CN105760577B - A Method for Estimating Acoustic-Vibration Fatigue Life of Metal Structures with Uncertainty - Google Patents

Abstract

The invention discloses a kind of evaluation methods containing uncertain metal structure sound and vibration fatigue life.This method initially sets up the finite element analysis model of metal structure, considers the uncertain effect of material and structural property parameter under the conditions of finite sample, rings analysis theories based on frequency and obtains system transter；Then according to random noise load the characteristics of, for the steady ergodic random noise load of exemplary wideband, each key event displacement is obtained with quadratic sum evolution (SRSS) method, the Root mean square response and stress power spectral density function (PSD) of stress, in conjunction with the uncertain analysis method for propagating second order Taylor series expansion method and frequency domain internal vibration fatigue of Dirlik model and section, establish the relationship between rain stream amplitude probability density function and power spectral density function, finally the sound and vibration fatigue life interval range containing uncertain metal structure is obtained using the linear progressive damage theory of Miner.The present invention has fully considered the dispersibility of structure and material parameter when calculating the structural life-time by typical random noise excitation, therefore obtained fatigue life is more reasonable.

Description

A Method for Estimating Acoustic-Vibration Fatigue Life of Metal Structures with Uncertainty

technical field

The invention relates to the technical field of noise and vibration fatigue of metal structures, in particular to a method for estimating the dynamic response of a structure to random noise loads and an acoustic fatigue life under the action of uncertainty. It is suitable for efficient prediction of the acoustic fatigue life of various structural types under typical complex noise loads, and provides assistance for the design of engineering acoustic fatigue resistant structures.

Background technique

The effect of noise load on the structure is essentially a spatially distributed dynamic random pressure load with certain frequency distribution characteristics. When the sound pressure level exceeds 140dB, it can produce a certain distributed stress response on the structure, especially when the frequency distribution characteristics of the noise and the dynamic characteristics of the structure it acts on are coupled with each other, the structure will produce a significant stress response. . Acoustic fatigue belongs to the problem of high cycle and low stress. Under the long-term action of this dynamic stress, fatigue cracks will form in the stress concentration and defect parts of the structure. The fatigue crack formation life is the acoustic-vibration fatigue life to be studied.

During the service process, the aircraft is in a complex noise environment caused by the coupling effect of engine jet, aerodynamic force and wall surface, and the working vibration of the body's own structure. With the increase of the flight speed of the aircraft, the increase of the thrust of the power plant and the improvement of the performance of the combat requirements, the magnitude of various noises generated in the operation of the aircraft continues to increase. Practice has shown that various types of acoustic fatigue damage often occur in the use of both military aircraft and civil aircraft. Most of them are manifested as: various wing skin and fuselage side skin cracks, wing rib and fuselage ring frame cracks, inner skin cracks in the air intake, various damage to the tail under the action of jet flow. There are many limitations in traditional acoustic fatigue life estimation. For example, when considering dynamic stress effects, only low-order frequencies are considered, and some only consider first-order natural frequencies, which have certain errors for the effects caused by loads with wide frequency distribution and high energy. ; In the preliminary design, the designer needs to know whether the material and structure type used by the object are the same as those of the existing curve. If they are the same, the specific structure type and the acoustic fatigue test curve of the material can be used to obtain the life after the root mean square stress is obtained. , but it is not the same, the structural parameter design needs to be redesigned, and the equivalent conversion and result experience correction are performed according to the existing curve, which is a large workload and low precision; the RMS life curve itself of specific structures and materials is very lacking. , the existing number is small, and a large amount of experimental data support is needed.

In addition, the initial defects and damage caused by the manufacturing process and material heterogeneity are unavoidable, and will continue to develop, spread and spread inside the structure during the long-term service in the future, which seriously affects the mechanical behavior and safety of the structure. It is of great practical significance to establish the uncertainty characterization technology based on the non-probabilistic theoretical framework and the estimation technology of the uncertain acoustic-vibration fatigue life of metal structures.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and provide a method for estimating the acoustic and vibration fatigue life of metal structures with uncertainty. The invention fully considers the uncertainty factors commonly existing in practical engineering problems, uses the non-probability interval method to characterize the uncertain quantity, introduces the uncertainty interval propagation theory, and the obtained design results are more in line with the real situation and have stronger engineering applicability.

The technical scheme adopted in the present invention is: a method for estimating the acoustic vibration fatigue life of a metal structure with uncertainty, and the implementation steps are as follows:

The first step: measure the bandwidth sound pressure level according to the flight mission profile time data and the state sound load, using Convert it to the spectral load of random noise, where L=L _b -10lg(Δf), P ₀ =2×10 ^-5 Pa is the reference sound pressure, L _b is the bandwidth sound pressure level, Δf is the frequency band width, G( f) is the converted noise power spectral density value;

Step 2: Introduce the interval vector x∈x ^I =[E,a,b] to reasonably quantify the uncertain parameters of the structure under the condition of poor information and few data, where E is the elastic modulus of the metal material, and a and b represent the structure, respectively Geometric parameters of different parts. Then the uncertainty with structural parameters can be expressed as: Represents the upper bound of the value of the parameter, x =[ E , a , b ]=[E ^c -E ^r , a ^c -a ^r , b ^{c -br} ], x represents the lower bound of the value of the parameter, where the superscript c Represents the center value, and the superscript r represents the radius;

The third step: establish the geometric model of the concerned structure, analyze the connection form of the components, divide the mesh reasonably and apply the boundary conditions to form the finite element analysis model. The unit uniform surface pressure load is loaded in the finite element analysis software, and the frequency variation range of the load is the same as the frequency range of the noise load obtained in the first step. After analyzing the frequency response of the model, the stress transfer function of each node of the structure is extracted;

Step 4: Apply the square sum square root (SRSS) method, read the stress transfer function obtained in the third step in the MSC.Patran random vibration module, and apply the spectral noise load obtained in the first step to obtain the stress power spectrum of the node Density (PSD) curve, where the random vibration analysis output file also includes the power spectral density of the frequency response, the autocorrelation function, the number of zero crossings per unit time in the direction of the positive slope, and the RMS value of the stress response;

Step 5: The typical feature of random noise is that the amplitude of the pressure time history changes randomly, that is, it is irregular and non-attenuating and cannot be expressed in the form of an analytical function. are all continuous. Combining the Dirlik model of a typical broadband stochastic process and the interval propagation analysis method, the stress PSD curve obtained in the previous step is used as the input, and the Taylor series expansion method in the non-probabilistic interval process theory is used to obtain the stress of each key node after the uncertainty variable is propagated Rainflow amplitude probability density function (PDF) variation range;

Step 6: For the continuously distributed stress state, express the number of stress cycles within the stress range (S _i , S _i +ΔS _i ) within the time T as _ni =vTp(S _i )ΔS _i . In the formula, v represents the number of stress cycles per unit time, which is determined by the number of peak points per second, E[P], that is, v=E[P], and p(S _i ) represents the amplitude probability when the stress level is Si _. Density function value, ΔS _i is the variation range of small stress level;

Step 7: Select the SN curve of the corresponding metal material in MSC.Fatigue, its expression is N(S _i )=K/S ^m , apply Miner's linear cumulative damage theory D=∑D _{i =} ∑ni /N _i , when the overall damage degree D = 1, the time fatigue life of the fatigue failure of the component is obtained as:

Among them, K and m are the material constants, N is the number of cycles of the metal material, and D is the damage degree. The final calculation results in the time-life distribution cloud map of the component when fatigue failure occurs. According to the non-probabilistic interval propagation analysis theory, the life time range of the component is obtained.

Further, the interval uncertainty parameter vector x in the second step can be expressed as:

Among them, x ^c = (E ^c , a ^c , b ^c ), x ^r = (E ^r , a ^r , b ^r ), e∈Ξ ³ , Ξ ³ is defined as all elements contained in [-1,1] The 3-dimensional vector set of , the symbol "×" is defined as the corresponding elements of the two vectors, and the product is still a 3-dimensional vector.

Further, the Dirlik model applied in the fifth step is suitable for the simulation of typical broadband random processes, and the accuracy of the results for narrow-band or random processes with peak (ie, pulse amplitude) characteristics is for reference.

Further, the non-probability interval propagation analysis method in the fifth step uses the second-order Taylor series expansion method, and the upper and lower bounds of the response interval can be expressed as:

in, and Ψ _i represent i uncertain quantities and take the upper and lower bounds respectively The upper and lower bounds of the response result of x _i , Ψ _i (x _c ) represents the response value of the quantity concerned by the structure when the uncertain variable takes the median value x _c , represents the expanded value of the first derivative of Ψ _i (x _c ) at the midpoint of the i-th uncertain parameter, represents the second-order expansion at the midpoint of the uncertainty variable interval, and Δx _i and Δx _j represent the interval radius of the ith and jth uncertain variables, respectively.

Compared with the prior art, the present invention has the advantages that: the present invention provides a new way of estimating acoustic fatigue life, and makes up for and perfects the limitations of traditional theories. The traditional method of estimating acoustic fatigue can only be aimed at a specific structural form, and this method can calculate any structural form; the traditional method needs a RMS stress-life curve, and this method only needs the traditional fatigue life curve. When considering the dispersion of materials and structures, the method does not need to know the probability distribution form of uncertain parameters, but only needs to know the upper and lower limits of metal materials and structural geometric parameters, and it can easily solve the acoustic fatigue of any structural form of metal materials with uncertainties. The range of the life span is more convenient and reliable in terms of engineering practicality.

Description of drawings

Fig. 1 is the flow chart of the estimation method of the present invention for the acoustic vibration fatigue life of metal structures with uncertainty;

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

Fig. 3 is the finite element model after the present invention simplifies the cavity structure of the aircraft and applies boundary conditions;

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

Fig. 5 is the S-N curve quoted by the present invention for 7075-HV-T6 metal material;

Fig. 6 is the cloud diagram of the acoustic-vibration fatigue life distribution of metal materials calculated by the present invention;

FIG. 7 is the minimum life span range of nodes obtained for the structure with uncertain parameters according to the present invention.

Detailed ways

The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

As shown in Figure 1, the present invention proposes a method for estimating the acoustic and vibration fatigue life of metal structures with uncertainty, which includes the following steps:

(1) Acoustic fatigue is only considered when aircraft structural components are subjected to a sound pressure level of 130 dB above the human ear pain range, as specified in the general specification. The bandwidth sound pressure level (octave bandwidth or 1/3 octave bandwidth, etc.) is measured according to the flight mission profile time data and state sound load, using Convert it to the spectral load of random noise, where L=L _b -10lg(Δf), P ₀ =2×10 ^-5 Pa is the reference sound pressure, L _b is the bandwidth sound pressure level, Δf is the frequency band width, G( f) is the transformed noise power spectral density value.

Table 1 is an international standardized octave frequency table cited in the present invention, showing a frequency table recommended by the International Organization for Standardization. The noise bandwidth of any center frequency can be obtained by looking up the table. According to the measured bandwidth sound pressure level, according to the above conversion formula, the corresponding power spectral density is obtained. For example, for a sound field with a center frequency of 100 Hz, its bandwidth is 22.9 Hz. If the measured bandwidth sound pressure level is 127 dB, the power spectral density after conversion of the sound field is 87.544 Pa ² /Hz. If the time domain signal of the measured value of the noise field is converted into a spectral signal through the Welfare transform and then analyzed.

Table 1

lower frequency Center frequency upper limit frequency lower frequency Center frequency upper limit 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) The interval vector x∈x ^I = [E, a, b] is introduced to reasonably quantify the uncertain parameters of the structure under the condition of poor information and little data, where E is the elastic modulus of the metal material, and a and b represent different structures, respectively The geometric parameters of the part. Then the uncertainty with structural parameters can be expressed as: Represents the upper bound of the value of the parameter, x =[ E , a , b ]=[E ^c -E ^r , a ^{c -ar} , b ^{c -br} ], x represents the lower bound of the value of the parameter, where the superscript c represents the center value, and the superscript r represents the radius; the interval uncertainty parameter vector x can be expressed as:

where x ^c = (E ^c , a ^c , b ^c ), x ^r = (E ^r , a ^r , b ^r ), e∈Ξ ³ , Ξ ³ is defined as all elements contained in [-1, 1] The 3-dimensional vector set of , the symbol "×" is defined as the corresponding elements of the two vectors, and the product is still a 3-dimensional vector.

(3) Form a finite element analysis model, and load a unit uniform surface pressure load in MSC.Patran, where the frequency variation range of the load is the same as the frequency range of the noise load obtained in the first step. The frequency response function of the node, referred to here as the stress transfer function.

(4) Apply the square sum square root (SRSS) method, read the stress transfer function obtained in step (3) in the random vibration module, and apply the spectral noise load obtained in the first step to obtain the stress power spectral density of the node ( PSD) curve, where the random vibration analysis output file also includes the autocorrelation function of the frequency response, the number of zero crossings per unit time in the direction of the positive slope, and the RMS value of the stress response. The following is the theoretical procedure for calculating the mean square value of the stress response and the power spectral density.

For multi-degree-of-freedom problems excited by a single point:

where M, C and K represent the mass matrix damping matrix and stiffness matrix of the system, respectively, a(t) is the displacement response function of the system, g(t) represents the noise excitation of a zero-mean stationary random process, and its autocorrelation function is R _gg ( t), the power spectral density function is S _gg (f), and q is the load amplitude coefficient vector. Assuming that the damping matrix is proportional damping, the system response can be obtained by using the matrix superposition method:

in is the formation participation coefficient, is the jth-order matrix of the system, τ is the tiny time interval, and h _j (τ) is the transfer function of the system obtained in the third step.

According to the definition of the autocorrelation function, the autocorrelation matrix of the system response function is:

In the formula, R _aa (τ) and R _gg (τ) represent the autocorrelation function of response and excitation, respectively, and E represents the mean value of random variables. The above equation shows that the autocorrelation matrix of the response can be expressed as a double integral of the autocorrelation matrix of the excitation. Solve the self-power spectral density matrix with which it forms the Fourier transform pair by the Wiener relation:

Rewrite exp(-i2πfτ) in this formula as exp(-i2πfτ ₁ )·exp(-i2πfτ ₂ )·exp(-i2πf(τ+τ ₁ -τ ₂ )), then the triple integral can be rewritten as the following three A multiplication of integrals:

Here, the conclusion that the impulse response function and the frequency response function, the autocorrelation function and the autopower spectral function are respectively constituted by the Fourier transform pair is used. Then the self-power spectral density matrix of the response can be obtained as:

For the response of a multi-degree-of-freedom system under general multi-point excitation, the self-power spectral density matrix can be obtained from the self-power spectral density matrix S _qq (f) of the load and the transfer function matrix H (f) by the following formula:

S _aa (f) = H ^* (f) S _qq (f) H ^T (f)

Among them, H ^* (f) is the function obtained by taking the negative value of frequency in the frequency response function, and H ^T (f) is the transpose matrix of the frequency response function. In summary, the displacement and stress response of the system can be obtained by this method, and the stress power spectral density function (PSD) curve of the system can be obtained.

(5) Combining the Dirlik model of a typical broadband stochastic process and the interval propagation analysis method, the stress PSD curve obtained in the previous step is used as the input, and the vertex method in the non-probability interval process theory is used to obtain the stress of each key node after the uncertainty variable is propagated Rainflow amplitude probability density function (PDF) variation range. The Dirlik model is represented as follows:

Among them, p(S) represents the stress probability density function, m ₀ ～m ₄ are the spectral parameters, which are given by Obtained, S represents the stress level, and the above formula represents the method of directly extracting the PDF of the rain flow from the stress PSD.

The interval propagation analysis method uses the second-order Taylor series expansion method. The upper and lower bounds of its response interval can be expressed as:

in, and Ψ _i represent i uncertain quantities and take the upper and lower bounds respectively The upper and lower bounds of the response result with x _i , x _c represents the central value of the uncertain variable, Ψ _i (x _c ) represents the response value of the structure concerned when the uncertain variable takes the median value x _c , represents the expanded value of the first derivative of Ψ _i (x _c ) at the midpoint of the i-th uncertain parameter, represents the second-order expansion at the midpoint of the uncertainty variable interval, and Δx _i and Δx _j represent the interval radius of the ith and jth uncertain variables, respectively.

(6) For the continuously distributed stress state, the number of stress cycles in the stress range (S _i , S _i +ΔS _i ) within time T is (the frequency equals the total number times the probability) and can be expressed as n _i =vTp(S _i )ΔS _i . In the formula, v represents the number of stress cycles per unit time, which is determined by the number of peak points per second, E[P], that is, v=E[P], and p(S _i ) represents the amplitude probability when the stress level is Si _. Density function value, ΔS _i is the variation range of small stress level;

(7) Select the SN curve of the corresponding metal material in MSC.Fatigue, its expression is N(S _i )=K/S ^m , and apply Miner's linear cumulative damage theory D=∑D _i =∑n _i /N _i , When the overall damage degree D=1, the time fatigue life of the component sound fatigue failure is obtained as:

Among them, K and m are the material constants, N is the number of cycles of the metal material, and D is the damage degree. Figure 2 shows the flow chart of the analysis in the MSC series finite element software. Finally, the time-life distribution nephogram and the logarithmic time range of fatigue life of metal structures with uncertainties are obtained by the final calculation.

Example:

In order to more fully understand the characteristics of the invention and its applicability to engineering practice, the invention establishes a finite element model of the aircraft cavity structure shown in Figure 3 after simplifying and applying boundary conditions. The uncertainty information of the model is E=[67.45,74.55]GPa. The model is first loaded with the unit surface pressure that changes with frequency, and then the system transfer function is calculated, and then the random noise load is applied. Table 2 gives the model in the embodiment. Applying the converted noise power spectral density load (unit Pa ² /Hz), the first ten order natural frequencies of the structure are obtained, and the obtained stress power spectral density function of node 373 is shown in Figure 4. The introduced material is The SN curve of 7075 aluminum alloy is shown in Figure 5, and the cloud diagram of the life distribution is finally calculated as shown in Figure 6, and the logarithmic time life range is obtained by applying the Taylor series expansion interval propagation analysis method as shown in Figure 7.

Table 2

table 3

To sum up, the present invention proposes a method for estimating the acoustic-vibration fatigue life of metal structures with uncertainty. Firstly, according to the specific characteristics of structural geometry, materials, etc., the connection form of components is analyzed, and the mesh is reasonably divided to apply boundary conditions to form a finite element analysis model; secondly, uncertainty information is introduced into frequency response analysis and random vibration analysis and frequency domain. The Dirlik model is used to describe the amplitude information of the structural stress response with spectral parameters, and the rain flow stroke stress probability density function PDF is extracted from the stress PSD. Finally, the vibration fatigue under random noise load is obtained by the second-order Taylor expansion analysis method of interval propagation theory. life span.

Parts not described in detail in the present invention belong to the well-known technologies of those skilled in the art.

Claims (4)

1. A method for estimating the sound vibration fatigue life of a metal structure containing uncertainty is characterized by comprising the following implementation steps:

the first step is as follows: measuring the sound pressure level of bandwidth according to flight mission profile time data and state sound load by adoptingConverting it into a spectral load, where L ═ L_b-10lg(Δf)，P₀＝2×10^-5Pa is reference sound pressure, L_bIs the sound pressure level of the bandwidth, Δ f isFrequency bandwidth, G (f), is the converted noise power spectral density value;

the second step is that: introducing an interval vector x ∈ x^I＝[E,a,b]Reasonably quantifying uncertain parameters of the structure under poor information and few data conditions, wherein E is the elastic modulus of the metal material, a and b respectively represent geometric parameters of the structure, and the uncertainty containing the structural parameters can be represented as: represents the upper bound of the value of the parameter,x＝[E,a,b]＝[E^c-E^r,a^c-a^r,b^c-b^r]，xrepresenting the value lower bound of the parameter, wherein an upper mark c represents a central value, and an upper mark r represents a radius;

the third step: establishing a geometric model of the structure concerned, analyzing the connection form of the components, reasonably dividing grids and applying boundary conditions to form a finite element analysis model, loading unit uniform surface pressure load in finite element analysis software, wherein the frequency change range of the load is the same as the frequency range of the noise load obtained in the first step, and extracting the stress transfer function of each node of the structure after carrying out frequency response analysis on the model;

the fourth step: reading the stress transfer function obtained in the third step in an MSC.Patran random vibration module by applying a square sum evolution method, and applying the frequency spectrum noise load obtained in the first step to obtain a stress power spectral density curve of a node, wherein the random vibration analysis output file further comprises an autocorrelation function of frequency response, the number of zero-crossing points in the direction of a positive slope of each unit time and a mean square value of the stress response;

the fifth step: the random noise is characterized in that the pressure time history amplitude is changed randomly, namely, the random non-attenuation cannot be expressed by an analytic function, the change range of the noise frequency is wide, the spectrum value of the noise frequency is continuous until the high frequency, a Dirlik model simulating the typical broadband random process and an interval propagation analysis method are combined, the stress PSD curve obtained in the previous step is used as input, and a Taylor expansion analysis method in a non-probability interval process theory is introduced to obtain the change range of the stress rain flow amplitude probability density function of each key node after the expansion of an uncertain variable;

and a sixth step: for a continuously distributed stress state, the stress range (S) is determined within the time T_i,S_i+ΔS_i) The number of internal stress cycles is denoted as n_i＝vTp(S_i)ΔS_iWherein v represents the number of stress cycles per unit time and is represented by the number of peaks per second E [ P ]]Determining, i.e. v ═ E [ P [ ]]，p(S_i) Representing a stress level of S_iMagnitude of time probability density function value, Δ S_iThe range of variation of the micro stress level;

the seventh step: selecting an S-N curve corresponding to the metal material in MSC.Fatigue, wherein the characteristic expression of the curve is N (S)_i)＝K/S^mApplying Miner linear accumulated damage theory D ═ Sigma D_i＝∑n_i/N_iWhen the total damage degree D is 1, the time fatigue life of the member in which the sound fatigue failure is obtained is:

and finally calculating to obtain a time life distribution cloud chart and a minimum life time range of the key nodes when the member is in fatigue failure.

2. The method for estimating the sound vibration fatigue life of the metal structure with uncertainty according to claim 1, characterized in that: the inter-region uncertainty parameter vector x in the second step can be expressed as:

wherein x is^c＝(E^c,a^c,b^c)，x^r＝(E^r,a^r,b^r)，e∈Ξ³，Ξ³Is defined as all elements contained in [ -1,1 [ ]]The 3-dimensional vector set in the inner space, the symbol "x" is defined as the corresponding elements of two vectors, and the product is still a 3-dimensional vector.

3. The method for estimating the sound vibration fatigue life of the metal structure with uncertainty according to claim 1, characterized in that: the dirik model applied in the fifth step is suitable for simulation of a typical wideband stochastic process, the accuracy of the result being referenced for narrowband or stochastic processes with spiky characteristics.

4. The method for estimating the sound vibration fatigue life of the metal structure with uncertainty according to claim 1, characterized in that: the non-probability interval propagation analysis method in the fifth step uses a second-order taylor series expansion method, and the upper and lower bounds of the response interval can be expressed as follows:

wherein,andΨ_i indicating that i uncertain quantities take upper and lower bounds respectivelyAndx _iupper and lower bounds of the response result of (2), Ψ_i(x_c) Representing the uncertainty variable by taking the median x_cThe response value of the quantity of interest of the structure,denotes Ψ_i(x_c) The first derivative at the point in the ith uncertainty parameter evolves,representing a second order expansion, Δ x, at a midpoint of an uncertain variable interval_iAnd Δ x_jRespectively representing the section radius of the ith and jth uncertain variables.