CN107589178A - Method for realizing wave front regulation and control of sound waves by utilizing super-structure surface formed by Helmholtz resonators - Google Patents

Abstract

A method for realizing wave front regulation and control of sound waves by utilizing a super-structure surface formed by a Helmholtz resonator comprises the steps of forming micro-structure units by utilizing the Helmholtz resonator, forming the micro-structure surfaces by utilizing a plurality of micro-structure units, and changing the sound velocity of the sound waves in the super-structure surfaces by adjusting the width of a slit in each micro-structure unit under the condition that the unit size of the super-structure surfaces is far smaller than the wavelength of the sound waves, so that the phase of the sound waves is changed, and the wave front regulation and control of the sound waves are realized. The invention provides a super-structure surface which is simple in structure and easy to realize sound wave regulation.

Description

A metasurface composed of Helmholtz resonators to achieve acoustic wavefront Regulation method

technical field

The invention relates to the use of a Helmholtz resonator, and under the condition that the unit size of the acoustic metastructure material is much smaller than the wavelength of the sound wave, the control of the acoustic wave front is realized by using a metasurface composed of the Helmholtz resonator.

Background technique

Acoustic metasurface (Acoustic Metasurface) constructs some kind of artificial microstructure unit with special functions to form an orderly regulation of the acoustic wave front at the microunit scale, and obtain acoustic properties that are completely different from natural materials. Utilizing the characteristics of acoustic metasurfaces that can regulate the wave field, it is possible to control and change the transmission mode of the acoustic signal, and realize the regulation of the acoustic wave front, such as realizing anomalous refraction and non-diffracting Bessel beams, etc. In the previous design of acoustic metasurfaces, artificial microstructure units are usually composed of spatial folded structures, labyrinth structures, or five-mode structures. Their structural forms are relatively complex, which limits the practical application of metasurfaces. How to design a metasurface with a simple structure and easy manipulation of acoustic waves is of great significance.

Contents of the invention

The purpose of the present invention is to propose a metasurface with a relatively simple structure and easier realization of sound wave regulation, aiming at the problem that the existing metasurface structure is relatively complex and practically inconvenient.

Technical scheme of the present invention is:

The invention provides a method for controlling the acoustic wave front by using a metasurface composed of Helmholtz resonators. On the surface, when the scale of the metasurface unit is much smaller than the wavelength of the sound wave, the sound velocity of the sound wave in the metasurface can be changed by adjusting the width of the slit in the microstructure unit, and then the phase of the sound wave can be changed, so as to realize the regulation of the sound wave front .

Further, the microstructure unit is vertically carved at least three Helmholtz resonators on a metal medium, and the right side of each Helmholtz resonator has a rectangular slit structure; multiple microstructure units are arranged horizontally way to form a metasurface.

Further, the height H of the metal medium, that is, the thickness of the metasurface is 32mm, the period constant L of the microstructure unit is 8mm, and the width of the slit is d; the neck length and width of the Helmholtz resonator are respectively h=2mm and l=1mm, the height and width of the Helmholtz resonator cavity are a=6mm and b=2.5mm respectively.

Further, the acoustic wave velocity c _eff in the metasurface specifically satisfies the following formula:

Among them: ρ ₀ is the air density, equal to 1.21kg/m ³ ; B _eff is the equivalent bulk modulus after introducing the Helmholtz resonator, the expression is

Where: B ₀ =ρ ₀ c ₀ ² is the bulk modulus of air, where c ₀ =343m/s is the sound velocity in the air, so B ₀ is a constant; ω ₀ is the resonance angle of the Helmholtz resonator Frequency, (here its magnitude is f ₀ =ω ₀ /2π=7331Hz), ω is the frequency of the input sound wave signal; F=ab/Ld is the ratio of the cavity area of the Helmholtz resonator to the corresponding slit area, L represents the period constant of the microstructure unit, d represents the width of the slit in the microstructure unit; a and b represent the height and width of the Helmholtz resonator cavity, respectively.

Beneficial effects of the present invention:

Compared with the prior art, the present invention has the following characteristics. The structure of the metasurface unit is simple, and the adjustment of the sound velocity can be realized by adjusting the width of the slit of the unit structure, which is flexible and convenient; Impedance matching is realized, thereby greatly improving the transmission efficiency of sound waves, and high-efficiency transmission can be realized in a wide frequency band. This method can be extended to acoustic wavefront manipulation in the full phase range, and can be applied to super-resolution imaging, focusing and detection in acoustics.

Other features and advantages of the present invention will be described in detail in the detailed description that follows.

Description of drawings

The above and other objects, features and advantages of the present invention will become more apparent by describing the exemplary embodiments of the present invention in more detail with reference to the accompanying drawings, wherein, in the exemplary embodiments of the present invention, the same reference numerals generally represent same parts.

Figure 1 Block diagram of the experimental system

Figure 2 Schematic diagram of the structure of the metasurface composed of Helmholtz resonators and slits

Figure 3 realizes the anomalous refraction of sound waves through the metasurface, where

Figure 3a Schematic diagram of abnormal refraction of sound waves

Figure 3b Schematic diagram of the change of sound velocity gradient: the solid line is the law of sound velocity change under ideal conditions, and the dotted line is the change of sound velocity gradient realized by the metasurface

Figure 3c The sound pressure field distribution of abnormal refraction after the sound wave passes through the metasurface

Figure 4 realizes acoustic non-diffracting Bessel beams through metasurfaces, where

Figure 4a Schematic diagram of Bessel beamforming

Figure 4b Schematic diagram of the change of sound velocity gradient: the solid line is the law of sound velocity change under ideal conditions, and the dotted line is the change of sound velocity gradient realized by the metasurface

Figure 4c The sound intensity distribution of non-diffracting Bessel beams formed by sound waves passing through the metasurface

detailed description

Preferred embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although preferred embodiments of the invention are shown in the drawings, it should be understood that the invention may be embodied in various forms and should not be limited to the embodiments set forth herein.

The invention provides a method for controlling the acoustic wave front by using a metasurface composed of Helmholtz resonators. On the surface, when the scale of the metasurface unit is much smaller than the wavelength of the sound wave, the sound velocity of the sound wave in the metasurface can be changed by adjusting the width of the slit in the microstructure unit, and then the phase of the sound wave can be changed, so as to realize the regulation of the sound wave front .

Further, the microstructure unit is vertically carved at least three Helmholtz resonators on a metal medium, and the right side of each Helmholtz resonator has a rectangular slit structure; multiple microstructure units are arranged horizontally way to form a metasurface.

Further, the height H of the metal medium, that is, the thickness of the metasurface is 32mm, the period constant L of the microstructure unit is 8mm, and the width of the slit is d; the neck length and width of the Helmholtz resonator are respectively h=2mm and l=1mm, the height and width of the Helmholtz resonator cavity are a=6mm and b=2.5mm respectively.

Further, the acoustic wave velocity c _eff in the metasurface specifically satisfies the following formula:

Among them: ρ ₀ is the air density, equal to 1.21kg/m ³ ; B _eff is the equivalent bulk modulus after introducing the Helmholtz resonator, the expression is

Where: B ₀ =ρ ₀ c ₀ ² is the bulk modulus of air, where c ₀ =343m/s is the sound velocity in the air, so B ₀ is a constant; ω ₀ is the resonance angle of the Helmholtz resonator Frequency, (here its magnitude is f ₀ =ω ₀ /2π=7331Hz), ω is the frequency of the input sound wave signal; F=ab/Ld is the ratio of the cavity area of the Helmholtz resonator to the corresponding slit area, L represents the period constant of the microstructure unit, d represents the width of the slit in the microstructure unit; a and b represent the height and width of the Helmholtz resonator cavity, respectively.

When implementing it:

We have carried out numerical analysis on the effectiveness and feasibility of this invention. For the anomalous refraction of sound waves, according to the generalized Snell's law, the reciprocal of the speed of sound waves propagating along the x-axis direction can be expressed as

In the formula, H is the thickness of the metamaterial, c ₀ =343m/s is the sound velocity in air, the refraction angle θ _t =20°, and c(0) is the sound velocity at the left boundary of the metasurface. For this metasurface, there are 12 unit structures in total, as shown in Figure 3c, we can adjust the sound velocity of sound wave propagation by adjusting the width of the slits of the unit structure. We set the sound wave at the far left end of the metasurface to have the largest sound velocity c(0), and the sound wave at the far right end has the smallest sound speed c(D), and the specific values are c(0)=c ₀ /2.2 and c(D )=c ₀ /3.4, where D is the width of the metasurface. In order to realize the adjustment of the speed of sound in the metasurface, the width of the slits in the 12 unit structures varies from 4.5 mm to 2.3 mm from left to right, with a step size of 0.2 mm. The waveform diagram of the abnormal refraction formed by the sound wave passing through the metasurface at 6970 Hz is shown in Figure 3c.

For a non-diffracting Bessel beam, according to the generalized Snell's law, the reciprocal of the velocity of the sound wave propagating along the x-axis direction can be expressed as

In the formula, H, c ₀ , θ _t =20° have the same meaning as the above formula (1), and c(0) is the minimum sound velocity in the middle of the metasurface. For this metasurface, there are 23 unit structures in total, as shown in Figure 4c, we can adjust the sound velocity of sound wave propagation by adjusting the width of the slits of the unit structure. We set the sound waves at the left and right ends of the metasurface to have the maximum sound velocity c(±D/2), and the minimum sound velocity c(0) in the middle, the specific values are respectively c(±D/2)=c ₀ /2.2 and c(0)=c ₀ /3.4, where D is the width of the metasurface. In order to realize the adjustment of the speed of sound in the metasurface, the width of the slit in the left unit structure is changed from 4.5 mm at the left end to 2.3 mm at the middle position, while the width of the slit in the unit structure on the right is changed from the middle position From 2.3mm to the rightmost 4.5mm, the change step is 0.2mm. The sound intensity waveform at 6970 Hz of the non-diffracting Bessel beam formed after the sound wave passes through the metasurface is shown in Fig. 4c.

The present invention proposes to use Helmholtz resonators and slits to form the unit structure of the metasurface, and to change the sound velocity of the sound waves in the metasurface by adjusting the width of the slits, thereby realizing the control of the sound wave front, such as Form anomalous refraction of sound waves, non-diffracting Bessel beams, etc. This method can be extended to acoustic wavefront manipulation in the full phase range, and can be applied to super-resolution imaging, focusing and detection in acoustics.

Having described various embodiments of the present invention, the foregoing description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and alterations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments.

Claims (5)

1. A method for controlling the acoustic wave front by using a metasurface composed of Helmholtz resonators. The method uses Helmholtz resonators to form a microstructure unit, and multiple microstructure units form a metasurface , which is characterized in that when the scale of the metasurface unit is much smaller than the wavelength of the sound wave, the sound velocity of the sound wave in the metasurface can be changed by adjusting the width of the slit in the microstructure unit, and then the phase of the sound wave can be changed, so as to realize the adjustment of the sound wave front regulation. 2. The method according to claim 1, wherein a metasurface composed of a Helmholtz resonator is used to realize the regulation of the acoustic wavefront, wherein the microstructure unit is vertically engraved on a metal medium by at least three Helmholtz resonators, the right side of each Helmholtz resonator has a rectangular slit structure. 3. the method according to claim 2 utilizing a metasurface composed of a Helmholtz resonator to realize the regulation of the acoustic wavefront, characterized in that the height H of the metal medium, i.e. the thickness of the metasurface, is 32mm , the period constant L of the microstructure unit is 8mm, the width of the slit is d; the neck length and width of the Helmholtz resonator are h=2mm and l=1mm respectively, and the height of the cavity of the Helmholtz resonator and width are a=6mm and b=2.5mm, respectively. 4. The method according to claim 1 utilizing a metasurface composed of Helmholtz resonators to realize the regulation and control of the acoustic wavefront, characterized in that the plurality of microstructure units are arranged horizontally to form a metasurface surface. 5. the method according to claim 1 utilizing a metasurface composed of a Helmholtz resonator to realize the regulation and control of the acoustic wavefront is characterized in that the acoustic wave velocity c in the _metasurface specifically satisfies the following formula: <mrow><mfrac><mn>1</mn><msub><mi>c</mi><mrow><mi>e</mi><mi>f</mi><mi>f</mi></mrow></msub></mfrac><mo>=</mo><msqrt><mfrac><msub><mi>&amp;rho;</mi><mn>0</mn></msub><msub><mi>B</mi><mrow><mi>e</mi><mi>f</mi><mi>f</mi></mrow></msub></mfrac></msqrt><mo>=</mo><msqrt><mrow><mfrac><msub><mi>&amp;rho;</mi><mn>0</mn></msub><msub><mi>B</mi><mn>0</mn></msub></mfrac><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mfrac><mrow><msup><msub><mi>F&amp;omega;</mi><mn>0</mn></msub><mn>2</mn></msup></mrow><mrow><msup><msub><mi>&amp;omega;</mi><mn>0</mn></msub><mn>2</mn></msup><mo>-</mo><msup><mi>&amp;omega;</mi><mn>2</mn></msup></mrow></mfrac><mo>)</mo></mrow></mrow></msqrt><mo>=</mo><msqrt><mrow><mfrac><msub><mi>&amp;rho;</mi><mn>0</mn></msub><msub><mi>B</mi><mn>0</mn></msub></mfrac><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mfrac><mrow><msup><msub><mi>ab&amp;omega;</mi><mn>0</mn></msub><mn>2</mn></msup></mrow><mrow><mi>L</mi><mi>d</mi><mrow><mo>(</mo><msup><msub><mi>&amp;omega;</mi><mn>0</mn></msub><mn>2</mn></msup><mo>-</mo><msup><mi>&amp;omega;</mi><mn>2</mn></msup><mo>)</mo></mrow></mrow></mfrac><mo>)</mo></mrow></mrow></msqrt></mrow> Among them: ρ ₀ is the air density, equal to 1.21kg/m ³ ; B _eff is the equivalent bulk modulus after introducing the Helmholtz resonator, the expression is <mrow><mfrac><mn>1</mn><msub><mi>B</mi><mrow><mi>e</mi><mi>f</mi><mi>f</mi></mrow></msub></mfrac><mo>=</mo><mfrac><mn>1</mn><msub><mi>B</mi><mn>0</mn></msub></mfrac><mrow><mo>(</mo><mn>1</mn><mo>-</mo><mfrac><mrow><msup><msub><mi>F&amp;omega;</mi><mn>0</mn></msub><mn>2</mn></msup></mrow><mrow><msup><mi>&amp;omega;</mi><mn>2</mn></msup><mo>-</mo><msup><msub><mi>&amp;omega;</mi><mn>0</mn></msub><mn>2</mn></msup></mrow></mfrac><mo>)</mo></mrow></mrow> Where: B ₀ =ρ ₀ c ₀ ² is the bulk modulus of air, where c ₀ =343m/s is the sound velocity in the air, so B ₀ is a constant; ω ₀ is the resonance angle of the Helmholtz resonator Frequency, ω is the frequency of the input sound wave signal; F=ab/Ld is the ratio of the cavity area of the Helmholtz resonator to the area of the corresponding slit, L represents the period constant of the microstructure unit, and d represents the slit in the microstructure unit The width of; a, b respectively represent the height and width of the Helmholtz resonator cavity.