CN110880311B - Underwater sub-wavelength space coiling type acoustic metamaterial - Google Patents
Underwater sub-wavelength space coiling type acoustic metamaterial Download PDFInfo
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- CN110880311B CN110880311B CN201811034463.4A CN201811034463A CN110880311B CN 110880311 B CN110880311 B CN 110880311B CN 201811034463 A CN201811034463 A CN 201811034463A CN 110880311 B CN110880311 B CN 110880311B
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- G—PHYSICS
- G10—MUSICAL INSTRUMENTS; ACOUSTICS
- G10K—SOUND-PRODUCING DEVICES; METHODS OR DEVICES FOR PROTECTING AGAINST, OR FOR DAMPING, NOISE OR OTHER ACOUSTIC WAVES IN GENERAL; ACOUSTICS NOT OTHERWISE PROVIDED FOR
- G10K11/00—Methods 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
- G10K11/16—Methods or devices for protecting against, or for damping, noise or other acoustic waves in general
- G10K11/162—Selection of materials
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- G—PHYSICS
- G10—MUSICAL INSTRUMENTS; ACOUSTICS
- G10K—SOUND-PRODUCING DEVICES; METHODS OR DEVICES FOR PROTECTING AGAINST, OR FOR DAMPING, NOISE OR OTHER ACOUSTIC WAVES IN GENERAL; ACOUSTICS NOT OTHERWISE PROVIDED FOR
- G10K11/00—Methods 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
- G10K11/16—Methods or devices for protecting against, or for damping, noise or other acoustic waves in general
- G10K11/172—Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using resonance effects
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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Abstract
The invention discloses an underwater subwavelength space coiled acoustic metamaterial which comprises a square water area 1 and a stainless steel entity 2 at the periphery of the square water area 1. The stainless steel body 2 has eight quarter turn acoustic channels (3, 4, 5, 6, 7, 8, 9 and 10). Each quarter turn acoustic channel turns twice at right angles, forming a zigzag shape. The two ends of the right angle turning sound channel are respectively communicated with the external water area 11 and the internal square water area 1. The eight quarter turn acoustic channels are mirror symmetric about the central axis (12 and 13) and the diagonal (14 and 15). The underwater subwavelength space coiled acoustic metamaterial has a complete band gap at low frequency. The complete band gap can intercept the propagation path of the sound wave, and the sound wave is totally reflected to prevent the sound wave from continuing to propagate forwards, so that the possibility that the underwater object is detected by the sonar due to the radiation noise of the underwater object is reduced. The underwater subwavelength space coiled acoustic metamaterial provided by the invention has a Dirac-like point at low frequency. The sound wave near the Dirac-like point can realize zero phase difference propagation without changing the wave front array shape of the sound wave, and the possibility that the underwater obstacle is actively detected by the sonar is reduced.
Description
Technical Field
The invention relates to a space bending structure, dirac-like points and an acoustic metamaterial, in particular to an underwater subwavelength space coiling acoustic metamaterial.
Background
The wave length of the underwater sound wave is long because the propagation speed of the sound wave in the water is high. The wavelength of the underwater sound wave at the same frequency is more than 4 times of that of the air. The lowest band gap of a conventional phonon crystal corresponds to a wavelength 2 times the lattice constant. Therefore, to realize shielding of underwater low-frequency noise, sound stealth, and the like, a large lattice constant is required. The larger lattice constant can cause the volume of phonon crystals to be too large, thereby severely limiting the engineering utility value. However, important national defense equipment such as submarines, warships and the like and important underwater military and civil facilities now put urgent demands on sound absorption, sound shielding, sound stealth and the like of underwater low-frequency noise. Taking sound stealth of important national defense equipment such as submarines and the like as an example, noise emitted by a submarine engine becomes a main sound source of sonar passive detection, and shielding of low-frequency noise of the engine needs to adopt thicker sound absorption materials, is high in price, and can severely limit optimization of comprehensive performance of the submarine body. In addition, the rapid development of active sonar technology improves the detectability of the submarine more seriously, and reduces the stealth performance of the submarine. The development of the underwater sub-wavelength space coiled acoustic metamaterial can greatly promote effective shielding and sound stealth of underwater low-frequency vibration noise, and can be well applied to various occasions such as submarine stealth.
Disclosure of Invention
The invention aims to solve the technical problem of providing an underwater subwavelength space coiled acoustic metamaterial which can efficiently absorb noise in a complete band gap of subwavelength and block sound sources from radiating noise outwards; the method can realize zero phase difference propagation of sub-wavelength sound waves at Dirac-like points, and reduce the detectability of important facilities under water.
In order to solve the technical problems, the invention provides an underwater subwavelength space coiled acoustic metamaterial. The underwater sub-wavelength space coiled acoustic metamaterial is square; comprises a square water area and eight right angle turning sound channels. Each quarter turn acoustic channel turns twice at right angles, forming a zigzag shape. The two ends of the right angle turning sound channel are respectively communicated with the external water area and the internal square water area.
As the improvement of the underwater sub-wavelength space coiling type acoustic metamaterial, the invention: the underwater sub-wavelength space coiled acoustic metamaterial adopts a square structure.
As a further improvement of the underwater subwavelength space coiled acoustic metamaterial of the invention: the square structure is internally provided with a square water area.
As a further improvement of the underwater subwavelength space coiled acoustic metamaterial of the invention: eight right angle turning sound channels are distributed on the periphery of the square water area.
As a further improvement of the underwater subwavelength space coiled acoustic metamaterial of the invention: the entrance of the quarter turn acoustic channel is located at 1/4 of the boundary side of the acoustic metamaterial.
As a further improvement of the underwater subwavelength space coiled acoustic metamaterial of the invention: the quarter turn acoustic channel is perpendicular to the acoustic metamaterial boundary.
As a further improvement of the underwater subwavelength space coiled acoustic metamaterial of the invention: the quarter turn acoustic channel turns right at 1/2 of the vertical distance between the acoustic metamaterial boundary and the square water boundary.
As a further improvement of the underwater subwavelength space coiled acoustic metamaterial of the invention: the quarter turn sound channel makes a second quarter turn at 1/4 of the boundary side of the square water area after the first quarter turn.
As a further improvement of the underwater subwavelength space coiled acoustic metamaterial of the invention: the outlet of the quarter turn acoustic channel is located at 1/4 of the square water boundary.
As a further improvement of the underwater subwavelength space coiled acoustic metamaterial of the invention: the eight quarter turn acoustic channels are mirror symmetric about the central axis.
As a further improvement of the underwater subwavelength space coiled acoustic metamaterial of the invention: the eight quarter turn acoustic channels are mirror symmetric about a diagonal.
Compared with the background technology, the invention has the beneficial effects that:
the underwater subwavelength space coiled acoustic metamaterial can be processed by adopting materials with higher rigidity (such as stainless steel, aluminum alloy and the like), and is low in production cost. The underwater sub-wavelength space coiling type acoustic metamaterial has a complete band gap. The underwater sub-wavelength space coiled acoustic metamaterial can realize strong reflection of sound waves in a complete band gap. The Dirac-like point of the underwater sub-wavelength space coiled acoustic metamaterial can generate zero dynamic mass density. The underwater sub-wavelength space coiled acoustic metamaterial can guide the zero-phase difference transmission of sound waves near the frequency of zero dynamic mass density. According to the invention, through the strong reflection of the underwater sub-wavelength space coiled acoustic metamaterial, the sound wave is blocked from continuously propagating forwards, so that the noise reduction effect is realized. According to the invention, the wave front array shape of the sound wave is not changed through zero phase difference propagation of the underwater sub-wavelength space coiled acoustic metamaterial, so that the underwater sound stealth effect is achieved.
The invention will be further described with reference to the drawings and the specific examples.
Drawings
FIG. 1 is an underwater sub-wavelength space-coiling acoustic metamaterial according to the present invention;
FIG. 2 is a positive and negative diagraph of a Bravais square lattice of an underwater subwavelength spatially coiled acoustic metamaterial according to the invention;
FIG. 3 is an energy band structure of an underwater sub-wavelength spatially coiled acoustic metamaterial and a common rigid photonic crystal of the present invention;
FIG. 4 is a frequency response function of an underwater sub-wavelength spatially coiled acoustic metamaterial according to the present invention;
FIG. 5 is a plot of the acoustic pressure level within the band gap of an underwater subwavelength spatially coiled acoustic metamaterial according to this invention;
FIG. 6 is a zero-phase difference transmission diagram of Dirac points of an underwater sub-wavelength space coiled acoustic metamaterial according to the present invention;
FIG. 7 is a diagram of the sound hiding effect of Dirac points of an underwater sub-wavelength space coiled acoustic metamaterial according to the present invention;
FIG. 8 is a sound wave reflection graph of an underwater subwavelength spatially coiled acoustic metamaterial according to this invention removed.
Detailed Description
Fig. 1 shows an underwater subwavelength spatially coiled acoustic metamaterial. The underwater sub-wavelength space coiled acoustic metamaterial is square. (1) Is a square water area of the underwater sub-wavelength space coiled acoustic metamaterial. The periphery of the water area is a solid structure (2), and the material of the structure is a material with higher rigidity (such as stainless steel and the like). The stainless steel body (2) has eight quarter turn acoustic channels (3, 4, 5, 6, 7, 8, 9 and 10) which communicate with the outer body of water (11) and the inner square body of water (1). The eight quarter turn acoustic channels turn twice at right angles. The eight quarter turn acoustic channels are mirror symmetrically distributed about the central axis and diagonal.
The working principle of the underwater sub-wavelength space coiling type acoustic metamaterial is as follows:
(1) The geometric parameters of the underwater subwavelength space coiled acoustic metamaterial unit cell are l=100mm, t= 0.05657 l= 5.657mm, and alpha= 0.4667 l= 46.667mm.
(2) As shown in fig. 2, the underwater subwavelength spatially coiled acoustic metamaterial was placed in a Bravais square lattice with a lattice constant of 100 mm. The basis vector of the Bravais square lattice is e= (e) 1 ,e 2 ). Any other primitive cell can be defined as a set of integer pairs (n 1 ,n 2 ). When n is 1 =0 and n 2 When=0, the initial primitive cell is indicated. Any other primordial cell can be located along e 1 Translation of direction n 1 Step, edge e 2 Translation of direction n 2 And obtaining the product.
The response of a lattice point r in the initial primitive cell can be expressed as u (r). Since the Bravais hexagonal lattice is periodic, the primordia (n 1 ,n 2 ) Is also periodic:
u(r)＝u(r+R n ) (1)
wherein R is n ＝n 1 e 1 +n 2 e 2 Is a positive lattice vector.
The Fourier series form of the periodic function u (r) can be expressed as:
substituting formula (2) into formula (1) yields:
G j ·R n ＝2πk (3)
wherein G is j Is an inverted lattice vector, and its basis vector can be expressed as
(3) And calculating the energy band structure diagram of the structure by adopting a finite element method. An elastic wave equation with linear elasticity, anisotropy, and inhomogeneous medium can be expressed as:
wherein r= (x, y, z) represents a bit vector; u=(u x ,u y ,u z ) Representing a displacement vector;representing a gradient operator; c (r) represents an elastic tensor; ρ (r) represents the density tensor.
When the elastic wave is a simple harmonic, the displacement vector u (r, t) can be expressed as:
u(r,t)＝u(r)e iωt (5)
wherein the method comprises the steps ofω represents angular frequency. Substituting equation (5) into equation (4), the elastic wave equation can be simplified as:
since only longitudinal waves are present in the fluid, the fluid's simple harmonic acoustic equation can be expressed as:
wherein c l (r) is the wave velocity of the longitudinal wave; p (r) represents the flow field pressure.
The fluid-solid coupling interface needs to meet the conditions of normal particle acceleration and normal pressure continuity:
wherein n is f And n s A normal vector representing fluid and solid coupling surface fluid and solid; v denotes particle vibration velocity; p is p f Representing flow field pressure; sigma (sigma) ij Representing the stress component of the solid.
Spatially, the Bravais lattice is infinitely periodic. Using Bloch theory, the displacement vector u (r) and the flow field pressure p (r) can be expressed as
Where k= (k) x ,k y ,k z ) Representing wave vectors; u (u) k (r) and p k (r) represents a periodic displacement vector and a periodic flow field vector of the lattice. The band structure diagram of the periodic structure can be calculated in the initial primitive cell by adopting a finite element method by applying a Bloch-Floquet condition on the periodic boundary. The discrete finite element eigenvalue equation for the initial primitive cell is:
wherein K is s And K f A stiffness matrix that is solid and fluid; m is M s And M f A mass matrix that is a solid and a fluid; q is a fluid-solid coupling matrix.
In order to obtain a complete band structure, if the structural unit has enough symmetry, the mode frequencies corresponding to all wave vectors k should be theoretically calculated. In the Bloch theory, wave vector k in the inverted lattice vector is symmetrical and periodic. Thus, wave vector k may be limited to the first irreducible Brillouin zone of the inverted lattice vector. Furthermore, since the extremum of the band gap always occurs at the boundary of the first irreducible Brillouin zone, the wave vector k may be further defined to the boundaries X→Γ, Γ→M and M→X of the first irreducible Brillouin zone.
(4) As shown in FIG. 3a, the underwater subwavelength spatially coiled acoustic metamaterial has a complete band gap [6614Hz, 86221 Hz]. The band gap has a normalized frequency range of [ f r1 R/c 0 ＝0.444，f r2 R/c 0 ＝0.578]. Wherein f r1 And f r2 Up and down frequencies for the band gap; r is a lattice constant; c 0 Is the propagation velocity of the sound wave. As shown in FIG. 3b, the underwater sub-wavelength space coiled acoustic metamaterial was replaced with a common rigid photonic crystal which was found to have a narrow band gap [9107Hz,9432Hz]. The band gap has a normalized frequency range of [ f r3 R/c 0 ＝0.611，f r4 R/c 0 ＝0.633]. Wherein f r3 And f r4 Up and down frequencies for the band gap; r is the lattice constant. Because the standardized frequency of the underwater sub-wavelength space coiled acoustic metamaterial is smaller than that of a common phonon crystal, the underwater sub-wavelength space coiled acoustic metamaterial is of a sub-wavelength structure, has a wider sub-wavelength band gap, and can effectively shield sound wave propagation with longer wavelength in a wider frequency band compared with the common phonon crystal.
(5) The underwater sub-wavelength space coiled acoustic metamaterial is periodically arranged around the point sound source, and 4 layers are arranged on the upper side, the lower side, the left side and the right side respectively. The excitation frequency band of the point sound source is 100Hz-10500Hz, and the frequency response function of the sound wave penetrating through the underwater sub-wavelength space coiled acoustic metamaterial is shown in figure 4. The sound pressure value drops sharply within the complete band gap. This shows that the underwater subwavelength spatially coiled acoustic metamaterial effectively blocks sound wave propagation within a complete band gap.
The sound pressure level distribution diagram of 7800Hz is shown in figure 5. The sound pressure excitation of the sound source of the internal point of the underwater sub-wavelength space coiling type acoustic metamaterial is 0dB. The sound pressure field profile shows that the sound pressure of the outside radiated sound field is-52 dB. Therefore, the radiated sound pressure outside the underwater sub-wavelength space coiled acoustic metamaterial is far lower than that of the internal point sound source. This shows that at 7800Hz, the sound wave transmission is perfectly blocked, effectively reducing the likelihood that the interior point source will be sonar due to its radiated noise.
(6) Because the underwater sub-wavelength space coiled acoustic metamaterial has mirror symmetry, energy bands of the underwater sub-wavelength space coiled acoustic metamaterial linearly intersect near a Dirac cone. The linear energy band satisfies the two-dimensional Hamiltonian equation H (k) =v x k x σ x +v y k y σ y . Wherein v is i ，k i Sum sigma i Respectively representing group velocity, momentum and Pauli matrix. As shown in fig. 3, the underwater subwavelength space coiled acoustic metamaterial has two energy bands linearly intersected at the point Γ of the brillouin zone, and a flat band passes through the linear intersection point to form a Dirac-like point.
The standardized frequency of the Dirac point of the underwater sub-wavelength space coiling type acoustic metamaterial is 0.871 and is lower than the standardized frequency 1.158 of the Dirac point of a common phonon crystal. Therefore, the underwater subwavelength space coiled acoustic metamaterial has subwavelength Dirac points.
(7) At the Dirac-like point, the dynamic mass density of the underwater subwavelength space coiled acoustic metamaterial is 0. Dynamic sound wave propagation speed c of underwater sub-wavelength space coiling type acoustic metamaterial m Can be expressed as:
wherein B is m For dynamic bulk modulus ρ m Is a dynamic mass density. When dynamic mass density ρ m When 0, the equivalent dynamic sound wave propagation speed c m Approaching infinity.
Wave number k of sound propagation m Can be expressed as:
k m ＝ω/c m (12)
when equivalent dynamic acoustic wave propagation velocity c m Wave number k of sound wave propagation at infinity m And also 0. In this case, the acoustic wave does not change its phase when propagating in the underwater sub-wavelength space coiled acoustic metamaterial, as shown in fig. 6. The underwater subwavelength space coiled acoustic metamaterial can guide zero-phase difference transmission of sound waves near the zero dynamic mass density frequency without changing the wave front array shape of the sound waves, and further plays a role in underwater sound stealth.
(8) The underwater subwavelength space coiled acoustic metamaterial is periodically arranged around an underwater object. As shown in fig. 7, when the plane wave passes through the underwater object surrounded by the underwater subwavelength space coiled acoustic metamaterial, the phase and waveform of the plane wave are unchanged as if the underwater object does not exist. The underwater subwavelength space coiled acoustic metamaterial is removed, as shown in fig. 8, plane waves are reflected strongly after encountering an underwater object, and an obvious shadow area is formed on the back side of the underwater object, so that the possibility is provided for active sonar detection.
Finally, it should also be noted that the above list is only one specific embodiment of the present invention. Obviously, the invention is not limited to the above embodiments, but many variations are possible, such as circular, equilateral triangle, tetra-variations, etc. All modifications directly derived or suggested to one skilled in the art from the present disclosure should be considered as being within the scope of the present invention.
Claims (3)
1. An underwater subwavelength space coiled acoustic metamaterial comprises a square water area (1) and a stainless steel entity (2) at the periphery of the square water area (1), wherein the stainless steel entity (2) is provided with eight right-angle turning sound channels (3, 4, 5, 6, 7, 8, 9 and 10), and the right-angle turning sound channels are communicated with an external water area (11) and an internal square water area (1); eight quarter turn acoustic channels (3, 4, 5, 6, 7, 8, 9 and 10) are distributed in mirror symmetry; wherein the first right angle turning sound channel (3) and the second right angle turning sound channel (4) are mirror symmetrical about a first central axis (12), the third right angle turning sound channel (5) and the eighth right angle turning sound channel (10) are mirror symmetrical about the first central axis (12), the fourth right angle turning sound channel (6) and the seventh right angle turning sound channel (9) are mirror symmetrical about the first central axis (12), the fifth right angle turning sound channel (7) and the sixth right angle turning sound channel (8) are mirror symmetrical about the first central axis (12); the first right angle turning sound channel (3) and the sixth right angle turning sound channel (8) are mirror symmetrical about a second central axis (13), the second right angle turning sound channel (4) and the fifth right angle turning sound channel (7) are mirror symmetrical about the second central axis (13), the third right angle turning sound channel (5) and the fourth right angle turning sound channel (6) are mirror symmetrical about the second central axis (13), and the seventh right angle turning sound channel (9) and the eighth right angle turning sound channel (10) are mirror symmetrical about the second central axis (13); the first right angle turning sound channel (3) and the eighth right angle turning sound channel (10) are mirror symmetrical about a first diagonal (14), the fourth right angle turning sound channel (6) and the fifth right angle turning sound channel (7) are mirror symmetrical about the first diagonal (14), the second right angle turning sound channel (4) and the seventh right angle turning sound channel (9) are mirror symmetrical about the first diagonal (14), the third right angle turning sound channel (5) and the sixth right angle turning sound channel (8) are mirror symmetrical about the first diagonal (14); the first right angle turning sound channel (3) and the fourth right angle turning sound channel (6) are mirror symmetrical about a second diagonal (15), the second right angle turning sound channel (4) and the third right angle turning sound channel (5) are mirror symmetrical about the second diagonal (15), the sixth right angle turning sound channel (8) and the seventh right angle turning sound channel (9) are mirror symmetrical about the second diagonal (15), and the fifth right angle turning sound channel (7) and the eighth right angle turning sound channel (10) are mirror symmetrical about the second diagonal (15).
2. The underwater subwavelength spatially coiled acoustic metamaterial according to claim 1, wherein: the center of the underwater sub-wavelength space coiled acoustic metamaterial is a square water area (1).
3. The underwater subwavelength spatially coiled acoustic metamaterial according to claim 1, wherein: the eight quarter turn acoustic channels turn twice at right angles.
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