud charts calculated when obtaining component generation fatigue rupture and logarithmic time scope fatigue life containing uncertain metal structure.

Embodiment:

In order to understand this characteristic feature of an invention and the suitability that engineering is actual thereof more fully, the aircraft cavity structure that the present invention sets up as shown in Figure 3 carries out the FEM (finite element) model after simplifying and apply boundary condition.The uncertain information of this model is E=[67.45,74.55] GPa, ssystem transfer function is calculated after model is first loaded the unit plane pressure with frequency change, then applying random noise load, table 2 gives noise power spectral density load (the unit Pa after applying conversion in embodiment on model²/ Hz), the front ten rank natural frequencies of this structure are drawn, the stress power spectral density function of the node 373 obtained is as shown in Figure 4, introducing material is 7075 aluminium alloys, its S-N curve is as shown in Figure 5, finally calculating life-span cloud charts such as Fig. 6, application Taylor series expansion interval propagation is analyzed method and is obtained logarithmic time life span such as Fig. 7.

Table 2

Table 3

In sum, the present invention proposes a kind of evaluation method shaken fatigue life containing uncertain metal structure sound.First, the specific features according to the situation such as construction geometry, material, analyze the type of attachment of component, classifying rationally grid applies boundary condition and forms finite element analysis model；Secondly, unascertained information is introduced the Dirlik model with the amplitude information composing parameter description scheme stress response in Frequency Response Analysis and random vibration analysis and frequency domain, from stress PSD, extract rain popular journey stress probability density function PDF；Finally, analyze method with the second Taylor series that interval propagation is theoretical and obtain the vibrating fatigue life span under random noise load.

Non-elaborated part of the present invention belongs to the known technology of those skilled in the art.

Claims (4)

1. the evaluation method shaken fatigue life containing uncertain metal structure sound, it is characterised in that realize step as follows:

The first step: according to flight mission profile time data and state acoustic load Measurement bandwidth sound pressure level, adoptsIt is converted into frequency spectrum load, wherein L=L_b-10lg (△ f), P₀=2 × 10^-5Pa is reference sound pressure, L_bFor bandwidth sound pressure level, △ f is bandwidth, and G (f) is the noise power spectral density value after converting；

Second step: introduce interval vector x ∈ x^IThe uncertain parameter of structure under the reasonable quantitative lean information of=[E, a, b], few data qualification, wherein E is metal material elastic modelling quantity, and a and b represents the geometric parameter of structure respectively, and the uncertainty containing structural parameters can be expressed as: $\stackrel{\‾}{x}=\[\stackrel{\‾}{E},\stackrel{\‾}{a},\stackrel{\‾}{b}\]=\[E^c+E^r,a^c+a^r,b^c+b^r\],$ Represent the value upper bound of parameter,x=[E,a,b]=[E^c-E^r,a^c-a^r,b^c-b^r],xRepresenting the value lower bound of parameter, wherein subscript c represents central value, and subscript r represents radius；

3rd step: set up the geometric model of interested structure, analyze the type of attachment of component, classifying rationally grid applies boundary condition and forms finite element analysis model, finite element analysis software loads unit uniform surface pressure loading, wherein the frequency range of load is identical with the frequency range of the acoustic loads of first step gained, extracts the Stress Transfer function of each node of structure after model carries out frequency response analysis；

4th step: application quadratic sum evolution (SRSS) method, MSC.Patran random vibration module reads the ssystem transfer function that the 4th step obtains, and the pectrum noise load applying first step gained obtains stress power spectrum density (PSD) curve of node, wherein random vibration analysis output file also includes the zero crossing number in the positive slope direction of the auto-correlation function of frequency response, time per unit and the mean-square value (RMS value) of stress response；

5th step: the typical feature of random noise is pressure time course amplitude is change at random, the form that namely irregular non-decay can not be expressed with analytical function, the excursion width of this kind of noise frequency, its spectrum is until significantly high frequency is all continuous print, method is analyzed with interval propagation in conjunction with the Dirlik model simulating this type of exemplary wideband stochastic process, with stress PSD curve obtained in the previous step for input, introduce Taylor expansion analytic process in non-probability interval procedural theory and obtain stress rain stream amplitude probability density function (PDF) excursion of each key event after uncertain variables is expanded；

6th step: for continuous distribution stress state, by time T inherent strain scope (S_i,S_i+△S_i) in stress-number of cycles be expressed as n_i=vTp (S_i)△S_i, the stress-number of cycles in the v representation unit time in formula, peak dot number E [P] per second determine, i.e. v=E [P], p (S_i) represent that stress level level is S_iTime amplitude probability density functional value, △ S_iFor minimal stress level excursion；

7th step: selecting the S-N curve of corresponding metal material in MSC.Fatigue, the feature expression of its curve is N (Si)=K/S^m, apply Miner linear progressive damage theory D=∑ D_i=∑ n_i/N_i, obtain as overall impairment degree D=1 component fatigue of voice destroy fatigue life time be:

$T=\frac{K}{E\[P\]\∫S^{m}P\left(S\right)dS}$

Wherein, K and m is material constant, and N is metal material cycle-index, and D is injury tolerance, and final calculating obtains time lifetime cloud charts when component fatigue destroys and key event minimum life time range.

2. a kind of evaluation method shaken fatigue life containing uncertain metal structure sound according to claim 1, it is characterised in that: in described second step, bounded-but-unknown uncertainty parameter vector x can be expressed as:

$\begin{array}{c}x=[\underset{-}{x},\stackrel{-}{x}]=[x^c-x^r,x^c+x^r]\\ =x^c+x^r[-\mathrm{1,1}]\\ =x^c+x^r\×e\end{array}$

Wherein, x^c=(E^c,a^c,b^c), x^r=(E^r,a^r,b^r), e ∈ Ξ³, Ξ³Being defined as the 3 dimensional vector set that all elements is included in [-1,1], symbol "×" is defined as two each corresponding elements of vector, and product is still 3 dimensional vectors.

3. a kind of evaluation method shaken fatigue life containing uncertain metal structure sound according to claim 1, it is characterized in that: in described 5th step, the Dirlik model of application is applicable to the simulation of exemplary wideband stochastic process, and its result accuracy of stochastic process for arrowband or with spike (i.e. pulse amplitude) characteristic is for reference.

4. a kind of evaluation method shaken fatigue life containing uncertain metal structure sound according to claim 1, it is characterized in that: in described 5th step, non-probability interval is propagated analysis method and used second order Taylor series expansion method, the bound in its response interval is represented by:

$\underset{\‾}{{\mathrm{\Ψ}}_i}={\mathrm{\Ψ}}_i\left(x_c\right)-\underset{j=1}{\overset{m}{\Σ}}\left|\frac{\∂{\mathrm{\Ψ}}_i\left(x_c\right)}{\∂x_j}\right|{\mathrm{\Δx}}_j-\frac{1}{2}{\left(\underset{i=1}{\overset{m}{\Σ}}\underset{j=1}{\overset{m}{\Σ}}\left|\frac{\∂{\mathrm{\Ψ}}_i\left(x_c\right)}{\∂x_j}\right|{\mathrm{\Δx}}_i{\mathrm{\Δx}}_j\right)}^2$

$\stackrel{\‾}{{\mathrm{\Ψ}}_i}={\mathrm{\Ψ}}_i\left(x_c\right)+\underset{j=1}{\overset{m}{\Σ}}\left|\frac{\∂{\mathrm{\Ψ}}_i\left(x_c\right)}{\∂x_j}\right|{\mathrm{\Δb}}_j+\frac{1}{2}{\left(\underset{i=1}{\overset{m}{\Σ}}\underset{j=1}{\overset{m}{\Σ}}\left|\frac{\∂{\mathrm{\Ψ}}_i\left(x_c\right)}{\∂x_j}\right|{\mathrm{\Δx}}_i{\mathrm{\Δx}}_j\right)}^2$

Wherein,WithΨ _i Represent that i Uncertainty takes bound respectivelyWithx _iThe bound of response results, Ψ_i(x_c) represent that uncertain variables takes intermediate value x_cTime the interested amount response value of structure,Represent Ψ_i(x_c) first derivative expansion value at i-th uncertain parameter midpoint,Represent the second order expension at uncertain variables interval midpoint place, △ x_iWith △ x_jRepresent the interval radius of i-th and jth uncertain variables respectively.