CN107169217B - A kind of equivalent method of turbulent boundary layer load model - Google Patents

A kind of equivalent method of turbulent boundary layer load model Download PDF

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CN107169217B
CN107169217B CN201710378734.7A CN201710378734A CN107169217B CN 107169217 B CN107169217 B CN 107169217B CN 201710378734 A CN201710378734 A CN 201710378734A CN 107169217 B CN107169217 B CN 107169217B
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费庆国
张鹏
李彦斌
吴邵庆
陈强
姜东�
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Southeast University
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Abstract

The invention discloses a kind of equivalent method of turbulent boundary layer load model, include the following steps：(1) turbulent boundary layer load model forms equivalent completely random face pressure load model after equivalent；(2) magnitude of the equivalent correlation function of the equivalent completely random face pressure load model is determined；(3) structural bending wavelength and turbulent boundary layer load characteristic wavelength are determined, and then calculates consistent resistant frequency, determines the applicable frequency range of equivalent random face pressure load model on this basis.A kind of equivalent method of turbulent boundary layer load model provided by the invention, it is a kind of technology that turbulent boundary layer load model is equivalent to completely random face pressure load model, the technology can effectively reduce the calculation amount of turbulent boundary layer load effect lower structure dynamic response analysis, shorten the design cycle, save design cost.

Description

A kind of equivalent method of turbulent boundary layer load model
Technical field
The present invention relates to random face pressure load model equivalent method field, and in particular to a kind of turbulent boundary layer load model Equivalent method.
Background technology
As spacecraft develops to high flying speed, it faces the environment such as the random noise of sternness in duty cycle, this It may cause structural failure or precision instrument, instrument malfunction.Therefore, in the design process of spacecraft, mechanical oscillation need to be considered With the influence of noise.The sound of something astir of test method, theoretical method and numerical method forecasting system under noise excitation can be used Should.Wherein, test method can obtain it is reliable as a result, but carry out analysis of experiments cost it is higher, design cycle length；Theoretical method It is only applicable to single system, it is difficult to solve the problems, such as the dynamic response indication of complication system；Numerical method can save design cost, shorten Design cycle, is effective supplementary means of analysis of experiments.
At present in a kind of generally acknowledged turbulent boundary layer load model, the coherence length of low-frequency range is longer, and high band is concerned with Length is shorter.The random response that mode superposition method analysis structure in using FInite Element is encouraged in turbulent boundary layer load When, with the rise of analysis frequency, the coherence length of turbulent boundary layer load shortens, it is desirable to and the size of finite element grid diminishes, This causes calculation amount to increase by geometric progression.Therefore, in higher frequency band, need to adopt an effective measure to solve above-mentioned turbulent boundary layer The problem of load model analysis efficiency is low, and then shorten the design cycle, save design cost.
The content of the invention
Goal of the invention：In order to overcome the deficiencies in the prior art, for a kind of existing turbulent boundary layer load mould Type in the application there are the problem of, the present invention provides a kind of equivalent method of the turbulent boundary layer load model, which can Effectively improve the efficiency of turbulent boundary layer load excitation lower structure dynamic response simulation analysis.
Technical solution：To achieve the above object, the technical solution adopted by the present invention is：
A kind of equivalent method of turbulent boundary layer load model, comprises the following steps：
Step 1：Turbulent boundary layer load model forms equivalent completely random face pressure load model after equivalent；
Step 2：Determine the magnitude of the equivalent correlation function of the equivalent completely random face pressure load model；
Step 3：The equivalent random face pressure load model is determined according to structural model and turbulent boundary layer load model It is applicable in frequency range.
Further, the turbulent boundary layer load model in the step 1 is：
Wherein ξxFor 2 points of distances in the direction of the x axis, ξyFor 2 points of distances in the y-axis direction, ω is angular frequency, S0 For the magnitude of load power spectrum, Dx=αx/kc、Dy=αy/kcThe respectively coherence length of downbeam and cross-wind direction, dimensionless Constant αx=8, αy=1.2, kc=ω/UcFor convection current wave number, Uc=0.7U is convection velocity, and U is speed of incoming flow.
Further, the equivalent completely random face pressure load model in the step 1 is：
Spp(ξx,ξy, ω) and=S0Ceq(ω)δ(ξx)δ(ξy) (2)
Wherein Ceq(ω) is the magnitude of equivalent correlation function, and function δ (ξ) is Kronecker function：
Further, in the step 2 the equivalent correlation function of equivalent completely random face pressure load model magnitude Ceq (ω) meets following formula：
Further, the magnitude C of the equivalent correlation function of the equivalent completely random face pressure load modeleq(ω) is：
Further, the applicable frequency range of equivalent completely random face pressure load model is f >=f in the step 3crit, fcritFor critical frequency.
Further, the critical frequency is：
fcrit=4fc (6)
Wherein fcFor consistent resistant frequency.
Further, the consistent resistant frequency fcTo make structural bending wavelength XB(ω) and reverberation field load characteristic wavelength XT (ω) equal i.e. λB(ω)=λTConsistent resistant frequency when (ω)：
Wherein, E is elasticity modulus of materials, and ρ is density of material, and ν is material Poisson's ratio, and h is thick for body structure surface plate class member Degree.
Beneficial effect：A kind of equivalent method of turbulent boundary layer load model provided by the invention is a kind of by turbulence edge Interlayer load model is equivalent to the technology of completely random face pressure load model, which can effectively reduce turbulent boundary layer load and swash The calculation amount of lower structure dynamic response analysis is encouraged, shortens the design cycle, saves design cost.
Brief description of the drawings
Fig. 1 is the logical procedure diagram of the present invention；
Fig. 2 is the schematic diagram of a rectangle simply supported slab；
Fig. 3 is the dynamic respond power spectral density schematic diagram at point A on rectangle simply supported slab.
Embodiment
The present invention is further described below in conjunction with the accompanying drawings.
Be a kind of logical procedure diagram of the equivalent method of turbulent boundary layer load model as shown in Figure 1, it is main include with Lower step：
Step (1) turbulent boundary layer load model forms equivalent completely random face pressure load model after equivalent；
(1.1) turbulent boundary layer load model, its cross-spectrum spatially at any two points between face pressure load are：
Wherein ξxFor 2 points of distances in the direction of the x axis, ξyFor 2 points of distances in the y-axis direction, ω is angular frequency, S0 For the magnitude of load power spectrum, Dx=αx/kc、Dy=αy/kcThe respectively coherence length of downbeam and cross-wind direction, dimensionless Constant αx=8, αy=1.2, kc=ω/UcFor convection current wave number, Uc=0.7U is convection velocity, and U is speed of incoming flow.
(1.2) equivalent completely random face pressure load model, spatially the cross-spectrum of face pressure is at any two points for it：
Spp(ξx,ξy, ω) and=S0Ceq(ω)δ(ξx)δ(ξy) (2)
Wherein Ceq(ω) is the magnitude of equivalent correlation function, and function δ (ξ) is Kronecker function：
Step (2)) determine the equivalent completely random face pressure load model equivalent correlation function magnitude Ceq(ω), into And determine the equivalent completely random face pressure load model；
The magnitude C of the equivalent correlation function of equivalent completely random face pressure load modeleq(ω) meets following formula：
Solution formula (4) obtains the magnitude C of the equivalent correlation function of equivalent completely random face pressure load modeleq(ω) is：
Step (3) determines the equivalent random face pressure load model according to structural model and turbulent boundary layer load model It is applicable in frequency range；Specifically include：
(3.1) bending wavelength of structure is determined：
Wherein, E is elasticity modulus of materials, and ρ is density of material, and ν is material Poisson's ratio, and h is thick for body structure surface plate class member Degree.
(3.2) characteristic wavelength of turbulent boundary layer load is determined：
λTThe π U of (ω)=2c/ω (7)
(3.3) when calculating makes structural bending wavelength and equal turbulent boundary layer load characteristic wavelength, i.e. λB(ω)=λD(ω) When consistent resistant frequency：
(3.4) critical frequency that equivalent completely random face pressure load model is applicable in is calculated：
fcrit=4fc (9)
(3.5) the applicable frequency range for determining the equivalent completely random face pressure load model in step (2) is f >=fcrit。
Embodiment
As shown in Fig. 2, by taking a rectangle simply supported slab as an example, consistent resistant frequency is calculated.The size of rectangle simply supported slab is：X-axis To length Lx=1m, y-axis is to length Ly=1m, thickness h=0.005m.The parameter of rectangle simply supported slab material therefor is：Elasticity modulus E=120GPa, density of material ρ=7800kg/m3, Poisson's ratio υ=0.3.As speed of incoming flow U=100m/s, by each parameter Value substitutes into formula (8) and obtains fc=102Hz.
The critical frequency being applicable in by the equivalent completely random face pressure load model of step (3.4) calculating is fcrit=408Hz.
Determine that the applicable frequency range of equivalent completely random face pressure load model is f >=f by step (3.5)crit, that is, work as When analyzing frequency f >=408Hz, in this example, formula can be replaced as the equivalent completely random face pressure load model shown in formula (2) (1) the turbulent boundary layer load model shown in.
The equivalent completely random face pressure load obtained as above-mentioned steps is put in the Simply-Supported Rectangular Plates shown in Fig. 2, is counted Calculate obtain point A (0.3m, 0.2m) place dynamic respond power spectral density (in units of dB, reference value 1m2Hz-1), such as Fig. 3 institutes Show.In Fig. 3 the result shows that, in this example, as f >=fcrit, i.e. during f >=408Hz, equivalent completely random face that above-mentioned steps obtain Ballast model can effectively represent turbulent boundary layer load model.
The effect explanation that the present embodiment finally obtains, method proposed by the invention can be effectively by turbulent boundary layer load Model conversion improves the efficiency that subsequent response is analyzed into equivalent completely random face pressure load model.
The above is only the preferred embodiment of the present invention, it should be pointed out that：For the ordinary skill people of the art For member, various improvements and modifications may be made without departing from the principle of the present invention, these improvements and modifications also should It is considered as protection scope of the present invention.

Claims (4)

  1. A kind of 1. equivalent method of turbulent boundary layer load model, it is characterised in that：Comprise the following steps：
    Step 1：Turbulent boundary layer load model forms equivalent completely random face pressure load model after equivalent；
    Step 2：Determine the magnitude of the equivalent correlation function of the equivalent completely random face pressure load model；
    Step 3：The equivalent completely random face pressure load model is determined according to structural model and turbulent boundary layer load model It is applicable in frequency range；
    Wherein：
    Turbulent boundary layer load model in the step 1 is：
    <mrow> <msub> <mi>S</mi> <mrow> <mi>p</mi> <mi>p</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;xi;</mi> <mi>x</mi> </msub> <mo>,</mo> <msub> <mi>&amp;xi;</mi> <mi>y</mi> </msub> <mo>,</mo> <mi>&amp;omega;</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>S</mi> <mn>0</mn> </msub> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mrow> <mo>|</mo> <msub> <mi>&amp;xi;</mi> <mi>x</mi> </msub> <mo>|</mo> </mrow> <mo>/</mo> <msub> <mi>D</mi> <mi>x</mi> </msub> </mrow> </msup> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mrow> <mo>|</mo> <msub> <mi>&amp;xi;</mi> <mi>y</mi> </msub> <mo>|</mo> </mrow> <mo>/</mo> <msub> <mi>D</mi> <mi>y</mi> </msub> </mrow> </msup> <msup> <mi>e</mi> <mrow> <mo>-</mo> <msub> <mi>jk</mi> <mi>c</mi> </msub> <msub> <mi>&amp;xi;</mi> <mi>x</mi> </msub> </mrow> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
    Wherein ξxFor 2 points of distances in the direction of the x axis, ξyFor 2 points of distances in the y-axis direction, ω is angular frequency, S0To carry The magnitude of lotus power spectrum, Dx=αx/kc、Dy=αy/kcThe respectively coherence length of downbeam and cross-wind direction, dimensionless constant αx=8, αy=1.2, kc=ω/UcFor convection current wave number, Uc=0.7U is convection velocity, and U is speed of incoming flow；
    Equivalent completely random face pressure load model is described in the step 1：
    Spp(ξx,ξy, ω) and=S0Ceq(ω)δ(ξx)δ(ξy) (2)
    Wherein Ceq(ω) is the magnitude of equivalent correlation function, and function δ (ξ) is Kronecker function：
    The magnitude C of the equivalent correlation function of equivalent completely random face pressure load model in the step 2eq(ω) meets following formula：
    <mrow> <msub> <mo>&amp;Integral;</mo> <mi>&amp;infin;</mi> </msub> <msub> <mo>&amp;Integral;</mo> <mi>&amp;infin;</mi> </msub> <msup> <mi>C</mi> <mrow> <mi>e</mi> <mi>q</mi> </mrow> </msup> <mrow> <mo>(</mo> <mi>&amp;omega;</mi> <mo>)</mo> </mrow> <mi>&amp;delta;</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;xi;</mi> <mi>x</mi> </msub> <mo>)</mo> </mrow> <mi>&amp;delta;</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;xi;</mi> <mi>y</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>d&amp;xi;</mi> <mi>x</mi> </msub> <msub> <mi>d&amp;xi;</mi> <mi>y</mi> </msub> <mo>=</mo> <msub> <mo>&amp;Integral;</mo> <mi>&amp;infin;</mi> </msub> <msub> <mo>&amp;Integral;</mo> <mi>&amp;infin;</mi> </msub> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mrow> <mo>|</mo> <msub> <mi>&amp;xi;</mi> <mi>x</mi> </msub> <mo>|</mo> </mrow> <mo>/</mo> <msub> <mi>D</mi> <mi>x</mi> </msub> </mrow> </msup> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mrow> <mo>|</mo> <msub> <mi>&amp;xi;</mi> <mi>y</mi> </msub> <mo>|</mo> </mrow> <mo>/</mo> <msub> <mi>D</mi> <mi>y</mi> </msub> </mrow> </msup> <msup> <mi>e</mi> <mrow> <mo>-</mo> <msub> <mi>jk</mi> <mi>c</mi> </msub> <msub> <mi>&amp;xi;</mi> <mi>x</mi> </msub> </mrow> </msup> <msub> <mi>d&amp;xi;</mi> <mi>x</mi> </msub> <msub> <mi>d&amp;xi;</mi> <mi>y</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
    The applicable frequency range of equivalent completely random face pressure load model in the step 3 is f >=fcrit, fcritFor critical frequency Rate.
  2. 2. the equivalent method of turbulent boundary layer load model according to claim 1, it is characterised in that：It is described equivalent complete The magnitude C of the equivalent correlation function of random face pressure load modeleq(ω) is：
    <mrow> <msup> <mi>C</mi> <mrow> <mi>e</mi> <mi>q</mi> </mrow> </msup> <mrow> <mo>(</mo> <mi>&amp;omega;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>4</mn> <msub> <mi>D</mi> <mi>x</mi> </msub> <msub> <mi>D</mi> <mi>y</mi> </msub> </mrow> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>D</mi> <mi>x</mi> </msub> <msub> <mi>k</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
  3. 3. the equivalent method of turbulent boundary layer load model according to claim 1, it is characterised in that：The critical frequency For：
    fcrit=4fc (6)
    Wherein fcFor consistent resistant frequency.
  4. 4. the equivalent method of the random face pressure load model of reverberation field according to claim 3, it is characterised in that：It is described consistent Resistant frequency fcTo make structural bending wavelength XB(ω) and reverberation field load characteristic wavelength XT(ω) equal i.e. λB(ω)=λTWhen (ω) Consistent resistant frequency：
    <mrow> <msub> <mi>f</mi> <mi>c</mi> </msub> <mo>=</mo> <mfrac> <msubsup> <mi>U</mi> <mi>c</mi> <mn>2</mn> </msubsup> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </mfrac> <msqrt> <mfrac> <mrow> <mn>12</mn> <mi>&amp;rho;</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>&amp;upsi;</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mrow> <mrow> <msup> <mi>Eh</mi> <mn>2</mn> </msup> </mrow> </mfrac> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, E is elasticity modulus of materials, and ρ is density of material, and ν is material Poisson's ratio, and h is body structure surface plate class member thickness.
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