Phononic crystal silencer for low and medium frequency noise reduction in pipeline and acoustic characteristic calculation method of phononic crystal silencer

Abstract

The invention discloses a photonic crystal silencer for low and medium frequency noise reduction in a pipeline and an acoustic characteristic calculation method thereof, and the method comprises the steps: constructing a kinetic equation of an acoustic vibration coupling system of a thin plate and a cavity medium in a photonic crystal based on the photonic crystal silencer for low and medium frequency noise reduction in the pipeline, obtaining an acoustic impedance model of the rectangular thin plate surface based on the kinetic equation; obtaining an acoustic impedance model of a single Helmholtz silencer according to the relationship between the sound pressure and the mass velocity in the Helmholtz silencer; according to the acoustic impedance model of the single Helmholtz silencer, obtaining an acoustic impedance model when a plurality of Helmholtz silencers are arranged in the circumferential direction; in combination with an acoustic impedance model when a plurality of Helmholtz silencers are arranged in the circumferential direction, obtaining a single crystal cell acoustic transfer matrix model with a plurality of silencers according to the relationship between sound pressure and mass point vibration velocity at an inlet and an outlet; and according to the single crystal cell acoustic transfer matrix model, obtaining a transfer matrix with a plurality of unit cells and the acoustic transfer loss of the phononic crystal silencer.

Description

Technical Field

[0001] The present invention belongs to the technical field of noise control, and in particular relates to a phononic crystal muffler for medium and low frequency noise reduction in a pipeline and a method for calculating the acoustic characteristics thereof. Background Art

[0002] In the industrial sector, controlling low-frequency and broadband noise in piping systems has long been a focus of research. Achieving low-frequency and broadband attenuation using compact structures is a significant challenge. As a reactive muffler, the Helmholtz resonator exhibits high transmission losses within a narrow band of its resonant frequency, and its resonant frequency is primarily determined by its geometric dimensions. Therefore, it is generally considered the preferred choice for attenuating low-frequency and narrowband noise. To achieve low-frequency and broadband noise attenuation in piping systems, much research has focused on improving the neck and cavity structures of Helmholtz mufflers. However, most Helmholtz mufflers still require large external dimensions to achieve adequate low-frequency noise attenuation, which is unfavorable for practical applications. Consideration could be given to incorporating membranes or thin plates into the muffler structure. Through acoustic-structure coupling, acoustic energy is converted into bending waves, which are then lost through radiation, reflection, or internal friction, thereby achieving low-frequency noise control using compact structures. Furthermore, further enhancement of low-frequency noise reduction and expansion of the low-frequency noise reduction bandwidth are also needed.

[0003] Local resonant phononic crystals are based on acoustic resonance structures, and produce local resonant band gaps near the resonant frequency, which can produce local resonant band gaps that attenuate sound waves. If a phononic crystal structure contains multiple acoustic resonance mechanisms at the same time, it will provide more possibilities for the control of medium, low-frequency and broadband noise in pipeline systems. However, in order to achieve low-frequency sound attenuation, the unit cell size of existing phononic crystal mufflers is often very large. The installation space constraint of the muffler is an important consideration for industrial applications. The present invention proposes a phononic crystal muffler for medium and low-frequency noise reduction in pipelines and a method for calculating its acoustic characteristics, which solves the problems in the prior art that the low-frequency noise reduction band range is not wide enough, the overall size of the muffler is relatively large, and it is not suitable for application scenarios with limited space size. Summary of the Invention

[0004] In order to solve the above technical problems, the present invention proposes a phononic crystal silencer for medium and low frequency noise reduction in pipelines and a method for calculating its acoustic characteristics. By adopting circumferential non-uniform parameters to arrange the silencer units, the noise reduction frequency band range can be broadened, thereby achieving medium and low frequency and wide-band noise attenuation in the pipeline system.

[0005] On the one hand, to achieve the above-mentioned object, the present invention provides a phononic crystal muffler for reducing medium and low frequency noise in a pipeline, comprising:

[0006] The phononic crystal muffler is composed of periodically arranged Helmholtz muffler units;

[0007] Each Helmholtz muffler unit includes a neck, a main cavity and an inner thin plate;

[0008] The thin plate divides the main cavity into a first cavity and a second cavity, and the vibration of the thin plate and the Helmholtz resonance act together to form a coupling effect of multiple local resonance sound attenuation areas.

[0009] On the other hand, to achieve the above-mentioned purpose, the present invention also provides a method for calculating the acoustic characteristics of a phononic crystal muffler for low- and medium-frequency noise reduction in a pipeline, comprising:

[0010] Based on a phononic crystal muffler for low- and medium-frequency noise reduction in pipelines, a dynamic equation of the acoustic-vibration coupling system between a thin plate and a cavity medium in the phononic crystal is constructed, and an acoustic impedance model of the rectangular thin plate surface is obtained based on the dynamic equation;

[0011] Obtaining an acoustic impedance model of a single Helmholtz muffler based on a relationship between sound pressure and mass velocity within the Helmholtz muffler in the phononic crystal;

[0012] Based on the acoustic impedance model of a single Helmholtz muffler, a single unit cell acoustic impedance model of multiple Helmholtz mufflers arranged circumferentially is obtained;

[0013] Combined with the single unit cell acoustic impedance model when multiple Helmholtz mufflers are arranged circumferentially, the acoustic transfer matrix model of the single unit cell equipped with multiple mufflers is obtained based on the relationship between the sound pressure and particle vibration velocity at the inlet and outlet.

[0014] According to the single unit cell acoustic transfer matrix model, a transfer matrix having multiple unit cells and an acoustic transfer loss of a phononic crystal muffler are obtained.

[0015] Technical effect of the invention: The present invention discloses a phononic crystal silencer for medium and low frequency noise reduction in pipelines and a method for calculating its acoustic characteristics. The phononic crystal includes periodically arranged Helmholtz silencer units, and each silencer unit is provided with a rectangular thin plate, which divides the cavity into two sub-cavities. By adding a thin plate to the Helmholtz silencer, a new peak of the transmission loss curve is introduced, which can widen the medium and low frequency attenuation range within 100-1000Hz. The compact structure obtained in this way is suitable for scenarios with limited noise reduction space. In the design of the phononic crystal silencer, the noise reduction frequency band can be widened by arranging the silencer units with circumferential non-uniform parameters. The acoustic simulation results show that the transmission loss is above 10dB in the range of 262Hz-809Hz. Compared with the prior art, the present invention provides technical support for medium and low frequency, wide band, and large amplitude noise attenuation in pipelines, is suitable for pipeline low frequency noise scenarios, and can be widely used in noise control in industrial pipelines, automobiles, medical equipment, household appliances and other fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying drawings:

[0017] Figure 1 Schematic diagram of the structure of a phononic crystal muffler for low- and medium-frequency noise reduction in a pipeline according to an embodiment of the present invention, wherein (a) is a perspective view, (b) is a front view, (c) is a left side view, and (d) is a top view;

[0018] Figure 2 This is a schematic structural diagram of a single unit cell according to an embodiment of the present invention, wherein 1 is a thin plate, 2 is a first cavity, and 3 is a second cavity.

[0019] Figure 3 This is a flow chart of a method for calculating the acoustic characteristics of a phononic crystal muffler for low and medium frequency noise reduction in a pipeline according to an embodiment of the present invention;

[0020] Figure 4 Schematic diagram of the sound transmission process of each Helmholtz muffler in an embodiment of the present invention;

[0021] Figure 5 Schematic diagrams of transmission loss curves for single-cell and multi-cell muffler structures according to embodiments of the present invention; (a) shows the theoretical, simulation, and experimental results of transmission loss for a single-cell muffler, as well as the theoretical results for a muffler with only the cavity and no thin plate; (b) shows the theoretical, simulation, and experimental results of transmission loss for a three-cell muffler.

[0022] Figure 6 Schematic diagram of the noise reduction characteristics of a phononic crystal muffler with non-uniform parameters according to an embodiment of the present invention. DETAILED DESCRIPTION

[0023] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0024] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0025] This embodiment provides a phononic crystal muffler for reducing medium and low frequency noise in a pipeline, comprising:

[0026] The phononic crystal muffler is composed of periodically arranged Helmholtz muffler units;

[0027] Each Helmholtz muffler unit includes a neck, a main cavity and an inner thin plate;

[0028] The thin plate 1 divides the main cavity into a first cavity 2 and a second cavity 3 . The vibration of the thin plate and the Helmholtz resonance act together to form a coupling effect of multiple local resonance sound attenuation areas.

[0029] Specifically, in this embodiment, the phononic crystal is as follows Figure 1 As shown, the three-dimensional structure diagram of the unit cell is as follows Figure 1 (a), Figure 1 (b) to (d) represent the corresponding front view, left view and top view respectively; the structure of a single unit cell is as follows Figure 2 , forming a coupling effect of multiple localized resonant sound attenuation regions, achieving effective attenuation of low-frequency, broadband noise. This embodiment further optimizes the sound attenuation frequency band by adjusting the thin plate size, cavity parameters, and the axial and circumferential non-uniform arrangement of the muffler, while maintaining a compact structure.

[0030] like Figure 3 As shown, this embodiment also provides a method for calculating the acoustic characteristics of a phononic crystal muffler for low and medium frequency noise reduction in a pipeline, including:

[0031] Based on a phononic crystal muffler for low- and medium-frequency noise reduction in pipelines, a dynamic equation of the acoustic-vibration coupling system between a thin plate and a cavity medium in the phononic crystal is constructed, and an acoustic impedance model of the rectangular thin plate surface is obtained based on the dynamic equation;

[0032] Obtaining an acoustic impedance model of a single Helmholtz muffler based on a relationship between sound pressure and mass velocity within the Helmholtz muffler in the phononic crystal;

[0033] Based on the acoustic impedance model of a single Helmholtz muffler, a single unit cell acoustic impedance model of multiple Helmholtz mufflers arranged circumferentially is obtained;

[0034] Combined with the single unit cell acoustic impedance model when multiple Helmholtz mufflers are arranged circumferentially, the acoustic transfer matrix model of the single unit cell equipped with multiple mufflers is obtained based on the relationship between the sound pressure and particle vibration velocity at the inlet and outlet.

[0035] According to the single unit cell acoustic transfer matrix model, a transfer matrix having multiple unit cells and an acoustic transfer loss of a phononic crystal muffler are obtained.

[0036] Furthermore, obtaining the acoustic impedance model of the rectangular thin plate surface based on the dynamic equation includes:

[0037] Based on the dynamic equation, according to the lateral vibration displacement and vibration velocity of the thin plate, the mechanical impedance of a certain mode of the thin plate is obtained;

[0038] An acoustic impedance model of the thin plate surface is obtained based on the mechanical impedance of each mode of the thin plate.

[0039] Specifically, the mechanical impedance Z of the thin plate in the (m, n)th order mode is obtained according to the expressions of the lateral vibration displacement and vibration velocity of the thin plate: mn :

[0040]

[0041] Among them, ρ A represents the surface density of the thin plate, ω mn represents the natural circular frequency of the (m,n)th order mode of the thin plate, ξ mn is the modal damping ratio of the thin plate;

[0042] The acoustic impedance model expression of the rectangular thin plate surface is obtained:

[0043]

[0044] in, l a Indicates the length of the thin plate, l b Indicates the width of the thin plate, S P represents the cross-sectional area of ​​the thin plate, X m (x) and Y n (y) represents the mode function.

[0045] Furthermore, according to the relationship between the sound pressure and mass velocity in the Helmholtz muffler in the phononic crystal, obtaining the acoustic impedance model of a single Helmholtz muffler includes:

[0046] Schematic diagram of a single muffler structure in a combined phononic crystal Figure 4 , we can get the relationship between sound pressure and mass velocity at points 3 to 7:

[0047]

[0048] Where T3 = T 3,4 T 4,5 T 6,7 ,

[0049] l′ n =l n +δ1+δ2 is the acoustic length of the connecting neck, c0 is the medium sound velocity, δ1 and δ2 are the end corrections at the connection between the connecting neck and the main pipe and cavity 1, respectively, S n is the cross-sectional area S of the Helmholtz muffler neck v1 =S v2 =S P .

[0050] Considering the wall of the Helmholtz muffler is rigid, the boundary condition u7=0, and further we can get the Figure 4 Relative acoustic impedance near the three points:

[0051]

[0052] Among them, Z r is the acoustic impedance model of a single Helmholtz muffler; T 31 The first row and first column element of T3; S n for Figure 4 The cross-sectional area of ​​the Helmholtz muffler neck; T 32 It is the element in the first row and second column of T3; c0 is the sound speed of the medium.

[0053] Furthermore, the single unit cell acoustic impedance model when multiple Helmholtz mufflers are arranged circumferentially includes:

[0054]

[0055] Among them, Z3 is the single unit cell acoustic impedance model when multiple Helmholtz mufflers are arranged circumferentially; Z rN is the relative acoustic impedance of the Nth Helmholtz muffler.

[0056] Furthermore, based on the relationship between the sound pressure and particle velocity at the inlet and outlet, the single unit cell acoustic transfer matrix model equipped with multiple mufflers is obtained, including:

[0057] Assuming that the main pipe and the neck of the Helmholtz muffler are all plane waves and ignoring the influence of gas flow, Figure 4 In the figure, the transfer matrix from point 1 to point 2 is obtained from the continuity of the sound pressure and mass velocity at the three points of the bifurcation:

[0058]

[0059] Among them, Z3 is the acoustic impedance model at three points when multiple Helmholtz mufflers are arranged circumferentially.

[0060] Assuming that there are only plane waves at the entrance and exit of each unit cell, the mth th Unit cell x = x m The expressions of sound pressure and particle velocity at are:

[0061]

[0062] Among them, x m is located at the center of the pipe in the mth periodic unit, and ρ0 is the density of the medium.

[0063] According to the mth thThe unit cell and the m+1th unit cell are at x=x m The relationship between the sound pressure and particle velocity at is:

[0064]

[0065] Obtaining the acoustic transfer matrix of a single unit cell with multiple mufflers involves:

[0066]

[0067] Where T1 is the acoustic transfer matrix model of a single unit cell equipped with multiple mufflers; a is the lattice constant, and k is the wave number.

[0068] Furthermore, obtaining a transfer matrix having a plurality of unit cells includes:

[0069] For the unit cell m th , according to the sound pressure and particle velocity at the inlet and outlet, the transfer matrix is:

[0070] T cell =T L T 1,2 T R ;

[0071] in, is the transfer matrix of the straight pipe region.

[0072] Considering the installation requirements, a length of l is installed on both sides of the muffler phonon transistor channel. u For a straight tube with M unit cells, the transfer matrix with multiple unit cells is obtained as follows:

[0073]

[0074] Among them, T total is a transfer matrix with multiple unit cells; is the transfer matrix of each straight pipe at both ends; is the transfer matrix of M unit cells.

[0075] Furthermore, obtaining the sound transmission loss of the phononic crystal muffler includes:

[0076]

[0077] Where TL is the sound transmission loss of the phononic crystal muffler; T total is the transfer matrix from the pipe inlet to the outlet.

[0078] The present invention also includes verifying the accuracy of the transmission loss curve calculated by this embodiment through simulation and experimental methods. By setting the muffler structural parameters of adjacent unit cells to different values, a non-uniformly distributed phononic crystal muffler is designed. By screening the design parameters, a phononic crystal muffler with mid-to-low frequency, wide bandwidth, and strong sound attenuation is obtained.

[0079] The transmission loss results calculated by the technical solution were verified by simulation and experimental methods. A single-cell muffler and a phononic crystal muffler with four cells were modeled in acoustic simulation software, and a plane wave of unit pressure was added to the pipe inlet to obtain the transmission loss curve. At the same time, the transmission loss curves of the single-cell and multi-cell muffler structures were tested using impedance tube acoustic experiments. Figure 5 As shown in (a) to (b), the acoustic characteristics of the phononic crystal silencer calculated by the technical solution are verified, and the calculated transfer matrix is ​​relatively reliable. Figure 5 Figure (a) shows that the introduction of the thin plate adds new peaks to the transmission loss curve. The first peak is primarily influenced by the vibration of the air within the cavity, while the second peak is primarily influenced by the vibration of the thin plate. The introduction of the thin plate adds an attenuation band to the low- and mid-frequency range, enriching the control mechanism for low- and mid-frequency sound attenuation and helping to control low- and mid-frequency noise in small structures.

[0080] By maintaining the periodicity of the unit cell spacing and making the parameters of each muffler in each unit cell the same, except for the different lengths of the thin plates between the unit cells, a phononic crystal muffler with non-uniform parameters is designed. By screening the design parameters, a phononic crystal muffler with medium and low frequencies, wide bandwidth, and strong sound attenuation is obtained, such as Figure 6 The noise reduction characteristics of a phononic crystal muffler with non-uniform parameters designed using this technical solution are shown. It can be seen that each peak in transmission loss corresponds to a resonant frequency of the muffler. The acoustic attenuation amplitude does not vary significantly, with the transmission loss remaining above 10dB within the range of 262Hz to 809Hz. Therefore, intentionally relaxing the periodicity requirement is an effective method for broadening the acoustic attenuation characteristics, resulting in excellent broadband mid- and low-frequency acoustic attenuation.

[0081] The present invention discloses a phononic crystal silencer for medium and low frequency noise reduction in pipelines and a method for calculating its acoustic characteristics. The phononic crystal includes periodically arranged Helmholtz silencer units, each of which is provided with a rectangular thin plate, dividing the cavity into two sub-cavities. By adding a thin plate to the Helmholtz silencer, a new peak of the transmission loss curve is introduced, which can widen the medium and low frequency attenuation range within 100-1000Hz. The compact structure obtained in this way is suitable for scenarios with limited noise reduction space. In the design of the phononic crystal silencer, the noise reduction frequency band can be widened by arranging the silencer units with circumferential non-uniform parameters. Acoustic simulation results show that the transmission loss is above 10dB in the range of 262Hz-809Hz. Compared with the prior art, the present invention provides technical support for medium and low frequency, wide band, and large amplitude noise attenuation in pipelines, is suitable for pipeline low frequency noise scenarios, and can be widely used in noise control in industrial pipelines, automobiles, medical equipment, household appliances and other fields.

[0082] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A phononic crystal muffler for low and medium frequency noise reduction in pipelines, characterized in that: include: The phononic crystal muffler is composed of periodically arranged Helmholtz muffler units; Each Helmholtz muffler unit includes a neck, a main cavity and an inner thin plate; The thin plate (1) separates the main cavity into a first cavity (2) and a second cavity (3), and the vibration of the thin plate (1) acts together with the Helmholtz resonance to form a coupling effect of multiple local resonance sound attenuation areas.

2. A method for calculating the acoustic characteristics of a phononic crystal muffler for low and medium frequency noise reduction in a pipeline according to claim 1, characterized in that: include: Based on a phononic crystal muffler for low- and medium-frequency noise reduction in pipelines, a dynamic equation of the acoustic-vibration coupling system between a thin plate and a cavity medium in the phononic crystal is constructed, and an acoustic impedance model of the rectangular thin plate surface is obtained based on the dynamic equation; Obtaining an acoustic impedance model of a single Helmholtz muffler based on a relationship between sound pressure and mass velocity within the Helmholtz muffler in the phononic crystal; Based on the acoustic impedance model of a single Helmholtz muffler, a single unit cell acoustic impedance model of multiple Helmholtz mufflers arranged circumferentially is obtained; Combined with the single unit cell acoustic impedance model when multiple Helmholtz mufflers are arranged circumferentially, the acoustic transfer matrix model of the single unit cell equipped with multiple mufflers is obtained based on the relationship between the sound pressure and particle vibration velocity at the inlet and outlet. According to the single unit cell acoustic transfer matrix model, a transfer matrix having multiple unit cells and an acoustic transfer loss of a phononic crystal muffler are obtained.

3. The method for calculating the acoustic characteristics of a phononic crystal muffler for low and medium frequency noise reduction in a pipeline according to claim 2, characterized in that: The acoustic impedance model of the rectangular thin plate surface obtained based on the dynamic equation includes: Based on the dynamic equation, the mechanical impedance of a certain mode of the thin plate is obtained according to the lateral vibration displacement and vibration velocity of the thin plate; An acoustic impedance model of the thin plate surface is obtained based on the mechanical impedance of each mode of the thin plate.

4. The method for calculating the acoustic characteristics of a phononic crystal muffler for low and medium frequency noise reduction in a pipeline according to claim 2, characterized in that: According to the sound pressure and mass velocity transfer matrix T3 from point 3 of the muffler neck to point 7 of the muffler bottom, the acoustic impedance model of a single Helmholtz muffler is obtained, including: Among them, Z r is the acoustic impedance model of a single Helmholtz muffler; T 31 The first row and first column element of T3; S n is the cross-sectional area of ​​the Helmholtz muffler neck; T 32 It is the element in the first row and second column of T3; c0 is the sound speed of the medium.

5. The method for calculating the acoustic characteristics of a phononic crystal muffler for low and medium frequency noise reduction in a pipeline according to claim 2, characterized in that: The single-cell acoustic impedance model for circumferentially arranged multiple Helmholtz mufflers includes: Among them, Z3 is the single unit cell acoustic impedance model when multiple Helmholtz mufflers are arranged circumferentially; Z rN is the relative acoustic impedance of the Nth Helmholtz muffler.

6. The method for calculating the acoustic characteristics of a phononic crystal muffler for low and medium frequency noise reduction in a pipeline according to claim 2, characterized in that: Obtaining the acoustic transfer matrix of a single unit cell with multiple mufflers involves: Where T1 is the acoustic transfer matrix model of a single unit cell equipped with multiple mufflers; a is the lattice constant, and k is the wave number.

7. The method for calculating the acoustic characteristics of a phononic crystal muffler for low and medium frequency noise reduction in a pipeline according to claim 2, characterized in that: Obtaining a transfer matrix with multiple unit cells involves: Among them, T total is a transfer matrix with multiple unit cells; is the transfer matrix of each straight pipe at both ends; is the transfer matrix of M unit cells.

8. The method for calculating the acoustic characteristics of a phononic crystal muffler for low and medium frequency noise reduction in a pipeline according to claim 2, characterized in that: Obtaining the acoustic transmission loss of the phononic crystal muffler includes: Where TL is the sound transmission loss of the phononic crystal muffler; T total is the transfer matrix from the pipe inlet to the outlet.

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