A method of reducing and controlling the acoustic impedance of an isotropic material

Abstract

The application provides a method for reducing and controlling the sound wave impedance of isotropic material, belongs to the technical field of material sound wave impedance, and solves the problem of difficulty in detecting gas characteristics.The technical scheme comprises the following steps: step one, selecting isotropic material;step two, obtaining the motion equation of the isotropic material;step three, using a plane wave to solve a differential equation, and obtaining the sound wave impedance Z of the material according to a sound wave impedance definition formula;step four, rotating a vector Omega = {0, eta omega, 0} to represent rotating the material along an x2 axis, and rotating a vector Omega = {0, 0, eta omega} to represent rotating the material along an x3 axis;step five, changing the sound wave impedance of the material under the condition of rotating the axis.The beneficial effects of the application are as follows: the application can introduce the Coriolis force caused by rotation into the motion equation of the isotropic material, find the relationship between the sound wave impedance and rotation, and use rotation to reduce and control the sound wave impedance.

Description

Technical Field

[0001] This invention relates to the field of acoustic impedance technology, specifically a method for reducing and controlling the acoustic impedance of isotropic materials. Background Technology

[0002] Acoustic impedance is the product of the density of an isotropic material and the plane wave velocity, i.e.: In the field of ultrasonic gas sensors, the primary problem encountered when ultrasound propagates from a solid to a gas is the extreme difference in acoustic impedance between the gas and the solid, which makes the transmission coefficient close to zero, making it difficult for ultrasonic energy to be transferred from one medium to another.

[0003] Therefore, it is very difficult to directly use solid materials to detect gas properties. Currently, this problem can be bypassed by using media with lower density, such as P(VDF / TrFE) materials, or chemical reaction films, transition layers, and resonant cavities.

[0004] How to solve the above problems is the challenge facing this invention. Summary of the Invention

[0005] The purpose of this invention is to provide a method for reducing the acoustic impedance of isotropic materials. This method incorporates the Coriolis force caused by rotation into the equation of motion of isotropic materials, discovers the relationship between acoustic impedance and rotation, and uses rotation to reduce and control acoustic impedance.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution: a method for reducing and controlling the acoustic impedance of isotropic materials, the method comprising:

[0007] Step 1: Select an isotropic material with its fourth elastic tensor C ijkl The relational expression is:

[0008] (1)

[0009] Where: δ ij It is the delta function, where i, j, k, l are the corresponding subscripts;

[0010] Step 2: Coriolis force K caused by rotation in different materials j Different; the equations of motion for isotropic materials are obtained:

[0011] (2)

[0012] in, Indicates density, For time, Displacement vector For elastic tensors, To replace the tensor, It is the rotational velocity vector;

[0013] make Represents the rotation ratio, where It is the wave frequency;

[0014] Step 3: Solve the differential equation (2) using plane waves:

[0015] (3)

[0016] in: x is a slow vector i It is a coordinate component, s i x i It is about x i The first-order expression indicates that the wavefront is a plane, therefore formula (3) represents a plane wave. , yes Displacement amplitude ;

[0017] Step 4: Adjust the rotation ratio As the horizontal axis, the acoustic impedance ratio Z0 represents the vertical axis. The acoustic impedance at time, where the rotation vector This is represented by rotating the material about the x2 axis. This indicates a rotation about x3;

[0018] Step 5: With x2 or x3 as the rotation axis, the acoustic impedance of different materials decreases as the rotation ratio increases.

[0019] Furthermore, in step one, when the index i=j, δ ij =1; i≠j, δ ij =0, (i,j,k,l=1,2,3); for A constant; its expression is:

[0020] (4)

[0021] (5)

[0022] Where: E is the Young's modulus of the material. The Poisson's ratio of the material; It is the product of Young's modulus and Poisson's ratio of the material.

[0023] Furthermore, in step two, the Coriolis force K caused by rotation j Different materials require different calculations of the Coriolis force K. j equation:

[0024] (6).

[0025] Furthermore, in step three, by substituting formula (3) into formula (2) and summing the vector parts, we obtain:

[0026] (7)

[0027] In the above formula, These are the corresponding amplitudes of different subscript displacements (i=1,2,3);

[0028] In the formula

[0029] (8)

[0030] in, Represents the propagation vector of the wave. Indicate wave speed; substitute (8) into (7) and consider Not all values ​​are 0, so we get information about Solve for a characteristic polynomial equation;

[0031] According to the definition of acoustic impedance:

[0032] (9)

[0033] The acoustic impedance Z of the material is obtained.

[0034] Furthermore, in step five, with x2 as the rotation axis and a rotation ratio of 1, the acoustic impedance of silicon, steel, and platinum materials decreases to 74.29%, 75.16%, and 76.13% of that without rotation, respectively. That is, the acoustic impedance of the transverse waves of silicon, steel, and platinum decreases to 8039359.4 Pa·sm. -3 18885098.2 Pa.sm -3 8868970.632 Pa.sm -3 With x3 as the rotation axis and a rotation ratio of 1, the wave impedance decreases by the same amount, reaching 57.735% of the level without rotation. This means the acoustic impedance of silicon, steel, and platinum transverse waves decreases to 6,192,479.6 Pa·sm, respectively. -3 14352674.6 Pa.sm -3 6651727.9 Pa.sm -3 .

[0035] Furthermore, in step five, the case without rotation is... The wave impedances of silicon, steel, and platinum are 10863999.3 Pa·sm, respectively. -325180131 Pa.sm -3 11669698.2 Pa.sm -3 .

[0036] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0037] (1) The present invention introduces the Coriolis force caused by rotation into the equation of motion of isotropic materials, which can reduce the acoustic impedance of isotropic materials;

[0038] (2) Since different rotation speeds correspond to different acoustic impedances, the present invention can control the acoustic impedance of isotropic materials;

[0039] (3) The present invention enables isotropic materials and gases to interact directly, and enables more ultrasonic energy to be transferred from isotropic materials to gases. Attached Figure Description

[0040] To more clearly illustrate the technical solutions of the embodiments of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and detailed embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0041] Figure 1 The isotropic material of the present invention and in n i A schematic diagram of a wave propagating in a certain direction;

[0042] Figure 2 This is a graph showing the trend of wave impedance as a function of rotation ratio with x2 as the rotation axis in this invention.

[0043] Figure 3 This is a graph showing the trend of wave impedance as a function of rotation ratio when x3 is the rotation axis in this invention. Detailed Implementation

[0044] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0045] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0046] Secondly, the present invention is described in detail with reference to the schematic diagrams. When detailing the embodiments of the present invention, for ease of explanation, the cross-sectional views illustrating the device structure may be partially enlarged, not according to the usual scale. Furthermore, the schematic diagrams are merely examples and should not limit the scope of protection of the present invention. In addition, actual fabrication should include three-dimensional spatial dimensions of length, width, and depth.

[0047] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0048] A method for reducing and controlling the acoustic impedance of isotropic materials, the method comprising:

[0049] Step 1: Select an isotropic material with its fourth elastic tensor C ijkl The relational expression is:

[0050] (1)

[0051] Where: δ ij It is the delta function, where i, j, k, l are the corresponding subscripts;

[0052] Step 2: Coriolis force K caused by rotation in different materials j Different; the equations of motion for isotropic materials are obtained:

[0053] (2)

[0054] in, Indicates density, For time, Displacement vector For elastic tensors, To replace the tensor, It is the rotational velocity vector;

[0055] make Represents the rotation ratio, where It is the wave frequency;

[0056] Step 3: Solve the differential equation (2) using plane waves:

[0057] (3)

[0058] in: x is a slow vector i It is a coordinate component, s i x i It is about x i The first-order expression indicates that the wavefront is a plane, therefore formula (3) represents a plane wave. , yes Displacement amplitude ;

[0059] Step 4: Adjust the rotation ratio As the horizontal axis, the acoustic impedance ratio Z0 represents the vertical axis. The acoustic impedance at time, where the rotation vector This is represented by rotating the material about the x2 axis. This indicates a rotation about x3;

[0060] Step 5: With x2 or x3 as the rotation axis, the acoustic impedance of different materials decreases as the rotation ratio increases.

[0061] In step one, when index i=j, δ ij =1; i≠j, δ ij =0, (i,j,k,l=1,2,3); for A constant; its expression is:

[0062] (4)

[0063] (5)

[0064] Where: E is the Young's modulus of the material. The Poisson's ratio of the material; It is the product of Young's modulus and Poisson's ratio of the material.

[0065] In step two, the Coriolis force K caused by rotation j Different materials require different calculations of the Coriolis force K. j equation:

[0066] (6).

[0067] In step three, substitute formula (3) into formula (2) and sum the vector parts to obtain:

[0068] (7)

[0069] In the above formula, These are the corresponding amplitudes of different subscript displacements (i=1,2,3);

[0070] In the formula

[0071] (8)

[0072] in, Represents the propagation vector of the wave. Indicate wave speed; substitute (8) into (7) and consider Not all values ​​are 0, so we get information about Solve for a characteristic polynomial equation;

[0073] According to the definition of acoustic impedance:

[0074] (9)

[0075] The acoustic impedance Z of the material is obtained.

[0076] In step five, with x2 as the rotation axis and a rotation ratio of 1, the acoustic impedance of silicon, steel, and platinum decreases to 74.29%, 75.16%, and 76.13% of that without rotation, respectively. This means the acoustic impedance of the transverse waves of silicon, steel, and platinum decreases to 8039359.4 Pa·sm. -3 18885098.2 Pa.sm -3 8868970.632 Pa.sm -3 With x3 as the rotation axis and a rotation ratio of 1, the wave impedance decreases in the same way, reaching 57.735% of the state without rotation. Specifically, the acoustic impedance of silicon, steel, and platinum transverse waves decreases to 6,192,479.6 Pa·sm. -3 14352674.6 Pa.sm -3 6651727.9 Pa.sm -3 .

[0077] In step five, without rotation, it is: The wave impedances of silicon, steel, and platinum are 10863999.3 Pa·sm, respectively. -3 25180131 Pa.sm -3 11669698.2 Pa.sm -3 .

[0078] To demonstrate the effect of rotation on wave impedance, several typical isotropic materials were tested, and the relevant parameters are shown in Table 1.

[0079] Table 1 Material parameters of isotropic materials

[0080]

[0081] Use the material parameters in the table above, and define them in... Wave propagation vector in a plane = To calculate the acoustic impedance.

[0082] As an example, the rotation ratio As the horizontal axis, the acoustic impedance ratio Z0 represents the vertical axis. To determine the acoustic impedance, calculations were performed on the three materials listed in Table 1: silicon, steel, and platinum. The changes in acoustic impedance ratio with rotation ratio under different rotating axes were obtained, as shown below. Figure 2 As shown.

[0083] Rotation vector This is represented by rotating the material about the x2 axis. This indicates a rotation about x3.

[0084] First, we obtain the case without rotation ( Silicon, steel, and platinum have acoustic impedances of 10863999.3 Pa·sm, respectively. -3 25180131 Pa.sm -3 11669698.2 Pa.sm -3 .

[0085] according to Figure 2 With x2 as the rotation axis, the acoustic impedance of transverse waves from silicon, steel, and platinum decreases as the rotation ratio increases. At a rotation ratio of 1, the impedances of silicon, steel, and platinum decrease to 74.29%, 75.16%, and 76.13% of their values ​​without rotation, respectively. This translates to an acoustic impedance of 8039359.4 Pa·sm for the transverse waves of silicon, steel, and platinum. -3 18885098.2Pa.sm -3 8868970.632 Pa.sm -3 .

[0086] according to Figure 3 With x3 as the rotation axis, the variation trend is the same for all materials. When the rotation ratio is 1, the wave impedance decreases to 57.73% of the value without rotation. That is, the acoustic impedance of silicon, steel, and platinum transverse waves decreases to 6192479.6 Pa·sm, respectively. -3 14352674.6 Pa.sm -3 6651727.9 Pa.sm -3 .

[0087] Example 1:

[0088] First, the Young's modulus and Poisson's ratio from the isotropic material parameters in Table 1 are used to compare the materials. The constant is calculated, and the result is substituted into Formula 1 to obtain the elastic tensor.

[0089] Substituting the Coriolis force into the constitutive equation, we get:

[0090]

[0091] Then, using the plane wave solution, substituting it into the above formula, we get:

[0092]

[0093] Substituting j=1,2,3 into the formula yields formula (6);

[0094]

[0095] Because U i If not all values ​​are zero, then the determinant of its coefficient matrix must be zero. Based on this equation, the sound wave velocity v can be obtained, and the sound wave impedance formula can be used. The acoustic impedance of the material can then be obtained; see the example below. Figures 2-3 .

[0096] Although the present invention has been described above with reference to embodiments, various modifications can be made and components can be replaced with equivalents without departing from the scope of the invention. In particular, as long as there is no structural conflict, the features in the disclosed embodiments can be combined with each other in any manner. The lack of an exhaustive description of these combinations in this specification is merely for the sake of brevity and resource conservation. Therefore, the present invention is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A method for reducing and controlling the acoustic impedance of isotropic materials, characterized in that, The method includes the following steps: Step 1: Select an isotropic material with its fourth elastic tensor C ijkl The relational expression is: C ijkl =λδ ij d kl +μ(d ik d jl +d il d jk ) (1) Where: δ ij It is the delta function, where i, j, k, l are the corresponding subscripts; Step 2: Coriolis force K caused by rotation in different materials j Different; the equations of motion for isotropic materials are obtained: Where ρ represents density, t is time, and u j Displacement vector, C ijkl Let ε be the elastic tensor. jik For the permutation tensor, Ω i It is the rotational velocity vector; Let η i =Ω i / ω represents the rotation ratio, where ω is the wave frequency; Step 3: Solve the differential equation (2) using plane waves: Where: s i x is a slow vector i It is a coordinate component, s i x i It is about x i The first-order expression indicates that the wavefront is a plane, therefore formula (3) represents a plane wave. U i is u i The amplitude of the displacement (i = 1, 2, 3); Step 4: Set the rotation ratio η = Ω i / ω is used as the horizontal axis, and the acoustic impedance ratio Z / Z0 is used as the vertical axis, where Z0 represents the acoustic impedance when η=0, and the rotation vector Ω={0,ηω,0} represents the rotation of the material about the x2 axis, and Ω={0,0,ηω} represents the rotation about the x3 axis. Step 5: With x2 or x3 as the rotation axis, the acoustic impedance of different materials decreases as the rotation ratio increases.

2. The method for reducing and controlling the acoustic impedance of isotropic materials according to claim 1, characterized in that, In step one, when the index i = j, δ ij =1; i≠j, δ ij =0, (i,j,k,l=1,2,3); λ and μ are Lamé constants; Its expression is: Where: E is the Young's modulus of the material, ν is the Poisson's ratio of the material; Eν is the product of the Young's modulus and the Poisson's ratio of the material.

3. The method for reducing and controlling the acoustic impedance of isotropic materials according to claim 1, characterized in that, In step two, the Coriolis force K caused by rotation j Different materials require different calculations of the Coriolis force K. j equation:

4. In the method for reducing and controlling the acoustic impedance of isotropic materials according to claim 1, in step three, formula (3) is substituted into formula (2), and the vector parts are summed to obtain: In the above formula, U i These are the corresponding amplitudes of different subscript displacements (i = 1, 2, 3); In the formula s i =n i / v (8) in, n i Let v represent the wave propagation vector and v represent the wave speed; substituting (8) into (7), consider U i Since not all values ​​are 0, we obtain a characteristic polynomial equation for v, which can be solved. According to the definition of acoustic impedance: Z=ρv (9) The acoustic impedance Z of the material is obtained.

5. The method for reducing and controlling the acoustic impedance of isotropic materials according to claim 1, characterized in that, In step five, with x2 as the rotation axis and a rotation ratio of 1, the wave impedance of silicon, steel, and platinum materials decreases to 74.29%, 75.16%, and 76.13% of the value without rotation, respectively. With x3 as the rotation axis and a rotation ratio of 1, the wave impedance of different materials decreases by the same amount, to 57.735% of the value without rotation.

6. The method for reducing and controlling the acoustic impedance of isotropic materials according to claim 5, characterized in that, In step five, without rotation, η = 0, and the wave impedances of silicon, steel, and platinum are 10863999.3 Pa·sm, respectively. -3 25180131Pa.sm -3 11669698.2Pa.sm -3 .

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