A local resonance type phononic crystal and phononic crystal device

Abstract

The present invention proposes a phononic crystal and a phononic crystal device based on a local resonance type, which solves the problem that the frequency order of magnitude corresponding to the existing phononic crystal is large and is not conducive to practical integrated applications. The phononic crystal includes a plurality of crystal unit cell structures and a first base elastic connection part, each of which is composed of a loss scatterer unit, a gain scatterer unit and a second base elastic connection part. A negative imaginary part and a positive imaginary part are applied to the two scatterer units respectively. The application of the negative imaginary part and the positive imaginary part causes the energy band of the phononic crystal to be degenerate. The frequency at which the dividing point between the energy band degeneration and non-degeneration is located is located in the local resonance band gap. The frequency corresponding to the local resonance band gap is more than one order of magnitude lower than the frequency corresponding to the Bragg band gap. Although the frequency order of magnitude corresponding to the phononic crystal is low, the purpose of "small size controlling large wavelength" can be achieved, which is conducive to practical integrated applications and has high practical value.

Description

Technical Field

[0001] The present invention relates to the technical field of acoustic transmission processing, and more specifically, to a local resonance type phononic crystal and a phononic crystal device. Background Art

[0002] Phononic crystals refer to materials or structures with elastic band gaps, elastic constants, and periodic distribution of density. Inside the phononic crystal, the elastic constants, mass density, and other parameters of the material components change periodically. According to the periodicity of the structure in three orthogonal directions in the rectangular coordinate system, phononic crystals can be divided into one-dimensional, two-dimensional, and three-dimensional phononic crystals. Currently, phononic crystals have been applied to many fields, such as structural seismic isolation, noise reduction, and controlled transmission of acoustic waves, in order to improve the performance and life of various devices.

[0003] An important feature of phononic crystals is the phonon bandgap (or acoustic bandgap), that is, elastic waves (acoustic waves) cannot pass through phononic crystals within this frequency range, or in other words, there are no phonon energy states within this frequency range. There are two main mechanisms for the generation of elastic wave (acoustic wave) bandgap: Bragg scattering and local resonance. The Bragg scattering mechanism is based on the periodic structure of the material, that is, the periodic variation of material properties interacts with elastic waves, so that waves of certain frequencies do not have corresponding vibration modes, and cannot propagate corresponding acoustic waves, thus generating a bandgap. The local resonance theory emphasizes the effect of the special structure of a single scatterer on the wave, that is, under the excitation of elastic waves of a specific frequency, a single scatterer resonates and interacts with the incident wave, preventing it from continuing to propagate.

[0004] The frequency of the currently designed phononic crystals is basically within the Bragg scattering band gap, which is comparable to the lattice constant. However, since the frequency range of the acoustic functional device is within the audible range of the human ear (about 20Hz to 20kHz) and the working background is generally air (the speed of sound is about 343m / s), the corresponding lattice constant reaches the meter level, which is not conducive to practical integrated applications. The frequency corresponding to the local resonance band gap is often more than one order of magnitude lower than the frequency corresponding to the Bragg band gap, so the lattice constant at this time is also reduced by more than one order of magnitude, making it more practical. On December 15, 2020, a phononic crystal cell structure was disclosed in a Chinese patent (publication number: CN112086083A). This patent designed a phononic crystal cell structure based on a spring oscillator, simplifying the phononic crystal into a spring-weight system, and using the vibration of the spring component to enhance the resonance ability of the resonant body of the phononic crystal, effectively adjusting and changing the bandgap frequency and width of the phononic crystal, overcoming the defects of existing research that uses increasing the geometric parameters of the phononic crystal cell structure to enhance the resonance ability of the resonant body, but the enhancement amplitude is limited and the excessively large geometric parameters make the phononic crystal device not conducive to practical applications. Summary of the invention

[0005] In order to solve the problem that the frequency corresponding to the existing phononic crystals is of a large order of magnitude and is not conducive to practical integrated applications, the present invention proposes a phononic crystal and a phononic crystal device based on local resonance. The designed phononic crystal corresponds to a low order of magnitude of frequency, but can achieve the purpose of "small size controlling large wavelength", thereby improving the practical value.

[0006] In order to achieve the above technical effects, the technical solution of the present invention is as follows:

[0007] A local resonance type phononic crystal comprises: j crystal unit cell structures and a first base elastic connection part, j is an integer greater than 1; the j-1th crystal unit cell structure is connected to the jth crystal unit cell structure through the first base elastic connection part, any crystal unit cell structure comprises a loss scatterer unit, a gain scatterer unit and a second base elastic connection part, the loss scatterer unit is connected to the gain scatterer unit through the second base elastic connection part, a first core structure for applying a negative imaginary part is provided inside the loss scatterer unit; a second core structure for applying a positive imaginary part is provided inside the gain scatterer unit, the application of the negative imaginary part and the positive imaginary part causes the energy band of the phononic crystal to be degenerate, and the frequency at which the boundary point between the energy band degeneration and non-degeneration is located is located in the local resonance band gap.

[0008] In the present technical scheme, a plurality of crystal unit cell structures and a first matrix elastic connection part together constitute a phononic crystal, and each crystal unit cell structure is composed of a loss scatterer unit, a gain scatterer unit and a second matrix elastic connection part, that is, the core is two scatterer units. In order to make the phononic crystal satisfy the PT symmetry condition, the two scatterer units and the second matrix elastic connection part are used as a basic crystal unit cell structure, and a negative imaginary part and a positive imaginary part are applied to the two scatterer units respectively. The application of the negative imaginary part and the positive imaginary part causes the energy band of the phononic crystal to become degenerate. The dividing point between the energy band degeneration and non-degeneration is also called a singular point. The frequency of the singular point is located in the local resonance band gap. The frequency corresponding to the local resonance band gap is more than one order of magnitude lower than the frequency corresponding to the Bragg band gap. Although the frequency corresponding to the phononic crystal is of a low order of magnitude, it can achieve the purpose of "small size controlling large wavelength", and asymmetric transmission can generally be achieved near the singular point, which is conducive to actual integrated application and has high practical value.

[0009] Preferably, the first substrate elastic connection part and the second substrate elastic connection part are both springs, and the elastic coefficient is K, that is, several crystal unit cell structures can be connected by a spring with an elastic coefficient of K, and the loss scatterer unit and the gain scatterer unit can also be connected by a spring with an elastic coefficient of K, and the materials selected for the first substrate elastic connection part and the second substrate elastic connection part can be the same.

[0010] Preferably, the lossy scatterer unit of any crystal unit cell structure includes a first unit cell cladding body, a first inner core body and a first elastic connecting part, the first inner core body and the first elastic connecting part constitute a first inner core structure, the first unit cell cladding body is a hollow sphere, the first inner core body is arranged inside the unit cell cladding body, and the outer surface of the first inner core body is connected to the inner surface of the first unit cell cladding body through the first elastic connecting part.

[0011] Preferably, the gain scatterer unit of any crystal unit cell structure includes a second unit cell cladding body, a second core body and a second elastic connecting part, the second core body and the second elastic connecting part constitute a second core structure, the second unit cell cladding body is a hollow sphere, the second core body is arranged inside the second unit cell cladding body, and the outer surface of the second core body is connected to the inner surface of the second unit cell cladding body through the second elastic connecting part.

[0012] Preferably, the negative imaginary part applied to the first core structure refers to applying the negative imaginary part to the first elastic connection part of the first core structure, which is G(1-αi), and the negative imaginary part applied to the second core structure refers to applying the positive imaginary part to the second elastic connection part of the second core structure, which is G(1+αi), satisfying the PT symmetry condition, wherein G represents the stiffness coefficient, i represents the imaginary part, and i represents the imaginary unit. The application of the negative imaginary part and the positive imaginary part causes the energy band of the phononic crystal to be degenerate, and the frequency at which the dividing point between the energy band degeneration and non-degeneration is located in the local resonance band gap.

[0013] Preferably, the first elastic connection part and the second elastic connection part are both springs.

[0014] Preferably, the lossy scatterer unit of any crystal unit cell structure includes a first unit cell cladding body made of soft rubber and a first core structure made of epoxy resin; the first unit cell cladding body is a hollow sphere, the first core structure is a solid sphere, and the outer surface of the first core structure is in contact with the inner surface of the first unit cell cladding body.

[0015] Preferably, the gain scatterer unit of any crystal unit cell structure includes a second unit cell cladding body made of soft rubber and a second core structure made of epoxy resin; the second unit cell cladding body is a hollow sphere, the second core structure is a solid sphere, and the outer surface of the second core structure is in contact with the inner surface of the second unit cell cladding body; a positive imaginary part is applied to the Lame constant of the first unit cell cladding body made of soft rubber, and its size is 0.3 times the real part, and a negative imaginary part is applied to the Lame constant of the second unit cell cladding body made of soft rubber, and its size is 0.3 times the real part, so as to satisfy the PT symmetry condition.

[0016] Preferably, the first base elastic connecting portion and the second base elastic connecting portion can be equivalent to water

[0017] The present invention also provides a local resonance type phononic crystal device, and the phononic crystal device includes the local resonance type phononic crystal.

[0018] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0019] The present invention provides a local resonance type phononic crystal and a phononic crystal device. The phononic crystal includes a plurality of crystal unit cell structures and a first base elastic connection part. In order to make the phononic crystal meet the PT symmetry condition, each crystal unit cell structure is composed of a loss scatterer unit, a gain scatterer unit and a second base elastic connection part. A negative imaginary part and a positive imaginary part are applied to the two scatterer units respectively. The application of the negative imaginary part and the positive imaginary part causes the energy band of the phononic crystal to be degenerate. The frequency at the boundary point between the energy band degeneration and non-degeneration is located in the local resonance band gap. The frequency corresponding to the local resonance band gap is more than one order of magnitude lower than the frequency corresponding to the Bragg band gap. Although the frequency corresponding to the phononic crystal is of a low order of magnitude, the purpose of "small size controlling large wavelength" can be achieved, and asymmetric transmission can generally be achieved near the boundary point, which is conducive to actual integrated application and has high practical value. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 A schematic diagram showing the structure of a local resonance type phononic crystal proposed in an embodiment of the present invention;

[0021] Figure 2 Indicates that the present invention is implemented Figure 1 Taking the crystal unit cell structure shown as an example, the band diagram of the phononic crystal under different imaginary parts α;

[0022] Figure 3 A schematic diagram showing another crystal unit cell structure proposed in an embodiment of the present invention;

[0023] Figure 4 Indicates that the embodiment of the present invention Figure 3 A schematic diagram of a phononic crystal structure comprising 6 crystal unit cell structures, taking another crystal unit cell structure as an example;

[0024] Figure 5 The transmission spectra of the phononic crystal comprising 6 crystal unit cell structures proposed in the embodiment of the present invention at different frequencies are shown;

[0025] Figure 6 The diagram represents the sound pressure field of the phononic crystal comprising 6 crystal unit cell structures proposed in the embodiment of the present invention at different frequency points. DETAILED DESCRIPTION

[0026] The drawings are for illustrative purposes only and should not be construed as limiting the present patent;

[0027] In order to better illustrate the present embodiment, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the actual size;

[0028] It is understandable to those skilled in the art that descriptions of certain well-known contents in the drawings may be omitted.

[0029] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0030] Example 1

[0031] The positional relationships described in the drawings are only for illustrative purposes and should not be construed as limiting the present patent.

[0032] The present invention provides a local resonance type phononic crystal, comprising: j crystal unit cell structures 1 and a first base elastic connecting portion 2, where j is an integer greater than 1; the j-1 th crystal unit cell structure is connected to the j th crystal unit cell structure via the first base elastic connecting portion 2, and the overall structure is as follows Figure 1 As shown, in this embodiment, see Figure 1 , there are 6 crystal unit cell structures, see Figure 1 More specifically, any crystal unit cell structure includes a loss scatterer unit 11, a gain scatterer unit 12 and a second substrate elastic connecting portion 3. The loss scatterer unit 11 is connected to the gain scatterer unit 12 through the second substrate elastic connecting portion 3. A first core structure 4 for applying a negative imaginary part is provided inside the loss scatterer unit 11; a second core structure 5 for applying a positive imaginary part is provided inside the gain scatterer unit 12. The application of the negative imaginary part and the positive imaginary part causes the energy band of the phononic crystal to be degenerate, and the frequency of the dividing point between the energy band degeneration and non-degeneration is located in the local resonance band gap.

[0033] Specifically, the first base elastic connecting portion 2 and the second base elastic connecting portion 3 are both springs, and the elastic coefficient is K, see Figure 1 The loss scatterer unit 11 includes a first single-cell cladding body 111, a first core body 112 and a first elastic connecting part 113, the first core body 112 and the first elastic connecting part 113 constitute a first core structure 4, the first single-cell cladding body 111 is a hollow sphere, the first core body 112 is arranged inside the single-cell cladding body 111, and the outer surface of the first core body 112 is connected to the inner surface of the first single-cell cladding body 111 through the first elastic connecting part 113; the gain scatterer unit 12 includes a second single-cell cladding body 121, a second core body 122 and a second elastic connecting part 123, the second core body 122 and the second elastic connecting part 123 constitute a second core structure 5, the second single-cell cladding body 121 is a hollow sphere, the second core body 122 is arranged inside the second single-cell cladding body 121, and the outer surface of the second core body 122 is connected to the inner surface of the second single-cell cladding body 121 through the second elastic connecting part 123.

[0034] As a preferred specific implementation manner, “the loss scatterer unit 11 is provided with a first core structure 4 for applying a negative imaginary part; the gain scatterer unit 12 is provided with a second core structure 5 for applying a positive imaginary part” means that the first elastic connection part 113 of the first core structure 4 applies a negative imaginary part of G(1-αi), and the second elastic connection part 123 of the second core structure 5 applies a positive imaginary part of G(1+αi), thereby satisfying the PT symmetry condition, which is a mechanism for adjusting the satisfaction of the PT symmetry condition, wherein G represents the stiffness coefficient, α represents the imaginary part, and i represents the imaginary unit. In this implementation manner, the first elastic connection part 113 and the second elastic connection part 123 are both springs with a stiffness coefficient of G. The mass of the first unit cell cladding 111 is set to M, which is 0.5, the elastic coefficient of the first elastic connection part 113 of the first core structure 4 is G, which is 0.25, and the mass of the first core body 112 is m, which is 2; the mass of the second unit cell cladding 121 is set to M, which is 0.5, the elastic coefficient of the second elastic connection part 123 of the second core structure 5 is G, which is 0.25, and the mass of the second core body 122 is m, which is 2. The energy band diagrams of the phononic crystals under different imaginary parts α are shown in FIG. Figure 2 As shown, Figure 2 The energy band diagrams are α=0, α=0.15, α=0.3, and α=0.8 respectively. The horizontal axis represents the wave vector and the vertical axis represents the frequency. Figure 2 It can be seen that when α = 0, the energy band is not degenerate; when α = 0.15, the dividing points between the energy band degeneracy and non-degenerate are two points, A and B. With the introduction of the imaginary part, the energy band of the phononic crystal is degenerate. The dividing point between the energy band degeneracy and non-degenerate is called the singular point. By adjusting the size of the imaginary part, it is also found that the singular point will move with the increase of the size of the imaginary part. For example, when α = 0.3, the dividing points between the energy band degenerate and non-degenerate are three points, A, B and C. When α = 0.8, the dividing points between the energy band degenerate and non-degenerate are two points, B and D. The singular point The frequencies where the singular points are located are all located near the local resonance band gap and belong to the low frequency band. Generally speaking, asymmetric transmission phenomena will occur near the singular points. The energy band frequency of the phononic crystal structure designed by the present invention is located in the local resonance band gap, and when the frequency corresponding to the local resonance band gap is more than one order of magnitude lower than the frequency corresponding to the Bragg band gap, asymmetric transmission in the low frequency band can also be achieved. The frequency corresponding to the phononic crystal designed by the present invention is of a low order of magnitude, and an asymmetric transmission phenomenon of a wavelength more than one order of magnitude larger than the structural parameter (Bragg scattering band gap) is achieved, which has high practical value.

[0035] The following example further verifies the superiority of the phononic crystal designed in the present invention when α=0.3 and the number of singular points of the phononic crystal energy band is the largest (3). Specifically, another preferred equivalent specific implementation method is as follows: Figure 3As shown, in the lossy scatterer unit 11 of the crystal unit cell structure, the first core body 112 and the first elastic connecting portion 113 constitute the first core structure 4 which is directly made of epoxy resin with a density of 1180 kg / m 3 The first unit cell cladding body 111 is made of soft rubber with a density of 1180 kg / m 3 , see Figure 3 The first unit cell cladding body 111 is in the shape of a hollow sphere, the first core structure 4 is in the shape of a solid sphere, and the outer surface of the first core structure 4 is in contact with the inner surface of the first unit cell cladding body 111. Similarly, in the gain scatterer unit 12 of the crystal unit cell structure, the second core body 122 and the first elastic connecting part 123 constitute the second core structure 5 which is directly made of epoxy resin with a density of 1180kg / m 3 The first unit cell cladding body 121 is made of soft rubber with a density of 1180 kg / m 3 , the second unit cell cladding body 121 is in the shape of a hollow sphere, the second core structure 5 is in the shape of a solid sphere, the outer surface of the second core structure 5 is in contact with the inner surface of the second unit cell cladding body 121, for the sake of equivalence, the positive imaginary part is applied to the Lame constant of the first unit cell cladding body 121 made of soft rubber, the size of which is 0.3 times the real part, and the negative imaginary part is applied to the Lame constant of the second unit cell cladding body 121 made of soft rubber, the size of which is 0.3 times the real part, satisfying the PT symmetry condition, at this time, Figure 3 The crystal unit cell structure shown in FIG. 1 is a schematic diagram of a phononic crystal structure including six crystal unit cell structures. Figure 4 As shown, the first substrate elastic connection part 2 and the second substrate elastic connection part 3 can be equivalent to water at this time. When calculating the energy band, the left and right boundaries take periodic boundary conditions, where the unit on the left is a loss scatterer unit, and the positive imaginary part is applied to the corresponding Lame constant, and the unit on the right is a gain scatterer unit, and the negative imaginary part is applied to the corresponding Lame constant.

[0036] Figure 5 Indicates that it contains Figure 4 The transmission spectra of the phononic crystals of the six crystal unit cell structures at different frequencies are shown. The horizontal axis represents the frequency, and the vertical axis represents the values ​​of the left reflection coefficient, the right reflection coefficient and the transmission coefficient as the frequency changes. Figure 5 The curves in are: "◇" represents the numerical line of the left reflection coefficient changing with frequency, "○" represents the numerical line of the right reflection coefficient changing with frequency, and "□" represents the numerical line of the transmission coefficient changing with frequency. The left reflection coefficient at frequency point 1 is the same as the right reflection coefficient, both are zero, and the transmission coefficient is 1, which plays a contrast role. The corresponding transmission coefficient of frequency point 2 is 1, the left reflection coefficient is not 0, and the right reflection coefficient is 0. The frequency point 3 is just the opposite, the left reflection coefficient is 0, and the right reflection coefficient is not 0. Therefore, the phononic crystal can achieve asymmetric transmission at frequency points 2 and 3. Figure 5Further draw the sound pressure field diagram of the phononic crystal at different frequency points as shown in Figure 6 As shown, Figure 6 The sound pressure distribution at frequency point 1, frequency point 2 and frequency point 3 is shown in Figure 6 It can be more clearly seen that the asymmetric transmission effect that the local resonance phononic crystal proposed in the present invention can achieve, see Figure 6 The sound pressure field corresponding to frequency point 1 is the same for left and right incident situations, and there is no reflection. However, the sound pressure fields corresponding to frequency points 2 and 3 are obviously different for left and right incident situations. The situation of frequency point 2 is that there is reflection for the left incident situation but not for the right incident situation. The situation corresponding to frequency point 3 is opposite to that for frequency point 2. In summary, the phononic crystal structure designed in the present invention can realize the asymmetric transmission phenomenon of wavelengths that are more than one order of magnitude larger than its structural parameters (Bragg scattering band gap), that is, small size controls large wavelength, and has higher practical value. The phononic crystal designed by the present invention can constitute a variety of practical phononic crystal devices.

[0037] The positional relationships described in the drawings are only for illustrative purposes and should not be construed as limiting the present patent.

[0038] Obviously, the above embodiments of the present invention are only examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the embodiments here. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A local resonance type phononic crystal, characterized in that: include: j crystal unit cell structures and a first matrix elastic connection part, j is an integer greater than 1; the j-1th crystal unit cell structure is connected to the jth crystal unit cell structure through the first matrix elastic connection part, any crystal unit cell structure includes a loss scatterer unit, a gain scatterer unit and a second matrix elastic connection part, the loss scatterer unit is connected to the gain scatterer unit through the second matrix elastic connection part, a first core structure for applying a negative imaginary part is provided inside the loss scatterer unit; a second core structure for applying a positive imaginary part is provided inside the gain scatterer unit, the application of the negative imaginary part and the positive imaginary part causes the energy band of the phononic crystal to be degenerate, the frequency of the dividing point between the energy band degeneration and non-degeneration is located in the local resonance band gap, the frequency corresponding to the local resonance band gap is of a low order of magnitude, and an asymmetric transmission phenomenon is realized; Applying a negative imaginary part to the first core structure means applying a negative imaginary part to the first elastic connection part of the first core structure, which is G(1-αi); applying a positive imaginary part to the second core structure means applying a positive imaginary part to the second elastic connection part of the second core structure, which is G(1+αi), satisfying the PT symmetry condition, wherein G represents the stiffness coefficient, i represents the imaginary part, and α represents the imaginary unit.

2. The local resonance type phononic crystal according to claim 1, characterized in that: The first base elastic connecting part and the second base elastic connecting part are both springs, and the elastic coefficients are both K.

3. The local resonance type phononic crystal according to claim 1, characterized in that: The lossy scatterer unit of any crystal unit cell structure includes a first unit cell cladding body, a first inner core body and a first elastic connecting part. The first inner core body and the first elastic connecting part constitute a first inner core structure. The first unit cell cladding body is a hollow sphere. The first inner core body is arranged inside the unit cell cladding body. The outer surface of the first inner core body is connected to the inner surface of the first unit cell cladding body through the first elastic connecting part.

4. The local resonance type phononic crystal according to claim 3, characterized in that: The gain scatterer unit of any crystal unit cell structure includes a second unit cell cladding body, a second core body and a second elastic connecting part. The second core body and the second elastic connecting part constitute a second core structure. The second unit cell cladding body is a hollow sphere. The second core body is arranged inside the second unit cell cladding body. The outer surface of the second core body is connected to the inner surface of the second unit cell cladding body through the second elastic connecting part.

5. The local resonance type phononic crystal according to claim 4, characterized in that: The first elastic connection part and the second elastic connection part are both springs.

6. The local resonance type phononic crystal according to claim 1, characterized in that: The lossy scatterer unit of any crystal unit cell structure includes a first unit cell cladding body made of soft rubber and a first core structure made of epoxy resin; the first unit cell cladding body is a hollow sphere, the first core structure is a solid sphere, and the outer surface of the first core structure is in contact with the inner surface of the first unit cell cladding body.

7. The local resonance type phononic crystal according to claim 6, characterized in that: The gain scatterer unit of any crystal unit cell structure includes a second unit cell cladding body made of soft rubber and a second core structure made of epoxy resin; the second unit cell cladding body is in the shape of a hollow sphere, the second core structure is in the shape of a solid sphere, and the outer surface of the second core structure is in contact with the inner surface of the second unit cell cladding body; a positive imaginary part is applied to the Lame constant of the first unit cell cladding body made of soft rubber, and the size is 0.3 times the real part, and a negative imaginary part is applied to the Lame constant of the second unit cell cladding body made of soft rubber, and the size is 0.3 times the real part, so as to satisfy the PT symmetry condition.

8. The local resonance type phononic crystal according to claim 7, characterized in that: The first base elastic connecting part and the second base elastic connecting part can both be equivalent to water.

9. A local resonance type phononic crystal device, characterized in that: The phononic crystal device comprises the local resonance type phononic crystal according to any one of claims 1 to 8.

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