CN109300464A - A kind of design method of gradual change section low frequency absorption body - Google Patents

A kind of design method of gradual change section low frequency absorption body Download PDF

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CN109300464A
CN109300464A CN201811340120.0A CN201811340120A CN109300464A CN 109300464 A CN109300464 A CN 109300464A CN 201811340120 A CN201811340120 A CN 201811340120A CN 109300464 A CN109300464 A CN 109300464A
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sound
gradual change
sound absorber
frequency
absorption
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CN109300464B (en
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郭霞生
申雨晨
杨嫣烨
章东
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Nanjing University
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Nanjing University
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    • GPHYSICS
    • G10MUSICAL INSTRUMENTS; ACOUSTICS
    • G10KSOUND-PRODUCING DEVICES; METHODS OR DEVICES FOR PROTECTING AGAINST, OR FOR DAMPING, NOISE OR OTHER ACOUSTIC WAVES IN GENERAL; ACOUSTICS NOT OTHERWISE PROVIDED FOR
    • G10K11/00Methods or devices for transmitting, conducting or directing sound in general; Methods or devices for protecting against, or for damping, noise or other acoustic waves in general
    • G10K11/16Methods or devices for protecting against, or for damping, noise or other acoustic waves in general
    • G10K11/172Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using resonance effects

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Abstract

The invention discloses a kind of design methods of gradual change section low frequency absorption body, by constructing the gradual change cross section structure of space folding, stick the absorption low-frequency sound wave that effect enables the sound absorber potent using mesomerism and air heat.Relative to traditional uniform channel sound absorber, the sound absorber of this method building can reach lower sound absorption frequency under same volume, and can change sound absorption frequency under conditions of not changing shape.By installing the different sound absorber of multiple peak values sound absorption frequencies side by side, the sound absorption of the broad band low frequency under sub-wavelength dimensions is may be implemented in the present invention.To sum up, the characteristics of sound absorber of the method for the present invention building has structure simple, and difficulty of processing is low and is easily installed use.

Description

A kind of design method of gradual change section low frequency absorption body
Technical field
The invention belongs to noise controls and architectural acoustics field, are related to a kind of design method of low frequency absorption body, more specifically Ground is said, a kind of method for sticking the potent absorption low-frequency sound wave of effect with air heat using grading structure resonance is related to.
Background technique
Noise on human class and the production and living of the mankind have very big negative effect, and continual noise may be different Influence to degree the sense of hearing and nervous system of people.For many years, many related noise reduction technologies come out one after another, in passive technology Have the technologies such as conventional porous sound-absorbing material and microperforated panel in field, but due in the case of long wavelength sound energy loss it is weaker, to decline Subtract the energy of low-frequency sound wave (< 500Hz), their thickness will reach with the comparable size of wavelength, which has limited this kind of sound absorptions The use scope of body;In active technique field, can effectively be controlled using active noise controlling as a series of technologies of representative low Frequency sound wave, but this technology principle is complex and higher cost, do not popularized all the time.
In recent years, the material with resonance characteristics is found to effectively realize better low frequency with sub-wavelength thickness Sound absorption, people realize this target by constructing various resonance absorbers.The decorating film being such as widely studied Resonating body [Mei, J., et al., Nat.Commun.3 (2): 756], it is made of soft film class and additional small mass block, Can realize good sound absorption in the frequency range of 100Hz~1000Hz, but it is prestressed additional in process and Being adhered for decorative quality is complex, increases the difficulty of actual production manufacture.In contrast, Helmholtz resonator is folded [Cai, X., et al.Applied Physics Letters, 105 (12): 1901] with fold Fabry-P é rot sound absorber [Zhang, C.and X.Hu, Phys.Rev.applied.6 (6)] structure is more simple, and only passes through 3D printer Processing and manufacturing, but what the class formation used at present is uniform channel, it is caused not realize using space effectively The sound absorption of more low frequency, and inevitably will lead to when changing the sound absorption frequency of this kind of sound absorber the change of its shape, This is a urgent problem to be solved in actual installation.
Summary of the invention
Technical problem: the present invention provides a kind of gradual change section low frequency suction that easy mode realizes low frequency with broadband sound absorption The design method of sound body.
Technical solution: the design method of gradual change section low frequency absorption body of the invention, comprising the following steps:
Step 1: first by the noise frequency f in measurement environment to determine sound absorber sound absorption frequency;
Step 2: according to the gradual change section sound absorber of the corresponding sound absorption frequency of noise frequency f design of step 1 measurement, Specific steps include:
(1) type of fade that proposed adoption is determined according to actual processing precision and sound absorption frequency range, obtains according to FInite Element The formula arrived calculates the tip inlet area ratio m and length l of one group of gradual change section sound absorber;
(2) number of folds needed for combining the thickness W for proposing meter sound absorber to calculateHereRefer to the knot to l/W Fruit rounds up;
(3) the channel size recurrence formula that area ratio m and number of folds N are brought into corresponding type of fade, is calculated gradual change Coefficient g further calculates the width w in each channel in sound absorberi
(4) the wall thickness D for proposing meter sound absorber is combined to determine the length and height of sound absorber shape, wherein length L=(N+1) D+w1+w2+…+wN, highly depending on the size of actual installation position, wherein w1,w2…wNRespectively refer to the width in i-th of channel Degree;
Step 3: calculating the gradual change section sound absorber for meeting the above-mentioned geometric parameter that step 2 determines using transfer matrix method Absorption coefficient curve, judge whether the absorption coefficient curve meets actual use demand, four entered step if meeting, otherwise Give up m, l and return step two;
Step 4: gradual change section sound absorber is processed according to the geometric parameter that step 2 determines, by commenting with theoretical value comparison The practical sound absorbing performance of the valence gradual change section sound absorber completes sound absorber design if meeting the requirements, right if not meeting Channel width and gradual change coefficient are finely tuned to meeting the requirements.
Further, in the method for the present invention, FInite Element obtains in step (1) formula are as follows:
Have in formula: m=S1/S2It is sound absorber end and entry passage area ratio, ceqTo consider the glutinous effect of heat and channel The airequivalent velocity of sound in the identical uniform cross-section pipe of number, flinAnd fexpRespectively linear and exponential fade channel sound absorber suction Acoustic frequency.
Further, in the method for the present invention, channel size recurrence formula is determined according to type of fade in step (3), specifically Are as follows:
To linear passageway type of fade, channel size recurrence formula are as follows:
G=mw1/(N-1)
Wherein w1For first channel width of initial preset;
To index channel formula type of fade, channel size recurrence formula are as follows:
G=ln (m)/(N-1).
Further, in the method for the present invention, in step 3, judge whether the absorption coefficient curve meets actual use demand Method are as follows: if at frequency f acoustic absorptivity be less than expected acoustic absorptivity, then do not meet, otherwise meet actual use demand.
Further, in the method for the present invention, channel width and gradual change coefficient are finely tuned in step 4, are by with the frequency that absorbs sound The 1/100 of rate corresponding wavelength is that step-length increases and decreases initial channel width, is added further according to by other counted channel widths of recurrence relation Work sound absorber.
Further, in the method for the present invention, when the noise frequency in environment that measures in step 1 is multiple, then needle Sound absorber, which absorbs sound frequency, to be determined to each frequency noise, and respectively according to the process design sound absorber of step 2 to step 4, And obtained multiple sound absorbers are assembled into one side by side.
Further, in the method for the present invention, in step 4 with the reality of the theoretical value comparative evaluation gradual change section sound absorber Sound absorbing performance is to compare peak value sound absorption frequency actual value and theoretical value, and error then meets less than 5% such as compared with theoretical value It is required that otherwise, it is undesirable;Error is relative error herein, i.e., " (actual frequency-theoretic frequency)/theoretic frequency ".
Or peak value acoustic absorptivity actual value and theoretical value compare, error is then conformed to less than 5% such as compared with theoretical value It asks, it is otherwise, undesirable.Error is absolute error herein, i.e., " actual coefficients-theoretical coefficient ".
The cross section structure for one of gradual change section sound absorber that the design method designs is as shown in Figure 2 a.The structure It is made of multiple folding channels, the sectional dimension in each channel is not quite similar.Constant and number of folds (i.e. port number) N mono- in shape In the case where fixed, the internal structure of the structure can be by wall thickness D, the equivalent length l in each channeli, width wiIt determines.Here it keeps Wall thickness is certain, originates channel width w by changing1Structure design is carried out with channel gradual change coefficient g, the width of rest channels can lead to Cross w1It is obtained with the recurrence relation of g.Such as i-th of channel, wi=w1+ g (i-1) and wi=w1eg(i-1)Correspond respectively to line The width of property gradation type and exponential fade type channel.Fig. 2 b is sound absorber appearance schematic diagram, and scale can be long by external height H L, wide W are determined.
Designed structure is subjected to space solution winding, the equivalent coaxial straight passage structures equivalent with its can be obtained, such as Shown in Fig. 2 c.Therefore, the sound absorbing performance of structure may be based on transfer matrix method and carry out model analysis in Fig. 2 a.The theory established Model consists of two parts, respectively the spoke of the impedance computation at channel end to feeder connection and feeder connection to exterior space Penetrate amendment.To first part, if the acoustic pressure and volume velocity at inlet starting feeder connection are pEAnd UE, the last one channel End acoustic pressure and volume velocity be respectively pFAnd UF.According to transmission matrix theory, following relationship can be obtained:
In formula (1)It is the transmission matrix in i-th of channel, can be written as
Hereinki=ω (ρi/Ci)1/2、liThe characteristic impedance in respectively i-th channel, equivalent wave Several and equivalent propagation distance.ρiAnd CiIt is the pipeline equivalent density and compression function for considering the glutinous effect of heat, is expressed as
Wherein, αk=(2k+1) π/wiAnd βn=(2n+1) π/H is unrelated with frequency, and numerical value is by channel size wiWith H and exhibition Open system number n and k are determined.P0It is atmospheric pressure and perfect gas specific heat ratio with γ.ν=μ/ρ in formula0, ν '=κ/ρ0Cv, μ, κ and Cv Respectively refer to viscous air, heat transfer and heat capacity at constant volume.
When slit from reflected acoustic wave is from structure inlet is radiated to free space, there are a radiation tail ends to correct, Corresponding transmission matrix is
To the slit of periodic arrangement, radiation tail end amendment length is represented by
Wherein ψ=w1/ L is the punching rate of sound absorber.
If sound absorber surface acoustic pressure is pSAnd US, because end rigid walls speed is zero, joint type (1) can be obtained
Therefore surface acoustic impedance is at structure inlet
The reflection coefficient r and acoustic absorptivity α of the sound absorber can be calculated by lower two formula
α=1- | r2|, (10)
Wherein Z0It is superficial air characteristic impedance.
For realize design convenience, this research by linearly and exponential fade sound absorber regard as respectively the upper figure of Fig. 3 and under The discretization of slow variable area pipe shown in scheming is approximate, uses the slow variable area pipe of two endpoint finite element method analysis both types Relationship between resonant frequency and geometric parameter.In coordinate system shown in Fig. 3, it is assumed that the sound wave propagated in pipe is only the flat of the direction x Surface wave, endpoint 1 and endpoint 2 are located at x=0 and x=LeqPlace, then the acoustic pressure in this two endpoints finite element at different location can It is expressed as
Wherein p1And p2It is the acoustic pressure at endpoint 1 and endpoint 2, L respectivelyeqIt is to consider revised sound absorber channel of pipe end etc. Imitate length.Acoustic pressure when resonance at endpoint 2 is equal to zero due to incidence wave inversely adds with back wave in slow variable area pipe, this season The kinetic energy of the finite element is equal with potential energy to can be obtained following formula
Here S (x) is the sectional area of slow variable area pipe, kresoSound wave wave number when being resonance.By formula (11) and formula (12) Simultaneous, can solve the resonant frequency of slow variable area pipe, to predict the peak value sound absorption frequency of corresponding gradual change section sound absorber.To preceding The linear and exponential fade variable-section tubular that text is discussed, resonant frequency are as follows
M=S in above formula1/S2It is sound absorber end and entry passage area ratio.In view of in formula (12) only meter and gradual section The kinetic energy and potential energy of sound wave in facial canal do not consider that the present invention is in formula (13) and formula (14) by heat viscid caused heat energy loss In take the velocity of sound to be the airequivalent velocity of sound c considered in the glutinous effect of heat and the identical uniform cross-section pipe of port numbereq
Compared with the sound absorber of conventional uniform section, gradual change section sound absorber can reach the present invention under conditions of identical appearance To lower sound absorption frequency.Structure shown in Fig. 2 a-2b is only the achievable one of sound absorber structure of the present invention, actual Structure is not limited thereto.Form that may be present is there are also three-dimensional channel sound absorber (three-dimensional gradual change variable-section tubular composition) and coplanar leads to Road sound absorber (gradual change variable-section tubular is coplanar to wind) etc..So if those of ordinary skill in the art are inspired by it, not In the case where being detached from the invention objective, frame mode similar with the technical solution and implementation are not inventively designed Example, is within the scope of protection of the invention.
The utility model has the advantages that the present invention has the following obvious advantages compared with existing well-known technique:
(1) show can be in sub-wavelength or depth Asia wave by using the resonant structure of added losses for existing theoretical research Long scale realizes that the perfect of low-frequency sound wave absorbs.Based on this theory, researchers are by constructing various sub-wavelength dimensions Resonating body mainly includes decorating film resonating body, folds helmholtz resonance body and folds Fabry-P é rot resonating body.Wherein Decorating film is prestressed additional and decorative quality in process to be adhered complex, and which increase practical manufactures Difficulty;Acoustic impedance needed for class resonating body provides resonance essentially by folding channel is folded, it can pass through 3D printing Technology is easily manufactured, but currently used folding channel is uniform channel, this is unfavorable for real in a limited space The now sound absorption of more low frequency.Gradual change section sound absorber design method proposed by the invention, and folds that class sound absorber is identical has Convenient feature is fabricated, and very fast feature is transmitted by using gradual change cross-sectional passage impedance, it can be in the confined space The sound wave of interior sound absorption more low frequency;
(2) existing folding class resonance absorber because channel cross-section it is constant, when need substantially to change resonating body sound absorption frequency When inevitably will cause sound absorber shape variation.Gradual change section sound absorber proposed by the invention can pass through change The type of fade in gradual change section, (about 200Hz) adjusts the sound absorption frequency of sound absorber in very wide frequency range, while absorbing sound and being Number is 90% or more, this is conducive to improve the convenience when actual installation uses;
(3) the sound absorber shape of reason the method for the invention design is identical, therefore can be arranged side by side to broadband noise situation The different sound absorber of multiple resonant frequencies is installed to realize that broadband absorbs sound.
Detailed description of the invention
Fig. 1 is the design flow diagram of gradual change section system sound absorber of the invention;
Fig. 2 a is gradual change section sound absorber three dimensional structure diagram of the invention;
Fig. 2 b is the structural schematic diagram at the interface XY of the present invention;
Fig. 2 c is the equivalent structure after unfolding of the present invention;
Fig. 3 is the corresponding continuous slow variable area pipe of the present invention;
Fig. 4 be three sound absorber sample acoustic absorptivities and frequency relation curve described in the embodiment of the present invention 1 theoretical value with Measured value;
Fig. 5 a is the described two sound absorber schematic cross-sections of the embodiment of the present invention 2;
Fig. 5 b is acoustic absorptivity and frequency relation curve after the coupling of the described two sound absorbers of the embodiment of the present invention 2.
Specific embodiment
To further appreciate that the contents of the present invention, the present invention is described in detail in conjunction with the accompanying drawings and embodiments.
Embodiment 1
For the advantage for comparing gradual change section sound absorber, the present embodiment devises three gradual changes according to design cycle shown in Fig. 1 Different types of sound absorber (exponential type, linear and uniformly), compared their sound absorbing performance.Specific steps are as follows:
Step 1: determining sound absorption frequency.Because this implementation purpose is to compare the advantage of gradual change section sound absorber, in advance Sound absorber shape is set as L × W × H=60mm × 20mm × 50mm, and design obtains every kind of gradual change class under this form factor Type, which (is greater than 99%) in the identical situation of acoustic absorptivity, can reach the gradual change section sound absorber of minimum sound absorption frequency.
Step 2: determining type of fade according to machining accuracy and frequency range to be absorbed sound.Specially come from sound absorption frequency It says, exponential type gradual change is just lower than the minimum sound absorption frequency of linear passageway, but its original width is wider than linear passageway initial channel It spends narrow, therefore selects index channel that can reach lower frequency if machining accuracy height.If but from adjustable sound-absorbing frequency range For, the adjustable sound-absorbing range ratio index gradual change channel width in linear gradient channel, this is more advantageous to multifrequency sound absorption.Therefore it needs comprehensive It closes and considers that two aspect factors are selected, if purpose of design is using volume-absorption low frequency single-frequency as small as possible or low frequency and narrow bandwidth Noise is then recommended to use exponential fade sound absorber, if purpose of design is that absorption low frequency multifrequency as much as possible or broad band low frequency are made an uproar Sound is then recommended to use linear gradient sound absorber.The purpose of the present embodiment is the advantage for comparing gradual change section sound absorber, therefore use has The first method (formula (7) and formula (8)) of limit, which is determined as reaching, has determined three kinds of gradual change section sound absorbers required for frequency in step 1 Geometric parameter;
Step 3: judging whether obtained parameter meets design requirement using formula (1-6).The present embodiment is walked by repeating Rapid two and step 3 design to have obtained three sound absorbers A, B and C listed by table 1, they refer respectively to several gradual change sound absorbers, linear Gradual change sound absorber and conventional uniform section sound absorber, design parameter are shown in Table 1.
The geometric parameter of 1. 3 laboratory samples of table
Step 4: according to obtained structural parameters i.e. corresponding sound absorber can be processed, by with theoretical value comparative evaluation Practical sound absorbing performance.
Sample A, B and C correspond respectively to exponential fade sound absorber, linear gradient sound absorber and uniform channel sound absorber, it Be by 3D printing fabricate white polyactide (Polylactide, PLA) sound absorber sample, machining accuracy be ± 0.1mm。
Fig. 4 binding isotherm and the Comparison of experiment results acoustic absorptivity of three samples.Experiment measures the absorption of three samples Peak respectively appears in 315Hz, 325Hz and 365Hz, and peak value acoustic absorptivity is 95.0%, 91.7% and 94.1%;Measured Q value Respectively 0.159,0.154 and 0.144, compare theoretical expectation values (0.153,0.147 and 0.139) coincide very well.Experiment with Slight deviations between notional result may be caused by mismachining tolerance.Compared with common uniform channel sound absorber, gradual change section is inhaled Sound body can efficiently use space for absorption peak and move down 40-50Hz in the case where not changing shape.The thickness W of each sample It is only about the 1/55 of wavelength, it is meant that the sound absorber has depth sub-wavelength dimensions.
Schematically the present invention and embodiments thereof are described above, description is not limiting, institute in attached drawing What is shown is also one of embodiments of the present invention, and actual structure is not limited to this.The present embodiment show only index and The embodiment of linear two kinds of gradual change sections sound absorber, other any changes of section types for meeting certain functional relation are available In the such sound absorber of design.So if related technical personnel are enlightened by it, the case where not departing from the invention objective Under, frame mode similar with the technical solution and embodiment are not inventively designed, should belong to protection of the invention Range.
Embodiment 2
In different acoustic enviroments, noise frequency is not quite similar.Therefore shape is fixed and peak value sound absorption frequency is different Sound absorber installation with application in have very high practical value.Under broadband noise application scenarios, single narrowband sound absorber It is unable to reach ideal sound absorption effect, and is fixed by the way that two or more above-mentioned shapes are mounted side by side, peak value sound absorption frequency difference Sound absorber, wide band sound absorption can be further expanded.
The present embodiment devises two peak value sound absorption frequencies differences using step described in Fig. 1 but the identical gradual change of shape is cut Face sound absorber, it is two schematic cross-sections for installing sound absorber side by side that design parameter, which is shown in Table 2. Fig. 5 a, and Fig. 5 b illustrates two suctions The variation relation of absorption coefficient and frequency when sound body is used alone and installs side by side.When dotted line is that sound absorber is used alone in figure Absorption coefficient curve, solid line are absorption coefficient curves when sound absorber is mounted side by side.Calculated result shows suction when being used alone The peak value sound absorption frequency of sound body is 273Hz and 314Hz respectively, and bandwidth is 15.1% and 13.7%.Two sound absorbers are pacified side by side After dress, 50% wide band sound absorption of the coupling sound absorber can reach 30.1%, and bandwidth of the acoustic absorptivity greater than 0.8 is 20.4%.It should The thickness W=25mm of sound absorber combination, is still depth sub-wavelength dimensions.It can be expected that multiple sound absorbers ought be installed side by side When, the bandwidth for coupling sound absorber can be expanded further.This application for being it in practical noise reduction engineering provides possibility.
2. sound absorber parameter of table

Claims (7)

1. a kind of design method of gradual change section low frequency absorption body, which is characterized in that method includes the following steps:
Step 1: first by the noise frequency f in measurement environment to determine sound absorber sound absorption frequency;
Step 2: according to the gradual change section sound absorber of the corresponding sound absorption frequency of noise frequency f design of step 1 measurement, specifically Step includes:
(1) type of fade that proposed adoption is determined according to actual processing precision and sound absorption frequency range, obtains according to FInite Element Formula calculates the tip inlet area ratio m and length l of one group of gradual change section sound absorber;
(2) number of folds needed for combining the thickness W for proposing meter sound absorber to calculateHereRefer to the result of l/W to Upper rounding;
(3) the channel size recurrence formula that area ratio m and number of folds N are brought into corresponding type of fade, is calculated gradual change coefficient G further calculates the width w in each channel in sound absorberi
(4) the wall thickness D for proposing meter sound absorber is combined to determine the length and height of sound absorber shape, wherein length L=(N+1) D+w1+ w2+…+wN, highly depending on the size of actual installation position, wherein w1,w2…wNRespectively refer to the width in i-th of channel;
Step 3: calculating the suction for meeting the gradual change section sound absorber for the above-mentioned geometric parameter that step 2 determines using transfer matrix method Sonic system number curve, judges whether the absorption coefficient curve meets actual use demand, and four are entered step if meeting, is otherwise given up M, l and return step two;
Step 4: gradual change section sound absorber is processed according to the geometric parameter that step 2 determines, by being somebody's turn to do with theoretical value comparative evaluation The practical sound absorbing performance of gradual change section sound absorber completes sound absorber design, if not meeting, to channel if meeting the requirements Width and gradual change coefficient are finely tuned to meeting the requirements.
2. the design method of gradual change section low frequency absorption body according to claim 1, which is characterized in that the step (1) The formula that middle FInite Element obtains are as follows:
Have in formula: m=S1/S2It is sound absorber end and entry passage area ratio, ceqTo consider, heat sticks effect and port number is identical Uniform cross-section pipe in the airequivalent velocity of sound, flinAnd fexpRespectively linear and exponential fade channel sound absorber sound absorption frequency Rate.
3. the design method of gradual change section low frequency absorption body according to claim 1, which is characterized in that the step (3) Middle channel size recurrence formula is determining according to type of fade, specifically:
To linear passageway type of fade, channel size recurrence formula are as follows:
G=mw1/(N-1)
Wherein w1For first channel width of initial preset;
To index channel formula type of fade, channel size recurrence formula are as follows:
G=ln (m)/(N-1).
4. the design method of gradual change section low frequency absorption body according to claim 1,2 or 3, which is characterized in that the step In rapid three, judge whether the absorption coefficient curve meets the method for actual use demand are as follows: as acoustic absorptivity is less than in advance at frequency f The acoustic absorptivity of phase, then do not meet, and otherwise meets actual use demand.
5. the design method of gradual change section low frequency absorption body according to claim 1,2 or 3, which is characterized in that the step Channel width and gradual change coefficient are finely tuned in rapid four, are by initial for step-length increase and decrease with the 1/100 of the frequency corresponding wavelength that absorbs sound Channel width processes sound absorber further according to by other counted channel widths of recurrence relation.
6. the design method of gradual change section low frequency absorption body according to claim 1,2 or 3, which is characterized in that the step When the noise frequency in environment measured in rapid one is multiple, then sound absorber sound absorption frequency is determined for each frequency noise Rate, and respectively according to the process design sound absorber of step 2 to step 4, and obtained multiple sound absorbers are assembled into one side by side Body.
7. the design method of gradual change section low frequency absorption body according to claim 1,2 or 3, which is characterized in that the step In rapid four with the practical sound absorbing performance of the theoretical value comparative evaluation gradual change section sound absorber, be by peak value sound absorption frequency actual value with Theoretical value comparison, error then meets the requirements less than 5% such as compared with theoretical value, otherwise, undesirable;
Or peak value acoustic absorptivity actual value and theoretical value compare, error then meets the requirements less than 5% such as compared with theoretical value, Otherwise, undesirable.
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CN112347594A (en) * 2020-10-30 2021-02-09 南京大学 Broadband noise reduction structure applied to natural ventilation sound insulation window and design method thereof
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