A vector acceleration sensor base design method based on thin film vibration theory

Abstract

The application relates to a vector acceleration sensor base design method based on a thin film vibration theory and belongs to the field of underwater acoustic sensing. The method solves the problems of large mass, large volume and stress matching disorder of a vector acceleration sensor which is usually developed by pasting piezoelectric thin film material on the surface of a metal base to form a sensitive structure. The method comprises the following steps: step one, establishing a coordinate system; step two, establishing a vibration equation; and step three, solving the vibration equation. The application is suitable for a thin film sensitive element (such as a PVDF piezoelectric thin film). The thin film base and the thin film sensitive element have a good stress matching relationship, can effectively convert a weak vector acceleration signal into a shape of the thin film, and thus higher sensitivity is obtained. The application not only enables the vector acceleration sensor to have smaller size and lighter weight, but also can adjust the working frequency of the sensor and obtain higher sensitivity by adjusting the pre-stress applied to the thin film base.

Description

Technical Field

[0001] This invention relates to a design method for a vector acceleration sensor base, belonging to the field of underwater acoustic sensing. Background Technology

[0002] Vector hydrophones, as a type of low-frequency underwater acoustic transducer, can simultaneously acquire complete sound field information, including scalar information of sound pressure and vector information such as particle velocity, acceleration, and sound pressure gradient of underwater particles, compared to acoustic pressure hydrophones. The core component of a vector hydrophone is a vector sensor. Based on the working mechanism of vector sensors, vector hydrophones can be divided into co-vibration vector hydrophones and differential pressure vector hydrophones. Co-vibration vector hydrophones utilize vector acceleration sensors. With the increasing trend of underwater targets operating at lower frequencies, co-vibration vector hydrophones are theoretically more suitable for low-frequency operation. However, the structural design of co-vibration vector hydrophones requires the overall average density of the hydrophone to be close to the density of the water medium. Furthermore, the overall geometric dimensions of the hydrophone must be much smaller than the wavelength of the sound wave corresponding to the upper operating frequency. Therefore, research on co-vibration vector hydrophones emphasizes miniaturization and optimization of the overall mass and volume.

[0003] To further reduce the overall average density of vector hydrophones, researchers are seeking piezoelectric materials with even lower densities, such as piezoelectric thin film materials. However, researchers typically fabricate sensitive structures by attaching piezoelectric thin film materials to the surface of a metal substrate, such as... Figure 6 The diagram shows the stress and volume element stress of a circular thin-plate base under the condition of edge-fixed boundary. The circular thin-plate base is a non-flexible base. When the circular thin-plate base is subjected to an external load Q, the volume element experiences the following stress in cylindrical coordinates: Q θ , Q r and torque M θ M r M rθ ;

[0004] Assuming the circular thin-plate base is a thin plate, the plate thickness h in the z-direction can be neglected. Considering only the displacement w and load Q, and assuming a cylindrical coordinate system, we have:

[0005] w=w(r,θ) (1)

[0006] Q=Q(r,θ) (2)

[0007] According to the differential equation of elastic surfaces of thin plates in elasticity mechanics, the displacement w and the load Q satisfy the following relationship:

[0008]

[0009] Substituting this into cylindrical coordinates, we get:

[0010]

[0011] in, For partial differential operators, For the Laplace operator;

[0012] Where r is the radial coordinate of the thin plate;

[0013] In equation (4), the bending stiffness D of the thin plate is:

[0014]

[0015] Where: μ is Poisson's ratio, E is Young's modulus, and h is the thickness of the circular thin plate;

[0016] In cylindrical coordinates, the bending moment of the thin plate cross section is:

[0017]

[0018]

[0019]

[0020] The load is:

[0021]

[0022]

[0023] in,

[0024]

[0025] Therefore, the normal stress and shear stress of the cross section of the thin plate are:

[0026]

[0027]

[0028]

[0029] The shear stress components and normal stress of the thin plate element in the z-direction are:

[0030]

[0031]

[0032]

[0033] Under the condition of fixed surrounding boundaries, the turning angle (slope) is 0 (i.e.) Using this boundary condition, the differential equation can be solved:

[0034]

[0035] Where Q(r) and Q(θ) are the components of Q in the two coordinate directions r and θ, respectively;

[0036] Its analytical solution takes the following form, where w1 is a particular solution:

[0037] w(r) = C1lnr + C2r 2 lnr+C3r 2 +C4+w1 (19)

[0038] Where C1, C2, C3, and C4 are coefficients determined by the boundary conditions; ln is the logarithm sign with base 10; r is the radial coordinate in cylindrical coordinates; and w1 is a particular solution of the equation.

[0039] This time, the edge-fixed boundary condition w is applied. r＝a =0, dw / dr| r＝a If = 0, then the displacement distribution function is:

[0040]

[0041] Where q0 is the stress amplitude and a is the radius of the circular plate;

[0042] As can be seen from equation (20), the vibration displacement function of the circular thin plate base is only related to the material parameters and geometric parameters, and exhibits a linear relationship;

[0043] However, it suffers from poor matching between the thin film substrate and the thin film sensing element, and has a large mass.

[0044] Therefore, there is an urgent need to propose a vector acceleration sensor base design method based on thin film vibration theory to solve the above-mentioned technical problems. Summary of the Invention

[0045] The purpose of this invention is to address the problems of large mass in vector acceleration sensors typically fabricated by bonding piezoelectric thin film materials to a metal substrate to form a sensitive structure, and the large volume when designed as a hydrophone according to the principle of neutral buoyancy. Furthermore, there is a stress mismatch problem between the piezoelectric thin film material and the metal substrate. This invention provides a vector acceleration sensor substrate design method based on thin film vibration theory. A brief overview of the invention is given below to provide a basic understanding of certain aspects of the invention. It should be understood that this overview is not an exhaustive summary of the invention. It is not intended to identify key or essential parts of the invention, nor is it intended to limit the scope of the invention.

[0046] The technical solution of the present invention:

[0047] A method for designing a vector acceleration sensor base based on thin-film vibration theory includes the following steps:

[0048] Step 1: Establish a coordinate system;

[0049] Assuming the base is a flexible sheet of uniform thickness, and the force is the same in any direction, let's call it the base before deformation. Let the base before deformation be the xoy plane, and the normal direction of the base be the z-axis direction.

[0050] Step 2: Establish the vibration equation, including the following steps:

[0051] Step 2.1: Calculate the surface area of ​​the base before deformation;

[0052] Step 2.2: Calculate the surface area of ​​the base when it is in the deformed position during vibration;

[0053] Step 2.3: Calculate the change in potential energy of the base during the vibration process;

[0054] Step 2.4: Calculate the kinetic energy of the base;

[0055] Step 3: Solve the vibration equation.

[0056] Preferably, the base is square, rectangular, regular hexagonal, or circular.

[0057] Preferred: In step one, it is assumed that the circular film base is a flexible sheet of uniform thickness, stretched by the same force in any direction. The plane of the circular film base before deformation is the xoy plane, and the direction parallel to the normal direction of the circular film base plane is the z-axis direction, thus forming a right-handed coordinate system. Let the tension per unit length of the circular film base be T.

[0058] Preferred: In step two, before the thin circular film substrate undergoes vibration deformation, its surface area is:

[0059] S0=∫∫dS=∫∫dxdy (21)

[0060] During vibration, when the circular thin film substrate is in its deformed position, the surface area of ​​the thin film becomes:

[0061]

[0062] In the formula, W is the vibrational displacement of the thin film in the z-axis direction;

[0063] During the vibration process, the potential energy change of the circular thin film substrate is as follows:

[0064]

[0065] Where S is the surface area of ​​the thin film;

[0066] The kinetic energy of the circular thin film substrate is:

[0067]

[0068] According to Hamilton's principle, we can conclude that:

[0069]

[0070] And through variational operations, the dynamic equation for the transverse free vibration of the circular thin film substrate can be obtained:

[0071]

[0072] Among them, c 2 =T / ρ, where ρ is the mass per unit area; t is time; and c is the wave propagation speed. δ is a partial differential operator; δ is a variational operator.

[0073] Preferred method: In step three, the radius of the circular thin film base is set to l. The transverse free vibration of the circular thin film base under the edge fixed boundary condition is solved using polar coordinates (r, θ).

[0074] In polar coordinates, the boundary conditions for the circular thin film substrate are:

[0075] W(r,θ,t)| r＝l =0,W(r,θ,t)| θ＝0 =W(r,θ,t)| θ＝2π (27)

[0076] Solve using the method of separation of variables, let

[0077] W(r,θ,t)=φ(r,θ)q(t) (28)

[0078] Equation (26) becomes:

[0079]

[0080] Substituting equation (27) into equation (29) yields the two differential equations after separation of variables:

[0081]

[0082]

[0083] In the formula, ω is a constant to be solved;

[0084] The solution to equation (30) is:

[0085]

[0086] That is, the vibration of equation (30) is a simple harmonic motion with ω as its natural frequency; C1 is a constant; This is the initial phase;

[0087] Equation (31) is solved using the method of separation of variables, let

[0088] φ(r,θ)=R(r)Φ(θ) (33)

[0089] Substituting equation (33) into equation (31), we can separate two ordinary differential equations concerning r and θ:

[0090]

[0091] The order of the Bessel equations is n = 1, 2, 3, ...

[0092]

[0093] Where, λ 2 =ω 2 / c 2 The solution to equation (14) is:

[0094] Φ(θ)=C2sin(nθ+ψ) (36)

[0095] Where C2 is a constant; ψ is the initial phase;

[0096] From the boundary condition (27), we know that Φ(0) = Φ(2π). Substituting this into equation (36), we can see that n must be an integer. Equation (35) can be simplified to:

[0097]

[0098] This is an nth-order Bessel equation, and its solution is:

[0099] R(r) = C3J n (λr)+C4Y n (λr) (38)

[0100] Where C3 is a constant coefficient;

[0101] Among them, J n (λr) is a Bessel function of the first kind, Y n (λr) is a Bessel function of the second kind; considering that R(0) should be bounded, but Y n (0) = ∞, so C4 = 0 must be taken. Therefore:

[0102] R(r) = C3J n (λr) (39)

[0103] From the boundary condition (27), we can obtain R(l) = 0, that is:

[0104] J n (λl)=0 (40)

[0105] Let the m-th positive zero be denoted as . The intrinsic value of equation (40) is Therefore:

[0106]

[0107] ω mn It refers to the natural frequency, and its corresponding natural mode shape is:

[0108]

[0109] Where l is the base radius; J m It is the m-th order Bessel function of the first kind;

[0110] Finally, the general solution for the free vibration of the circular thin film substrate under the edge-fixed boundary condition is obtained as follows:

[0111]

[0112] Preferred: It also includes step four: simulation analysis, which includes the following steps:

[0113] Step 4.1: Establish a double-laminated structure for detecting vibration signals;

[0114] Step 4.2: Perform modal analysis on the thin-film sensing element oscillator based on a circular thin-film substrate.

[0115] Preferred: In step 4.1, the double-layer structure includes a thin-film sensing element, an electrode, and a circular thin-film base. The surface of the thin-film sensing element is coated with an electrode. The thin-film sensing element is fixed to the circular thin-film base. After applying a tension T around the base and fixing it, a double-layer structure that can be used to detect vibration signals is formed. The thin-film sensing element is a PVDF piezoelectric thin film.

[0116] In step 4.2, during finite element simulation, the characteristic frequency of the model is simulated using membrane physics. The simulation is performed according to the order of applying load first and then pasting the PVDF piezoelectric film. Prestress is applied to the base of the double-layer structure, but no prestress is applied to the PVDF piezoelectric film. The stress of the base is 5000 times that of the PVDF piezoelectric film. The non-uniform stress of the PVDF piezoelectric film is mainly caused by the displacement of the first-order vibration and can be ignored. Under different tension levels, the characteristic frequency, operating bandwidth, and sensitivity of the vector hydrophone are designed and adjusted by adjusting the structural dimensions of the PVDF piezoelectric film oscillator and the tension of the base.

[0117] The present invention has the following beneficial effects:

[0118] This invention is applicable to thin-film sensitive elements (such as PVDF piezoelectric films); the thin-film substrate and the thin-film sensitive element have a good stress matching relationship, which can effectively convert weak vector acceleration signals into thin-film deformation, thereby obtaining higher sensitivity;

[0119] This invention not only enables vector acceleration sensors to achieve smaller size and lighter weight, but also allows for adjustment of the sensor's operating frequency and higher sensitivity by adjusting the prestress applied to the thin-film substrate. Attached Figure Description

[0120] Figure 1 This is a schematic diagram of the force analysis of a circular thin film substrate;

[0121] Figure 2 This is a schematic diagram of the lateral vibration of a circular thin-film substrate;

[0122] Figure 3 This is a schematic diagram of a PVDF piezoelectric double-laminated thin-film sensing structure based on a circular thin-film substrate;

[0123] Figure 4 It is the stress distribution between the thin film substrate and the PVDF piezoelectric thin film;

[0124] Figure 5 This describes the performance variation law of the PVDF piezoelectric double-laminated thin film sensitive structure;

[0125] Figure 6 This is a schematic diagram showing the stress on a circular thin plate and the stress of its volumetric elements. Detailed Implementation

[0126] To make the objectives, technical solutions, and advantages of this invention clearer, the invention is described below with reference to specific embodiments shown in the accompanying drawings. However, it should be understood that these descriptions are merely exemplary and not intended to limit the scope of the invention. Furthermore, descriptions of well-known structures and technologies are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

[0127] Specific implementation method one: Combining Figure 1-6 This embodiment describes a vector acceleration sensor base design method based on thin-film vibration theory, comprising the following steps:

[0128] Step 1: Establish a right-handed coordinate system;

[0129] Assuming the base is a flexible sheet of uniform thickness, and the force is the same in any direction, let's call it the base before deformation. The base before deformation is the xoy plane, and the normal direction of the base is the z-axis direction. The stiffness of the base is provided by the tension of the film, and the bending vibration characteristic frequency of the film can also be adjusted by the tension of the film.

[0130] Step Two: Establish a mathematical model by setting up vibration equations, including the following steps:

[0131] Step 2.1: Calculate the surface area of ​​the base before deformation;

[0132] Step 2.2: Calculate the surface area of ​​the base when it is in the deformed position during vibration;

[0133] Step 2.3: Calculate the change in potential energy of the base during the vibration process;

[0134] Step 2.4: Calculate the kinetic energy of the base;

[0135] Step 3: Solve the vibration equation;

[0136] The vector acceleration sensor design method based on thin-film vibration theory proposed in this invention can not only enable the vector acceleration sensor to achieve a smaller size and lighter weight, but also adjust the operating frequency of the sensor and obtain higher sensitivity by adjusting the prestress applied to the thin-film substrate.

[0137] Specific Implementation Method Two: Combining Figure 1-6 This embodiment describes a vector accelerometer base design method based on thin-film vibration theory. The base is a square, rectangular, hexagonal, or circular thin film. These shapes of thin films, apart from their vibration equations, all share characteristics such as relying on external loads to provide in-plane tension, being completely flexible thin films of uniform thickness, having the same magnitude of tensile stress in any direction, not exhibiting bending or shear deformation, achieving smaller dimensions and lighter weight, being able to adjust the hydrophone's operating frequency band by adjusting the prestress applied to the thin-film base, and achieving higher sensitivity. A circular thin-film base is a typical example; it is easy to model, improving computational design efficiency, and its thin-film vibration mechanism can be extended to other shapes of thin films.

[0138] Specific implementation method three: Combining Figure 1-6 This embodiment describes a vector acceleration sensor base design method based on thin-film vibration theory. In step one, as follows... Figure 1 As shown, the circular thin-film substrate relies on an external load to provide tension. The circular thin-film substrate is balanced with the planar diaphragm under the lateral load, and the circular thin-film substrate does not need to resist bending and shear deformation. It is assumed that the circular thin-film substrate is a completely flexible sheet of uniform thickness, stretched by the same force in any direction. For ease of calculation, the plane of the circular thin-film substrate before deformation is taken as the xoy plane, and the direction parallel to the normal direction of the plane of the circular thin-film substrate is taken as the z-axis, thus forming a right-handed coordinate system. Let the tension per unit length of the circular thin-film substrate be T. The substrate of this invention is a completely flexible sheet of uniform thickness. The thin-film substrate has the same tensile stress in the membrane in any direction, and its deformation does not include bending and shear deformation. It is suitable for thin-film sensitive elements (such as PVDF piezoelectric films). The thin-film substrate and the thin-film sensitive element have a good stress matching relationship, which can effectively convert weak vector acceleration signals into thin-film deformation, thereby obtaining higher sensitivity.

[0139] Specific implementation method four: Combination Figure 1-6 This embodiment describes a vector acceleration sensor base design method based on thin-film vibration theory. In step two, before the thin circular thin-film base undergoes vibration deformation, its surface area is:

[0140] S0=∫∫dS=∫∫dxdy (21)

[0141] During vibration, when the circular thin film substrate is in its deformed position, the surface area of ​​the thin film becomes:

[0142]

[0143] In the formula, W is the vibrational displacement of the thin film in the z-axis direction;

[0144] During the vibration process, the potential energy change of the circular thin film substrate is as follows:

[0145]

[0146] The kinetic energy of the circular thin film substrate is:

[0147]

[0148] According to Hamilton's principle, we can conclude that:

[0149]

[0150] And through variational operations, the dynamic equation (two-dimensional wave equation) for the transverse free vibration of the circular thin film substrate can be obtained:

[0151]

[0152] Among them, c 2 =T / ρ, where ρ is the mass per unit area; t is time; and c is the wave propagation speed. δ is a partial differential operator; δ is a variational operator.

[0153] Specific Implementation Method Five: Combining Figure 1-6 This embodiment describes a vector acceleration sensor base design method based on thin-film vibration theory. In step three, as shown in the attached diagram... Figure 2 As shown, let the radius of the circular thin film base be l. Under the condition of edge fixed boundary, the transverse free vibration of the circular thin film base is more convenient to solve using polar coordinates (r,θ) since the base is circular.

[0154] In polar coordinates, the boundary conditions for the boundary-supported circular thin-film substrate are:

[0155] W(r,θ,t)| r＝l =0,W(r,θ,t)| θ＝0 =W(r,θ,t)| θ＝2π (27)

[0156] The method of separation of variables is used to solve the problem, decomposing W into a function of spatial quantities φ(r, θ) and a function containing time quantities q(t), letting...

[0157] W(r,θ,t)=φ(r,θ)q(t) (28)

[0158] Equation (26) becomes:

[0159]

[0160] Substituting equation (27) into equation (29) yields the two differential equations after separation of variables:

[0161]

[0162]

[0163] In the formula, ω is a constant to be solved; It is the second derivative of q(t);

[0164] The solution to equation (30) is:

[0165]

[0166] That is, the vibration of equation (30) is a simple harmonic motion with ω as its natural frequency; C1 is a constant; This is the initial phase;

[0167] Similarly, equation (31) is also solved using the method of separation of variables. For this purpose, φ is further decomposed into a radial function R(r) and a circumferential function Φ(θ) using the method of separation of variables, and let...

[0168] φ(r,θ)=R(r)Φ(θ) (33)

[0169] Substituting equation (33) into equation (31), we can separate two ordinary differential equations concerning r and θ:

[0170]

[0171] The order of the Bessel equations is n = 1, 2, 3, ...

[0172]

[0173] Where, λ 2 =ω 2 / c 2 The solution to equation (14) is:

[0174] Φ(θ)=C2sin(nθ+ψ) (36)

[0175] Where C2 is a constant; ψ is the initial phase;

[0176] From the boundary condition (27), we know that Φ(0) = Φ(2π). Substituting this into equation (36), we can see that n must be an integer. Equation (35) can be simplified to:

[0177]

[0178] This is an nth-order Bessel equation, and its solution is:

[0179] R(r) = C3J n (λr)+C4Y n (λr) (38)

[0180] Where C3 is a constant coefficient;

[0181] Among them, J n (λr) is a Bessel function of the first kind, Y n (λr) is a Bessel function of the second kind; considering that R(0) should be bounded, but Y n (0) = ∞, so C4 = 0 must be taken. Therefore:

[0182] R(r) = C3J n (λr) (39)

[0183] From the boundary condition (27), we can obtain R(l) = 0, that is:

[0184] Jn (λl)=0 (40)

[0185] Let the m-th positive zero be denoted as . The intrinsic value of equation (40) (the intrinsic value of the nth order Bessel function) is: Therefore:

[0186]

[0187] ω mn It refers to the natural frequency, and its corresponding natural mode shape is:

[0188]

[0189] Where l is the base radius; J m It is the m-th order Bessel function of the first kind;

[0190] Finally, the general solution for the free vibration of the circular thin film substrate under the edge-fixed boundary condition is obtained as follows:

[0191]

[0192] The coefficient A in equations (42) and (43) mn and It is related to initial conditions such as initial displacement, initial vibration velocity, and prestress;

[0193] As can be seen from equations (43) and (20), the vibrations of the circular thin plate base and the circular thin film base under the edge-fixed boundary conditions are completely different. Therefore, the results obtained from finite element simulation of thin structures by solid mechanical physical field and membrane physical field are also different. Therefore, it is very important to select the correct physical field for finite element simulation of solid thin structures.

[0194] Specific Implementation Method Six: Combination Figure 1-6 This embodiment describes a vector acceleration sensor base design method based on thin-film vibration theory, which further includes step four: a simulation analysis of a PVDF piezoelectric thin-film vector acceleration sensor based on the bending vibration theory of a circular thin-film base. For the PVDF piezoelectric thin-film vector acceleration sensor with a selected double-layer structure, modal analysis and sensitivity calculations were performed on its double-layer thin-film sensitive structure, including the following steps:

[0195] Step 4.1: Establish a double-laminated structure for detecting vibration signals;

[0196] Step 4.2: Modal analysis of the thin-film sensing element oscillator based on a circular thin-film substrate is performed using finite element simulation software. The vector acceleration sensor design method based on thin-film vibration theory proposed in this invention can not only enable the vector acceleration sensor to achieve a smaller size and lighter weight, but also adjust the operating frequency of the sensor and obtain higher sensitivity by adjusting the prestress applied to the thin-film substrate.

[0197] Specific implementation method seven: Combination Figure 1-6 This embodiment describes a vector accelerometer base design method based on thin-film vibration theory. In step 4.1, the double-layer structure includes a thin-film sensitive element, electrodes, and a circular thin-film base. The surface of the thin-film sensitive element is coated with electrodes. The thin-film sensitive element is fixed to the circular thin-film base. By applying a tension T around the base and then fixing it, a double-layer structure that can be used to detect vibration signals is formed. The thin-film sensitive element is made of PVDF piezoelectric film, and the base can be made of thin-film materials such as polyethylene terephthalate (PET) or thermoplastic polyurethane (TPU). The double-layer sensitive structure of the vector accelerometer based on the circular thin-film base needs to apply a uniform preload around the film to provide stress within the film base. The stress, tension, and preload are numerically the same. The preload is the force applied around the film, and the stress refers to the force received per unit area element within the film under the action of the preload. The stress magnitude is equal in all directions within the unit area element.

[0198] In step 4.2, the resonant frequency of the PVDF piezoelectric thin-film oscillator based on the circular thin-film substrate can be adjusted by adjusting the tension T applied around the thin-film substrate, thereby achieving adjustment of the operating frequency band and sensitivity of the vector hydrophone; as shown in the attached figure. Figure 4 As shown, modal analysis of a PVDF piezoelectric film oscillator based on a circular thin-film substrate was performed using finite element method (FEM) simulation software. In FEM simulation, the key to simulating the thin-film material is selecting a suitable physical field; the characteristic frequency simulation of the model (double-laminated structure) should be performed using the film's physical field. Since the film lacks stiffness, prestress is required to provide stiffness; therefore, prestress is a factor affecting the film's characteristic frequency. The simulation was performed by applying the load first, then attaching the PVDF piezoelectric film. Prestress was applied to the substrate of the double-laminated structure, but not to the PVDF piezoelectric film. (See attached image.) Figure 4 The figure shows the stress distribution between the film substrate and the piezoelectric film. This figure indicates that the stress (tension) of the substrate is 5000 times that of the PVDF piezoelectric film; the stress non-uniformity of the PVDF piezoelectric film is mainly caused by the displacement of first-order vibrations and can be ignored. (See attached figure.) Figure 5As shown in the figure, the performance of the PVDF piezoelectric film oscillator varies with the base radius under different tension levels. This figure demonstrates that the characteristic frequency, operating bandwidth, and sensitivity of the vector hydrophone can be designed and adjusted by modifying the structural dimensions of the PVDF piezoelectric film oscillator and the tension of the base. In other words, the characteristic frequency and sensitivity of the PVDF piezoelectric vector accelerometer based on a circular film base can be adjusted by modifying the size and tension of the film base.

[0199] It should be noted that in the above embodiments, as long as the technical solutions are not contradictory, they can be permuted and combined. Those skilled in the art can exhaust all possibilities based on the mathematical knowledge of permutation and combination. Therefore, the present invention will not describe the technical solutions after permutation and combination one by one, but it should be understood that the technical solutions after permutation and combination have been disclosed by the present invention.

[0200] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A design method for a vector acceleration sensor base based on thin-film vibration theory, characterized in that: Includes the following steps: Step 1: Establish a coordinate system; Assuming the base is a flexible sheet of uniform thickness, subjected to the same force in any direction, let's call this the base before deformation. xoy Plane, base normal direction is z Axial direction; Step 2: Establish the vibration equation, including the following steps: Step 2.1: Calculate the surface area of ​​the base before deformation; Step 2.2: Calculate the surface area of ​​the base when it is in the deformed position during vibration; Step 2.3: Calculate the change in potential energy of the base during the vibration process; Step 2.4: Calculate the kinetic energy of the base; In step two, before the thin circular film substrate undergoes vibrational deformation, its surface area is: (21) During vibration, when the circular thin film substrate is in its deformed position, the surface area of ​​the thin film becomes: (22) In the formula, W For thin films in z Vibration displacement in the axial direction; During the vibration process, the potential energy change of the circular thin film substrate is as follows: (23) The kinetic energy of the circular thin film substrate is: (24) According to Hamilton's principle, we can conclude that: (25) And through variational operations, the dynamic equation for the transverse free vibration of the circular thin film substrate can be obtained: (26) in, , ρ Mass per unit area; t denoted as time; c is the wave propagation speed; It is a partial differential operator; δ This is the variational operator; Step 3: Solve the vibration equation; In step three, let the radius of the circular thin film base be... l Lateral free vibration of a circular thin-film substrate under edge-fixed boundary conditions, using polar coordinates. Solve this problem; In polar coordinates, the boundary conditions for the circular thin film substrate are: (27) Solve using the method of separation of variables, let (28) Equation (26) becomes: (29) Substituting equation (27) into equation (29) yields the two differential equations after separation of variables: (30) (31) In the formula, ω Let be the constant to be solved; The solution to equation (30) is: (32) That is, the vibration of equation (30) is a... ω It is a simple harmonic motion with a natural frequency; C1 It is a constant; φ This is the initial phase; Equation (31) is solved using the method of separation of variables, let (33) Substituting equation (33) into equation (31), we can separate two related to... r and θ Ordinary differential equations: (34) Wherein, the order of the Bessel equation n= 1, 2, 3…. (35) in, The solution to equation (14) is: (36) in, C2 It is a constant; ψ This is the initial phase; From the boundary condition (27), we can see that Substituting into equation (36), we can obtain n It must be an integer; equation (35) can be simplified to: (37) This is n Step Bessel The solution to the (Bessel) equation is: (38) in, C3 The coefficients are constants. in, For a Bessel function of the first kind, It is a Bessel function of the second kind; considering It should be bounded, but Therefore, C4 must be set to 0, so: (39) From the boundary condition (27), we can obtain R ( l ) = 0, that is: (40) Record No. m The positive zero point is Then the intrinsic value of equation (40) is Therefore, we have: (41) It refers to the natural frequency, and its corresponding natural mode shape is: (42) in, l The base radius; Jm For the first m First-order Bessel function of the first kind; Finally, the general solution for the free vibration of the circular thin film substrate under the edge-fixed boundary condition is obtained as follows: (43)。 2. The vector acceleration sensor base design method based on thin-film vibration theory according to claim 1, characterized in that: The base can be square, rectangular, hexagonal, or circular.

3. The vector acceleration sensor base design method based on thin-film vibration theory according to claim 2, characterized in that: In step one, assume that the circular film base is a flexible sheet of uniform thickness, stretched by the same force in any direction. Take the plane of the circular film base before deformation as the xoy plane, and the direction parallel to the normal direction of the circular film base plane as the z-axis direction, thus forming a right-handed coordinate system. Let the tension per unit length of the circular film base be T.

4. The design method for a vector acceleration sensor base based on thin-film vibration theory according to claim 1, characterized in that: It also includes step four: simulation analysis, which includes the following steps: Step 4.1: Establish a double-laminated structure for detecting vibration signals; Step 4.2: Perform modal analysis on the thin-film sensing element oscillator based on a circular thin-film substrate.

5. The vector acceleration sensor base design method based on thin-film vibration theory according to claim 4, characterized in that: In step 4.1, the double-layer structure includes a thin-film sensing element (A), an electrode (B), and a circular thin-film base (C). The surface of the thin-film sensing element (A) is coated with the electrode (B). The thin-film sensing element (A) is fixed to the circular thin-film base (C). After applying a tension T around the base and fixing it, a double-layer structure that can be used to detect vibration signals is formed. The thin-film sensing element (A) is made of PVDF piezoelectric film. In step 4.2, during the finite element simulation, the characteristic frequency of the model is simulated using the membrane physics field, and the simulation is performed according to the order of applying the load first and then pasting the PVDF piezoelectric film. Prestress is applied to the base of the double-layer structure, while no prestress is applied to the PVDF piezoelectric film; the stress of the base is 5000 times that of the PVDF piezoelectric film; the non-uniform stress of the PVDF piezoelectric film is mainly caused by the displacement of the first-order vibration, which can be ignored; under different tension magnitudes, the characteristic frequency, operating bandwidth, and sensitivity of the vector hydrophone can be designed and adjusted by adjusting the structural dimensions of the PVDF piezoelectric film oscillator and the tension of the base.

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