CN107180132A - A kind of Design method of structural parameters for suppressing microperforated panel nonlinear effect - Google Patents
A kind of Design method of structural parameters for suppressing microperforated panel nonlinear effect Download PDFInfo
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Abstract
The invention discloses a kind of Design method of structural parameters for suppressing microperforated panel nonlinear effect, comprise the following steps：Step one：Frequency spectrum and sound pressure level analysis are carried out to loud intensity Sound Field, according to the frequency domain distribution situation of noise energy, restrictive condition parameter and parameter to be designed is determined；Step 2：Choose one group of { d, t/d } parameter；Step 3：Calculate corresponding punching rate σ；Step 4：According to parameter combination { d, t/d, σ } and known parameters f0, microperforated panel structure-borne sound impedance Z is drawn with incident sound pressure level P by numerical simulationiThe curve of change；Step 5：Acoustic impedance obtains the transformation sound pressure level that nonlinear acoustic impedance is functioned to the relation curve of incident sound pressure level change in observation of steps three.The present invention makes it have good linear sound absorbing capabilities in the range of given sound pressure level, the sound pressure level scope that microperforated panel soundabsorbing construction can be applied effectively is widened significantly by realizing effective suppression to the nonlinear effect of microperforated panel soundabsorbing construction under high sound intensity.
Description
Technical field
The present invention relates to a kind of Design method of structural parameters for suppressing microperforated panel nonlinear effect, sqouynd absorption lowering noise technology neck
Domain.
Background technology
Microperforated panel soundabsorbing construction has the advantages that cleaning, light weight, protection against the tide, high temperature resistant, sheet material diversity, is described as 21 generation
The environmental protection sound-absorbing material of discipline most attraction.Microperforated panel soundabsorbing construction be by China's acoustics authority's Ma Dayou teach in
Propose that, by the development of decades, (sound pressure level SPL is general under compared with low sound pressure levels linear conditions for microperforated panel structure within 1975
It is even more small less than 100dB) acoustic impedance theoretical model and correlation acoustics design it is theoretical quite perfect, but in tool
Under the application environment for having high intensity sound field, such as aero-engine, launching silo, the acoustic impedance of microperforated panel structure will be relied on
In incident sound pressure level, strong nonlinear effect is shown, now its acoustic impedance includes two parts, and a part is linear acoustic resistance
Anti-, another part is the nonlinear acoustic impedance caused by nonlinear effect.Linear acoustic impedance is unrelated with sound pressure level, can be using linear
Under the conditions of ripe acoustic impedance calculation formula accurately calculated, therefore set up the accurate acoustic resistance of microperforated panel structure under high sound intensity
The key of anti-model is the accurate acquisition of nonlinear acoustic impedance.Therefore, scholars are doing unremitting effort always, but it is sorry
, so far, the nonlinear acoustic impedance model on microperforated panel structure is substantially a kind of semiempirical, also no public affairs
The model or method recognized can be precisely calculated and be predicted to it.Entangle itself main reason is that, non-linear sound absorbing mechanism
It is that sound whirlpool energy caused by nose end jet and vortex shedding is changed, because sound whirlpool energy changes the complexity of this physical process,
The possibility for obtaining accurate acoustic impedance theoretical model under high sound intensity is blocked.Nonlinear effect not only makes microperforated panel structure
Perfect acoustic impedance theoretical model and acoustics design are theoretical no longer suitable under the conditions of linear, also result in the decline of its sound absorbing capabilities
And the problems such as be difficult to set up accurate acoustic impedance theoretical model.Because microperforated panel provides enough linear sound in itself
Resistance, if along with nonlinear acoustic resistance, sound absorbing capabilities can be caused to decline on the contrary.Although lot of domestic and foreign scholar is linear by reduction
Acoustic resistance, high sound pressure level can be extended to by the application of microperforated panel structure and (such as use aperture by being played a leading role using nonlinear acoustic resistance
Conventional punch plate more than 1mm), but this method does not solve the applicable sound pressure level scope of microperforated panel structure fundamentally
The problem of being limited to by nonlinear effect.Because nonlinear acoustic impedance can change with the change of sound pressure level size, thus be difficult
Pervasive design is carried out for different sound pressure levels.These all bring limitation to effective utilize of nonlinear effect.
Research shows, the acoustic impedance of microperforated panel structure can undergo one from linear stage to non-with the increase of sound pressure level
The transformation of linear stage, and one specific sound pressure level of correspondence at transformation, can be referred to as critical sound pressure level, it is non-linear
The critical condition that acoustic impedance is functioned to.If effective suppression to nonlinear effect can be realized, that is, improve critical acoustic pressure
The size of level, makes it have linear acoustical absorptivity, the then sound that can not only effectively apply microperforated panel below critical sound pressure level
Scope of arbitrarily downgrading is widened to high sound intensity, moreover it is possible to which perfect acoustics design is theoretical under application linear conditions is carried out accurately to its sound absorption characteristics
Prediction and required design.Such a method reduces linear acoustic resistance as far as possible with existing, and its application is expanded extremely by nonlinear acoustic impedance
The method of high sound intensity has the difference of essence, and there is not been reported.
The content of the invention
Purpose：The problem of being limited to for application of the microperforated panel soundabsorbing construction under high sound intensity by nonlinear effect, this hair
It is bright that a kind of method for suppressing microperforated panel nonlinear effect by design of Structural Parameters is provided, worn by realizing to micro- under high sound intensity
Effective suppression of the nonlinear effect of soundabsorbing construction, makes it have good linear sound absorption in the range of given sound pressure level
Performance, widens the sound pressure level scope that microperforated panel soundabsorbing construction can be applied effectively significantly.
Technical scheme：A kind of Design method of structural parameters for suppressing microperforated panel nonlinear effect, comprises the following steps：
Step one：Frequency spectrum and sound pressure level analysis are carried out to loud intensity Sound Field, according to the frequency domain distribution situation of noise energy,
Specify the linear sound pressure level scope and maximum noise reduction Frequency point of the desired work of microperforated panel, so determine restrictive condition parameter with
And parameter to be designed, it is known that parameter includes：
P0：The maximum sound pressure level of microperforated panel working environment, unit is dB；
f0：Noise under the maximum noise reduction Frequency point of microperforated panel, i.e. resonant frequency, this frequency is maximum, and unit is Hz；
Parameter to be designed：
d:The penetration hole diameter of microperforated panel, unit is m；
t/d:Dimensionless group, represents the draw ratio of microperforated panel, t is thickness of slab, and unit is m；
σ：The punching rate of microperforated panel, dimensionless group；
Step 2：One group of { d, t/d } parameter is chosen, d is less than 0.2 × 10-3M, t/d are more than 1.
Step 3：{ d, the t/d } parameter selected according to step 2, substitutes into formula (1) and calculates corresponding punching rate σ：
Wherein,Dimensionless variable, thus obtains parameter combination { d, t/d, σ }
Step 4：Parameter combination { d, t/d, σ } and known parameters f in step 30, draw micro- by numerical simulation
Perforated plate structure-borne sound impedance Z is with incident sound pressure level PiThe curve of change, wherein, PiIt is incident sound pressure PiiBe converted in units of dB
Expression, acoustic impedance Z and incident sound pressure P under high sound intensityiiBasic relational expression be：
Wherein,
X/ρ0c0=ω H/ σ c0-cot(ωLc/c0) (4)
In above-mentioned formula (2)~(4), Z is microperforated panel structure acoustic impedance, and unit is MKS rayls；RL is linear sound
Resistance, unit is MKS rayls；X is acoustic reactance, and unit is MKS rayls；PiiIt is incident sound pressure, unit is Pa；ρ0It is that air is close
Degree, unit is kg/m3；c0It is the velocity of sound in air, unit is m；The π f of ω=2 are angular frequencies, and unit is rad/s, and v is that motion is viscous
Stagnant coefficient；Unit is m2/ s, CDIt is discharge coefficient, expression is：
Wherein,
In the formula of above-mentioned (5)~(20), PpKUnit be Pa, deUnit be m, other parameters are dimensionless group.
KssIt is static viscous loss parameter, is dimensionless group：
Kss=13+10.23 (t/d)-1.44 (21)
KacIt is the viscous loss parameter of sound, is dimensionless group：
Kac=3+2.32 (t/d)-1 (22)
H is inertia length parameter：
κH=13.06 [1-exp (- 64.9 (t/d)4.365)] (25)
aH=0.725 (t/d)-1.227,bH=1.02 (t/d)-1.411, mH=3.42exp (- 0.117 (t/d)) (28)
In the formula of above-mentioned (23)~(28), H and HresUnit be m, remaining parameter being newly related to is dimensionless group；
During resonance：
Lc=(c0/2πf0)arccot(2πf0H/σc0) (29)；
Wherein, LcIt is cavity depth, unit is m；
Step 5：Microperforated panel structure-borne sound impedance Z is with incident sound pressure level P in observation of steps fouriThe curve of change, is obtained non-
The transformation sound pressure level that linear acoustic impedance is functioned to, i.e., critical sound pressure level Pt, unit is dB, if P0≤Pt, illustrate selected set
The nonlinear effect that meter parameter meets microperforated panel structure suppresses, if P0>Pt, illustrate that selected design parameter is unsatisfactory for, now,
Reduce aperture d or increase t/d, be then back to step 3, the structural parameters of nonlinear effect can be realized until obtaining.
Beneficial effect：The present invention uses a kind of method for suppressing microperforated panel nonlinear effect by design of Structural Parameters,
The application for overcoming microperforated panel soundabsorbing construction under high sound intensity is limited to by nonlinear effect, by according to actual noise feelings
Condition, determines maximum sound pressure level P0With maximum noise reduction Frequency point f0, can be designed that the micropunch for realizing that nonlinear effect effectively suppresses
Plate structural parameters, make it have good linear sound absorbing capabilities under high sound intensity.Produced with existing utilization nonlinear effect non-
Linear acoustic impedance carries out sqouynd absorption lowering noise and compared, and sound absorbing capabilities of the invention, thus will not be by incidence independent of nonlinear acoustic impedance
The influence of sound pressure level, sound sucting band is wider, and applicable sound pressure level scope is wider.
Brief description of the drawings
Fig. 1 is microperforated panel soundabsorbing construction Parameter Map；
Fig. 2 is the Design method of structural parameters particular flow sheet for suppressing microperforated panel nonlinear effect；
Fig. 3 is acoustic impedance in embodiment 1 with incident sound pressure level change curve；
Fig. 4 is the 1st group of corresponding acoustic impedance of parameter combination in embodiment 2 with incident sound pressure level change curve；
Fig. 5 is the 2nd group of corresponding acoustic impedance of parameter combination in embodiment 2 with incident sound pressure level change curve；
Fig. 6 is the 3rd group of corresponding acoustic impedance of parameter combination in embodiment 2 with incident sound pressure level change curve；
Embodiment
In order that those skilled in the art more fully understand the technical scheme in the application, it is real below in conjunction with the application
The accompanying drawing in example is applied, the technical scheme in the embodiment of the present application is clearly and completely described, it is clear that described implementation
Example only some embodiments of the present application, rather than whole embodiments.Based on the embodiment in the application, this area is common
The every other embodiment that technical staff is obtained under the premise of creative work is not made, should all belong to the application protection
Scope.
As shown in figs. 1 to 6, a kind of Design method of structural parameters for suppressing microperforated panel nonlinear effect, including following step
Suddenly：
Step one：Frequency spectrum and sound pressure level analysis are carried out to loud intensity Sound Field, according to the frequency domain distribution situation of noise energy,
Specify the linear sound pressure level scope and maximum noise reduction Frequency point of the desired work of microperforated panel, so determine restrictive condition parameter with
And parameter to be designed, it is known that parameter includes：
P0：The maximum sound pressure level of microperforated panel working environment, by design of Structural Parameters, sound pressure level P is met as long as realizingt<
P0When, the linear response of microperforated panel plays a leading role, and nonlinear effect can be ignored, and unit is dB；
f0：Noise under the maximum noise reduction Frequency point of microperforated panel, i.e. resonant frequency, this frequency is maximum, and unit is Hz；
Parameter to be designed：
d:The penetration hole diameter of microperforated panel, unit is m；
t/d:Dimensionless group, represents the draw ratio of microperforated panel, t is thickness of slab, and unit is m；
σ：The punching rate of microperforated panel, dimensionless group；
Step 2：One group of { d, t/d } parameter is chosen, d is less than 0.2 × 10-3M, t/d are more than 1.
Step 3：{ d, the t/d } parameter selected according to step 2, substitutes into formula (1) and calculates corresponding punching rate σ：
Wherein,Dimensionless variable, thus obtains parameter combination { d, t/d, σ }
Step 4：Parameter combination { d, t/d, σ } and known parameters f in step 30, draw micro- by numerical simulation
Perforated plate structure-borne sound impedance Z is with incident sound pressure level PiThe curve of change, wherein, PiIt is incident sound pressure PiiBe converted in units of dB
Expression, acoustic impedance Z and incident sound pressure P under high sound intensityiiBasic relational expression be：
Wherein,
X/ρ0c0=ω H/ σ c0-cot(ωLc/c0) (4)
In above-mentioned formula (2)~(4), Z is microperforated panel structure acoustic impedance, and unit is MKS rayls；RL is linear sound
Resistance, unit is MKS rayls；X is acoustic reactance, and unit is MKS rayls；PiiIt is incident sound pressure, unit is Pa；ρ0It is that air is close
Degree, unit is kg/m3；c0It is the velocity of sound in air, unit is m；The π f of ω=2 are angular frequencies, and unit is rad/s, and v is that motion is viscous
Stagnant coefficient；Unit is m2/ s, CDIt is discharge coefficient, expression is：
Wherein,
af=0.785-0.76 (1-e-3.63t/d),bf=3.63 (t/d)0.6 (18)
In the formula of above-mentioned (5)~(20), PpKUnit be Pa, deUnit be m, other parameters are dimensionless group.
KssIt is static viscous loss parameter, is dimensionless group：
Kss=13+10.23 (t/d)-1.44 (21)
KacIt is the viscous loss parameter of sound, is dimensionless group：
Kac=3+2.32 (t/d)-1 (22)
H is inertia length parameter：
κH=13.06 [1-exp (- 64.9 (t/d)4.365)] (25)
aH=0.725 (t/d)-1.227,bH=1.02 (t/d)-1.411, mH=3.42exp (- 0.117 (t/d)) (28)
In the formula of above-mentioned (23)~(28), H and HresUnit be m, remaining parameter being newly related to is dimensionless group；
During resonance：
Lc=(c0/2πf0)arccot(2πf0H/σc0) (29)；
Wherein, LcIt is cavity depth, unit is m；
Step 5：Microperforated panel structure-borne sound impedance Z is with incident sound pressure level P in observation of steps fouriThe curve of change, is obtained non-
The transformation sound pressure level that linear acoustic impedance is functioned to, i.e., critical sound pressure level Pt, unit is dB, if P0≤Pt, illustrate selected set
The nonlinear effect that meter parameter meets microperforated panel structure suppresses, if P0>Pt, illustrate that selected design parameter is unsatisfactory for, now,
Reduce aperture d or increase t/d, be then back to step 3, the structural parameters of nonlinear effect can be realized until obtaining.
Embodiment 1：The non-linear porous plate acoustic adsorption device structural parameters for being suppressed to 110dB are realized in design.
First, in step one, frequency spectrum is carried out to loud intensity Sound Field and sound pressure level is analyzed, actual noise environment is determined
Maximum sound pressure level is P0=110dB and maximum noise reduction Frequency point are f0=2000Hz；
Subsequently, as 110dB is moderate, considers from cost of manufacture, can first select larger aperture and smaller punching rate.Therefore first
Choose d=0.5 × 10-3M, t/d=1, calculate according to formula (1) and obtain punching rate σ=0.0084；
Then, known parameters are substituted into formula (2)~(28) and obtains cavity depth Lc=0.0032m and acoustic impedance are with entering
The curve of sound pressure level is penetrated, as shown in Figure 3.Observe Fig. 3, it can be seen that the transformation sound pressure level that nonlinear acoustic impedance is functioned to,
I.e. critical sound pressure level Pt=115dB.
Then, the maximum sound pressure level P of noise reduction needed for comparing actual noise environment0With the P of critical sound pressure leveltSize, P0<
Pt, therefore designed microperforated panel structural parameters meet requirement.
Embodiment 2：The non-linear porous plate acoustic adsorption device structural parameters for being suppressed to 140dB are realized in design.
First, in step one, frequency spectrum is carried out to loud intensity Sound Field and sound pressure level is analyzed, actual noise environment is determined
Maximum sound pressure level is P0=140dB and maximum noise reduction Frequency point are f0=3000Hz；
Subsequently, as 140dB is larger, can be first from smaller aperture due and smaller punching rate.Therefore d=0.1 × 10 are first chosen-3M,
T/d=4, calculates according to formula (1) and obtains punching rate σ=0.066；
Then, known parameters are substituted into formula (2)~(28) and obtains cavity depth Lc=0.0218m and acoustic impedance are with entering
The curve of sound pressure level is penetrated, as shown in Figure 4.Observe Fig. 4, it can be seen that the transformation sound pressure level that nonlinear acoustic impedance is functioned to,
I.e. critical sound pressure level Pt=125dB.
Then, the maximum sound pressure level P of noise reduction needed for comparing actual noise environment0With the P of critical sound pressure leveltSize, P0>
Pt, therefore designed microperforated panel structural parameters are unsatisfactory for requirement, repeat step three；
Because the part of the non-linear partial in total acoustic impedance is inversely proportional to 1/d and t/d, therefore reduces aperture d or improve plate
Thick t.Assuming that keeping aperture d constant, t/d=6 is improved, is now calculated according to formula (1) and obtains punching rate σ=0.0967；
Then, known parameters are substituted into formula (2)~(28) and obtains cavity depth Lc=0.022m and acoustic impedance are with entering
The curve of sound pressure level is penetrated, as shown in Figure 5.Observe Fig. 5, it can be seen that the transformation sound pressure level that nonlinear acoustic impedance is functioned to,
I.e. critical sound pressure level Pt=135dB；
Then, the maximum sound pressure level P of noise reduction needed for comparing actual noise environment0With the P of critical sound pressure leveltSize, P0>
Pt, therefore designed microperforated panel structural parameters are unsatisfactory for requirement, continue repeat step three；
Assuming that continuing to reduce aperture d to 0.8 × 10-2M, now t/d=7.5 according to formula (1) calculate obtain punching rate σ=
0.1464。
Then, known parameters are substituted into formula (2)~(28) and obtains cavity depth Lc=0.024m and acoustic impedance are with entering
The curve of sound pressure level is penetrated, as shown in Figure 6.Observe Fig. 6, it can be seen that the transformation sound pressure level that nonlinear acoustic impedance is functioned to,
I.e. critical sound pressure level Pt=140dB；
Then, the maximum sound pressure level P of noise reduction needed for comparing actual noise environment0With the P of critical sound pressure leveltSize, P0≤
Pt, therefore designed microperforated panel structural parameters meet requirement.
The foregoing description of the disclosed embodiments, enables professional and technical personnel in the field to realize or using the present invention.
A variety of modifications to these embodiments will be apparent for those skilled in the art, as defined herein
General Principle can be realized in other embodiments without departing from the spirit or scope of the present invention.Therefore, it is of the invention
The embodiments shown herein is not intended to be limited to, and is to fit to and principles disclosed herein and features of novelty phase one
The most wide scope caused.
Claims (1)
1. a kind of Design method of structural parameters for suppressing microperforated panel nonlinear effect, it is characterised in that comprise the following steps：
Step one：Frequency spectrum and sound pressure level analysis are carried out to loud intensity Sound Field, according to the frequency domain distribution situation of noise energy, clearly
The linear sound pressure level scope and maximum noise reduction Frequency point of the desired work of microperforated panel, and then determine restrictive condition parameter and treat
Design parameter, it is known that parameter includes：
P0：The maximum sound pressure level of microperforated panel working environment, unit is dB；
f0：Noise under the maximum noise reduction Frequency point of microperforated panel, i.e. resonant frequency, this frequency is maximum, and unit is Hz；
Parameter to be designed：
d:The penetration hole diameter of microperforated panel, unit is m；
t/d:Dimensionless group, represents the draw ratio of microperforated panel, t is thickness of slab, and unit is m；
σ：The punching rate of microperforated panel, dimensionless group；
Step 2：One group of { d, t/d } parameter is chosen, d is less than 0.2 × 10-3M, t/d are more than 1.
Step 3：{ d, the t/d } parameter selected according to step 2, substitutes into formula (1) and calculates corresponding punching rate σ：
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Step 4：Parameter combination { d, t/d, σ } and known parameters f in step 30, micropunch is drawn by numerical simulation
Hardened structure acoustic impedance Z is with incident sound pressure level PiThe curve of change, wherein, PiIt is incident sound pressure PiiBe converted to the table in units of dB
Show, acoustic impedance Z and incident sound pressure P under high sound intensityiiBasic relational expression be：
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<mn>2</mn>
</msup>
</mrow>
</msqrt>
<mo>+</mo>
<msub>
<mi>R</mi>
<mi>L</mi>
</msub>
<mo>/</mo>
<mn>2</mn>
<msub>
<mi>&rho;</mi>
<mn>0</mn>
</msub>
<msub>
<mi>c</mi>
<mn>0</mn>
</msub>
<mo>+</mo>
<mi>j</mi>
<mrow>
<mo>(</mo>
<mi>X</mi>
<mo>/</mo>
<msub>
<mi>&rho;</mi>
<mn>0</mn>
</msub>
<msub>
<mi>c</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein,
<mrow>
<msub>
<mi>R</mi>
<mi>L</mi>
</msub>
<mo>/</mo>
<msub>
<mi>&rho;</mi>
<mn>0</mn>
</msub>
<msub>
<mi>c</mi>
<mn>0</mn>
</msub>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>/</mo>
<mi>&sigma;</mi>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mi>v</mi>
<mo>/</mo>
<msub>
<mi>c</mi>
<mn>0</mn>
</msub>
<mi>d</mi>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>/</mo>
<mi>d</mi>
<mo>)</mo>
</mrow>
<mo>&lsqb;</mo>
<msub>
<mi>K</mi>
<mrow>
<mi>S</mi>
<mi>S</mi>
</mrow>
</msub>
<mo>+</mo>
<msqrt>
<mrow>
<mo>(</mo>
<msup>
<mi>&omega;d</mi>
<mn>2</mn>
</msup>
<mo>/</mo>
<mi>v</mi>
<mo>)</mo>
</mrow>
</msqrt>
<msub>
<mi>K</mi>
<mrow>
<mi>a</mi>
<mi>c</mi>
</mrow>
</msub>
<mo>&rsqb;</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
</mrow>
X/ρ0c0=ω H/ σ c0-cot(ωLc/c0) (4)
In above-mentioned formula (2)~(4), Z is microperforated panel structure acoustic impedance, and unit is MKS rayls；RL is linear acoustic resistance, single
Position is MKS rayls；X is acoustic reactance, and unit is MKS rayls；PiiIt is incident sound pressure, unit is Pa；ρ0It is atmospheric density, unit
For kg/m3；c0It is the velocity of sound in air, unit is m；The π f of ω=2 are angular frequencies, and unit is rad/s, and v is kinematic coefficient of viscosity；
Unit is m2/ s, CDIt is discharge coefficient, expression is：
<mrow>
<msub>
<mi>C</mi>
<mi>D</mi>
</msub>
<mo>=</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>C</mi>
<mrow>
<mi>D</mi>
<mi>r</mi>
<mi>e</mi>
<mi>s</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>a</mi>
<msub>
<mi>C</mi>
<mi>D</mi>
</msub>
</msub>
<msubsup>
<mi>f</mi>
<mrow>
<mi>n</mi>
<mi>o</mi>
<mi>n</mi>
</mrow>
<mn>2</mn>
</msubsup>
<mo>)</mo>
</mrow>
<mo>/</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>b</mi>
<msub>
<mi>C</mi>
<mi>D</mi>
</msub>
</msub>
<msubsup>
<mi>f</mi>
<mrow>
<mi>n</mi>
<mi>o</mi>
<mi>n</mi>
</mrow>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msub>
<mi>a</mi>
<msub>
<mi>C</mi>
<mi>D</mi>
</msub>
</msub>
<msubsup>
<mi>f</mi>
<mrow>
<mi>n</mi>
<mi>o</mi>
<mi>n</mi>
</mrow>
<mn>2</mn>
</msubsup>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein,
<mrow>
<msub>
<mi>C</mi>
<mrow>
<mi>D</mi>
<mi>r</mi>
<mi>e</mi>
<mi>s</mi>
</mrow>
</msub>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>a</mi>
<msub>
<mi>C</mi>
<mrow>
<mi>D</mi>
<mi>r</mi>
<mi>e</mi>
<mi>s</mi>
</mrow>
</msub>
</msub>
<msubsup>
<mi>V</mi>
<mrow>
<mi>n</mi>
<mi>o</mi>
<mi>n</mi>
</mrow>
<mn>2</mn>
</msubsup>
<mo>)</mo>
</mrow>
<mo>/</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>b</mi>
<msub>
<mi>C</mi>
<mrow>
<mi>D</mi>
<mi>r</mi>
<mi>e</mi>
<mi>s</mi>
</mrow>
</msub>
</msub>
<msubsup>
<mi>V</mi>
<mrow>
<mi>n</mi>
<mi>o</mi>
<mi>n</mi>
</mrow>
<mn>2</mn>
</msubsup>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>6</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>a</mi>
<msub>
<mi>C</mi>
<mrow>
<mi>D</mi>
<mi>r</mi>
<mi>e</mi>
<mi>s</mi>
</mrow>
</msub>
</msub>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<mn>110.5</mn>
<msup>
<mi>e</mi>
<mrow>
<mn>0.647</mn>
<mi>t</mi>
<mo>/</mo>
<mi>d</mi>
</mrow>
</msup>
<mo>)</mo>
</mrow>
<mo>/</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<mn>0.109</mn>
<msup>
<mi>e</mi>
<mrow>
<mn>0.647</mn>
<mi>t</mi>
<mo>/</mo>
<mi>d</mi>
</mrow>
</msup>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>7</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>b</mi>
<msub>
<mi>C</mi>
<mrow>
<mi>D</mi>
<mi>r</mi>
<mi>e</mi>
<mi>s</mi>
</mrow>
</msub>
</msub>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<mn>168.5</mn>
<msup>
<mi>e</mi>
<mrow>
<mn>0.647</mn>
<mi>t</mi>
<mo>/</mo>
<mi>d</mi>
</mrow>
</msup>
<mo>)</mo>
</mrow>
<mo>/</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<mn>0.109</mn>
<msup>
<mi>e</mi>
<mrow>
<mn>0.647</mn>
<mi>t</mi>
<mo>/</mo>
<mi>d</mi>
</mrow>
</msup>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>8</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>a</mi>
<msub>
<mi>C</mi>
<mi>D</mi>
</msub>
</msub>
<mo>=</mo>
<msub>
<mi>a</mi>
<mrow>
<mn>1</mn>
<msub>
<mi>C</mi>
<mi>D</mi>
</msub>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>a</mi>
<mrow>
<mn>2</mn>
<msub>
<mi>C</mi>
<mi>D</mi>
</msub>
</mrow>
</msub>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<msub>
<mi>a</mi>
<mrow>
<mn>3</mn>
<msub>
<mi>C</mi>
<mi>D</mi>
</msub>
</mrow>
</msub>
<msub>
<mi>V</mi>
<mrow>
<mi>n</mi>
<mi>o</mi>
<mi>n</mi>
</mrow>
</msub>
</mrow>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>9</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>a</mi>
<mrow>
<mn>1</mn>
<msub>
<mi>C</mi>
<mi>D</mi>
</msub>
</mrow>
</msub>
<mo>=</mo>
<mn>18.81</mn>
<mi>t</mi>
<mo>/</mo>
<mi>d</mi>
<mo>-</mo>
<mn>57.11</mn>
<msqrt>
<mrow>
<mi>t</mi>
<mo>/</mo>
<mi>d</mi>
</mrow>
</msqrt>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<mn>0.18</mn>
<mi>t</mi>
<mo>/</mo>
<mi>d</mi>
</mrow>
</msup>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>a</mi>
<mrow>
<mn>2</mn>
<msub>
<mi>C</mi>
<mi>D</mi>
</msub>
</mrow>
</msub>
<mo>=</mo>
<mi>exp</mi>
<mo>&lsqb;</mo>
<mo>(</mo>
<mn>33.5</mn>
<mi>h</mi>
<mo>/</mo>
<mi>d</mi>
<mo>-</mo>
<mn>78</mn>
<msup>
<mrow>
<mo>(</mo>
<mi>h</mi>
<mo>/</mo>
<mi>d</mi>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<mn>131</mn>
<msup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>/</mo>
<mi>d</mi>
<mo>)</mo>
</mrow>
<mn>3</mn>
</msup>
<mo>+</mo>
<mn>917</mn>
<msup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>/</mo>
<mi>d</mi>
<mo>)</mo>
</mrow>
<mn>4</mn>
</msup>
<mo>&rsqb;</mo>
<mo>/</mo>
<mo>&lsqb;</mo>
<mn>1</mn>
<mo>+</mo>
<mn>148</mn>
<msup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>/</mo>
<mi>d</mi>
<mo>)</mo>
</mrow>
<mn>4</mn>
</msup>
<mo>&rsqb;</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>11</mn>
<mo>)</mo>
</mrow>
</mrow>
1
<mrow>
<msub>
<mi>a</mi>
<mrow>
<mn>3</mn>
<msub>
<mi>C</mi>
<mi>D</mi>
</msub>
</mrow>
</msub>
<mo>=</mo>
<mn>43.2</mn>
<mi>t</mi>
<mo>/</mo>
<mi>d</mi>
<mo>-</mo>
<mn>147.1</mn>
<msqrt>
<mrow>
<mi>t</mi>
<mo>/</mo>
<mi>d</mi>
</mrow>
</msqrt>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<mn>0.19</mn>
<mi>t</mi>
<mo>/</mo>
<mi>d</mi>
</mrow>
</msup>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>b</mi>
<msub>
<mi>C</mi>
<mi>D</mi>
</msub>
</msub>
<mo>=</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>b</mi>
<mrow>
<mn>1</mn>
<msub>
<mi>C</mi>
<mi>D</mi>
</msub>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>b</mi>
<mrow>
<mn>2</mn>
<msub>
<mi>C</mi>
<mi>D</mi>
</msub>
</mrow>
</msub>
<msub>
<mi>V</mi>
<mrow>
<mi>n</mi>
<mi>o</mi>
<mi>n</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>/</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>b</mi>
<mrow>
<mn>3</mn>
<msub>
<mi>C</mi>
<mi>D</mi>
</msub>
</mrow>
</msub>
<msub>
<mi>V</mi>
<mrow>
<mi>n</mi>
<mi>o</mi>
<mi>n</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>13</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>b</mi>
<mrow>
<mn>1</mn>
<msub>
<mi>C</mi>
<mi>D</mi>
</msub>
</mrow>
</msub>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mn>3.44</mn>
<mo>-</mo>
<mn>0.182</mn>
<mi>t</mi>
<mo>/</mo>
<mi>d</mi>
<mo>)</mo>
</mrow>
<mo>/</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<mn>0.342</mn>
<mi>t</mi>
<mo>/</mo>
<mi>d</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>14</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>b</mi>
<mrow>
<mn>2</mn>
<msub>
<mi>C</mi>
<mi>D</mi>
</msub>
</mrow>
</msub>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mn>18.23</mn>
<mo>+</mo>
<mn>1.33</mn>
<mi>t</mi>
<mo>/</mo>
<mi>d</mi>
<mo>)</mo>
</mrow>
<mo>/</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<mn>0.151</mn>
<mi>t</mi>
<mo>/</mo>
<mi>d</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>15</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>b</mi>
<mrow>
<mn>3</mn>
<msub>
<mi>C</mi>
<mi>D</mi>
</msub>
</mrow>
</msub>
<mo>=</mo>
<mn>38</mn>
<mo>/</mo>
<mo>&lsqb;</mo>
<mn>1</mn>
<mo>+</mo>
<mn>1.3</mn>
<mo>&times;</mo>
<msup>
<mn>10</mn>
<mrow>
<mo>-</mo>
<mn>7</mn>
</mrow>
</msup>
<msup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>/</mo>
<mi>d</mi>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>&rsqb;</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>16</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>f</mi>
<mrow>
<mi>n</mi>
<mi>o</mi>
<mi>n</mi>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>f</mi>
<mrow>
<mi>N</mi>
<mi>L</mi>
</mrow>
</msub>
<mo>/</mo>
<mi>f</mi>
<mo>-</mo>
<mn>1</mn>
<mo>,</mo>
<msub>
<mi>f</mi>
<mrow>
<mi>N</mi>
<mi>L</mi>
</mrow>
</msub>
<mo>/</mo>
<mi>f</mi>
<mo>=</mo>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>a</mi>
<mi>f</mi>
</msub>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<msub>
<mi>b</mi>
<mi>f</mi>
</msub>
<msubsup>
<mi>V</mi>
<mrow>
<mi>n</mi>
<mi>o</mi>
<mi>n</mi>
</mrow>
<mn>2</mn>
</msubsup>
</mrow>
</msup>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>17</mn>
<mo>)</mo>
</mrow>
</mrow>
af=0.785-0.76 (1-e-3.63t/d),bf=3.63 (t/d)0.6 (18)
<mrow>
<msub>
<mi>V</mi>
<mrow>
<mi>n</mi>
<mi>o</mi>
<mi>n</mi>
</mrow>
</msub>
<mo>=</mo>
<msqrt>
<mrow>
<msub>
<mi>P</mi>
<mrow>
<mi>p</mi>
<mi>K</mi>
</mrow>
</msub>
<mo>/</mo>
<msub>
<mi>&rho;</mi>
<mn>0</mn>
</msub>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>&omega;d</mi>
<mi>e</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
<mo>,</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>p</mi>
<mi>K</mi>
</mrow>
</msub>
<mo>=</mo>
<msqrt>
<mn>2</mn>
</msqrt>
<msub>
<mi>P</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>19</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>d</mi>
<mi>e</mi>
</msub>
<mo>=</mo>
<mi>t</mi>
<mo>+</mo>
<mn>0.85</mn>
<mi>d</mi>
<mo>/</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<mn>1.25</mn>
<msqrt>
<mi>&sigma;</mi>
</msqrt>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>20</mn>
<mo>)</mo>
</mrow>
</mrow>
In the formula of above-mentioned (5)~(20), PpKUnit be Pa, deUnit be m, other parameters are dimensionless group.
KssIt is static viscous loss parameter, is dimensionless group：
Kss=13+10.23 (t/d)-1.44 (21)
KacIt is the viscous loss parameter of sound, is dimensionless group：
Kac=3+2.32 (t/d)-1 (22)
H is inertia length parameter：
<mrow>
<mi>H</mi>
<mo>/</mo>
<msub>
<mi>d</mi>
<mi>e</mi>
</msub>
<mo>=</mo>
<mn>1</mn>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<msub>
<mi>H</mi>
<mrow>
<mi>r</mi>
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κH=13.06 [1-exp (- 64.9 (t/d)4.365)] (25)
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aH=0.725 (t/d)-1.227,bH=1.02 (t/d)-1.411, mH=3.42exp (- 0.117 (t/d)) (28)
In the formula of above-mentioned (23)~(28), H and HresUnit be m, remaining parameter being newly related to is dimensionless group；
During resonance：
Lc=(c0/2πf0)arccot(2πf0H/σc0) (29)；
Wherein, LcIt is cavity depth, unit is m；
Step 5：Microperforated panel structure-borne sound impedance Z is with incident sound pressure level P in observation of steps fouriThe curve of change, is obtained non-linear
The transformation sound pressure level that acoustic impedance is functioned to, i.e., critical sound pressure level Pt, unit is dB, if P0≤Pt, illustrate selected design ginseng
The nonlinear effect that number meets microperforated panel structure suppresses, if P0>Pt, illustrate that selected design parameter is unsatisfactory for, now, reduce
Aperture d or increase t/d, is then back to step 3, the structural parameters of nonlinear effect can be realized until obtaining.
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| CN111581734A (en) * | 2020-05-22 | 2020-08-25 | 中国航空工业集团公司西安飞机设计研究所 | Method for designing turbofan engine nacelle perforation sound absorption structure |
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