Piezoelectric energy harvesting structure design method and system capable of maximizing output power

Abstract

The invention relates to a piezoelectric energy harvesting structure design method and system capable of maximizing output power, and the method comprises the steps: S1, discretizing a design domain of a piezoelectric energy harvesting structure to be designed into N finite elements, and for each finite element, obtaining N finite elements; a multiphase material interpolation model representing structural distribution of a substrate material, a piezoelectric material and a hollow material in the piezoelectric energy harvesting structure is constructed, an interpolation model of an external load resistor of the piezoelectric energy harvesting structure is constructed, and a design domain is a two-dimensional cross section of the piezoelectric energy harvesting structure; s2, constructing an objective function of an external load resistor of the piezoelectric energy harvesting structure, and constructing a topological optimization model with the maximum output power of the external load resistor based on the multiphase material interpolation model, the interpolation model of the load resistor and the objective function; and S3, solving the topological optimization model to obtain a designed piezoelectric energy harvesting structure. According to the invention, the piezoelectric energy harvesting structure with the maximum output power can be designed.

Description

Technical Field

[0001] The present invention relates to the technical field of piezoelectric energy harvesting structure design, and particularly to a method and system for designing a piezoelectric energy harvesting structure to maximize output power. Background Art

[0002] With the continuous development of sustainable energy, piezoelectric energy harvesters have been widely used in fields such as microelectronic devices, sensors, and wireless communication due to their high efficiency, environmental friendliness, and high energy density. Piezoelectric materials can convert mechanical strain into electrical energy, thus becoming an important energy harvesting method, especially showing great application potential in self-powered devices.

[0003] However, the performance of piezoelectric energy harvesters is usually affected by various factors such as structural design, material selection, and load matching, especially the influence of the electromechanical coupling effect on their output power performance. Therefore, how to optimize the structure of piezoelectric energy collectors to improve their energy conversion efficiency, especially the output performance under specific loads, has become a hot research issue.

[0004] Existing research shows that the key factors affecting the output power in piezoelectric energy harvesting structures include resonance frequency tuning, piezoelectric material properties, mass blocks, external energy harvesting circuits, structural strain distribution, and the layout of piezoelectric materials, etc. Changing the position of piezoelectric materials based on the structural strain distribution is a common method to improve the output power of energy harvesters.

[0005] Although existing research mainly focuses on optimizing the layout of piezoelectric materials themselves, in fact, piezoelectric energy harvesting structures usually consist of piezoelectric materials and substrate structures. The substrate structure has advantages in processing and manufacturing and has an important impact on the output power of energy harvesters. In the research on vibration excitation sources, existing literature mostly considers irrelevant loads (point loads or surface loads) under harmonic excitation. However, in practical applications, piezoelectric energy harvesters mostly rely on electromagnetic exciters for excitation, generating periodic voltages through the inertial deformation of the structure and outputting them to the load resistance through electrodes. Therefore, in the optimization design process, it is of great significance to consider the influence of factors such as the configuration of the substrate structure, dynamic inertial loads, and external circuit impedance matching on the output electrical power.

[0006] In summary, existing research mainly focuses on optimizing the layout of piezoelectric materials themselves, ignoring the influence of factors such as the configuration of the substrate structure, dynamic inertial loads, and external circuit impedance matching on the output electrical power. Summary of the Invention

[0007] Therefore, the technical problem to be solved by the present invention is to overcome the problem in the prior art that factors such as the configuration of the substrate structure, dynamic inertial loads, and external circuit impedance matching are ignored when studying piezoelectric energy harvesting structures.

[0008] To solve the above technical problems, the present invention provides a method for designing a piezoelectric energy harvesting structure to maximize the output power, including:

[0009] Step S1: Discretize the design domain of the piezoelectric energy harvesting structure to be designed into N finite elements. For each finite element, construct a multi-phase material interpolation model representing the distribution of the base material, piezoelectric material, and air material structure in the piezoelectric energy harvesting structure, and construct an interpolation model for the external load resistance of the piezoelectric energy harvesting structure, where the design domain is the two-dimensional cross-section of the piezoelectric energy harvesting structure;

[0010] Step S2: Construct an objective function for the external load resistance of the piezoelectric energy harvesting structure. Based on the multi-phase material interpolation model, the interpolation model of the load resistance, and the objective function, construct a topology optimization model with the maximum output power of the external load resistance;

[0011] Step S3: Solve the topology optimization model to obtain the designed piezoelectric energy harvesting structure.

[0012] In an embodiment of the present invention, the method for constructing the multi-phase material interpolation model representing the distribution of the base material and air material structure in the piezoelectric energy harvesting structure in step S1 includes:

[0013] Construct a multi-phase material interpolation model of the piezoelectric energy harvesting structure based on the RAMP model, expressed as:

[0014]

[0015] Among them, the design variable ρ E is used to determine whether there is material in this finite element, and the design variable ρ P is used to distinguish what kind of material this finite element is filled with. C, e, and k are the effective property matrices of the interpolated material. C pzt and C nonpzt are the elastic matrices of the piezoelectric material and the base material respectively. e pzt and κ pzt represent the piezoelectric coupling matrix and dielectric matrix of the piezoelectric material respectively. ρ represents the density of the multi-phase material after interpolation. ρ pzt and ρ nonpzt are the mass densities of the piezoelectric material and the base material respectively. q1, q2, q3, and q4 are penalty factors;

[0016] When the external load circuit of the piezoelectric energy harvesting structure is equivalent to a resistor, the resistor is used as the optimization design variable and a non-linear interpolation function is adopted, expressed as:

[0017]

[0018] Among them, R represents the resistor load in the external circuit of the piezoelectric energy harvesting structure after interpolation. ρ R,e is the resistor variable, Rmin and R max are the minimum and maximum allowable values of the resistance, respectively.

[0019] In an embodiment of the present invention, the objective function of the external load resistance of the piezoelectric energy harvesting structure constructed in step S2 is given by the formula:

[0020]

[0021] where J power is the electric power output by the external load resistance, R represents the resistance load in the external circuit, Φ is the global electric potential vector, is the complex conjugate vector of Φ, and L dummy is a symmetric angular matrix.

[0022] In an embodiment of the present invention, the topology optimization model for maximizing the output power of the external load resistance of the piezoelectric energy harvesting structure constructed in step S2 includes:

[0023] find: ρ i =[ρ E,e , ρ R,e

[0024]

[0025] subject to:

[0026]

[0027] V(ρ E,e) / V0 ≤ θ E

[0028] 0 ≤ ρ R,e ≤ 1, e = 1

[0029] 0 ≤ ρ E,e ≤ 1, e = 1, …, N

[0030] where K 11 , K 12 , K 21 and K 22 are respectively expressed as:

[0031]

[0032] The mechanical response of the structure is described by the matrix K 11 ; the matrices K 12 and K 21 are piezoelectric coupling matrices for coupling the structure and the electrical response; the dynamic characteristics in the matrix K 22 are determined by the resistance matrix R R of the external load resistance R of the piezoelectric energy harvesting structure., the dielectric matrix K φφ Combined.

[0033] In an embodiment of the present invention, when solving the topology optimization model in step S3, the derivatives of the design variables ρ E,e and ρ R,e are also optimized. Specifically:

[0034] Write the in the topology optimization model as a complex system equation:

[0035]

[0036] where S is the total system stiffness matrix, X is the system response vector, and F is the external load vector. Separating the real and imaginary parts of S, X, and F gives:

[0037]

[0038] where (·) r and (·) i represent the real and imaginary parts respectively, represents the conjugate of the complex number. Then the complex system equation is equivalently rewritten as:

[0039]

[0040] Express z(ρ i ) = z(ρ i , X(ρ i )) in the general form with respect to the design variable ρ i . The gradient of z(ρ i ) with respect to the design variable z(ρ i is rewritten as:

[0041]

[0042] Using the adjoint method, the augmented objective function z0 containing the design variable ρ i is obtained as:

[0043]

[0044] where λ1 and λ2 are complex Lagrange multiplier vectors; according to the additional term of the rewritten complex system equation being equal to zero, the augmented objective function z0(ρ i ) is equivalent to z(ρ i ) = z(ρ i , X(ρ i ));

[0045] Taking the derivative of the augmented objective function z0 with respect to the i-th design variable gives:

[0046]

[0047] After arranging the above formula, we get:

[0048]

[0049] Let the adjoint vector satisfy the following equation:

[0050]

[0051] Due to the arbitrariness of the stiffness matrix S and , comparing (λ1) T S and we get Therefore, we only need to solve either (λ1) T S or to obtain the adjoint vector in the arranged ; Substitute the adjoint vector into the arranged to get:

[0052]

[0053] where the adjoint vector λ satisfies the equation:

[0054]

[0055] Rewrite as a minimization problem:

[0056]

[0057] By taking the derivative of z(ρ i , R(ρ i ), X(ρ i )) we get:

[0058]

[0059] Substitute the derivative result of z(ρ i , R(ρ i ), X(ρ i )) into to obtain the adjoint vector solution equation as:

[0060]

[0061] Finally, the derivative of the objective function with respect to the design variables is calculated as:

[0062]

[0063] where

[0064]

[0065] Among them, and are the index intervals of the substrate material design variables and the resistance design variables, respectively;

[0066]

[0067] Among them, g is the acceleration due to gravity, and M is the global mass matrix.

[0068] In an embodiment of the present invention, the step S2 further includes: introducing the static compliance of the piezoelectric energy harvesting structure into the constraint conditions of the topology optimization model, and the formula is:

[0069]

[0070] Among them, C s is the static compliance, is the constraint value of the static compliance.

[0071] In an embodiment of the present invention, when the step S3 solves the topology optimization model, it further includes judging whether the external load resistance is variable; if so, using the MMA algorithm to update the substrate design variable ρ E and the resistance design variable ρ R ; if not, only updating the substrate design variable ρ E .

[0072] To solve the above technical problems, the present invention provides a piezoelectric energy harvesting structure design system for maximizing the output power, including:

[0073] Discrete module: used to discretize the design domain of the piezoelectric energy harvesting structure to be designed into N finite elements. For each finite element, a multi-phase material interpolation model representing the structure distribution of the substrate material, piezoelectric material, and air material in the piezoelectric energy harvesting structure is constructed, and an interpolation model of the external load resistance of the piezoelectric energy harvesting structure is constructed, where the design domain is the two-dimensional cross-section of the piezoelectric energy harvesting structure;

[0074] Construction module: used to construct the objective function of the external load resistance of the piezoelectric energy harvesting structure, and based on the multi-phase material interpolation model, the interpolation model of the load resistance, and the objective function, construct a topology optimization model with the maximum output power of the external load resistance;

[0075] Solution module: used to solve the topology optimization model to obtain the designed piezoelectric energy harvesting structure.

[0076] To solve the above technical problems, the present invention provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, the steps of the piezoelectric energy harvesting structure design method for maximizing the output power as described above are implemented.

[0077] To solve the above technical problems, the present invention provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the piezoelectric energy harvesting structure design method for maximizing the output power as described above are implemented.

[0078] The above technical solution of the present invention has the following advantages compared with the prior art:

[0079] The piezoelectric energy harvesting structure design method for maximizing the output power according to the present invention can effectively improve the load output power of the piezoelectric energy harvesting structure by optimally distributing the positions of the substrate materials and matching the load resistance. The present invention adjusts the distribution of the substrate materials to change the fundamental frequency of the structure and make it close to the external excitation frequency, thereby achieving the maximization of the output power. In the optimal design of the output power of the fixed-load resistance energy harvester, when the resistances are 4×10 4 Ω and 5×10 4 Ω respectively, the maximum output powers are 5.91 mW and 0.089 mW. By performing impedance matching on the optimized piezoelectric energy harvesting structure, the optimal matching resistances are found to be [values not provided in the original] and the corresponding load output powers are 66.93 mW and 6.14 mW respectively, which are 10.32 times and 67.99 times higher than the output powers under the fixed load resistance. In the co-optimization design of the substrate structure and the load resistance, the load resistance with the best impedance matching is 6.20×10 4 Ω, and the load output power of the corresponding piezoelectric energy harvesting structure is 100.44 mW. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] In order to make the content of the present invention easier to be clearly understood, the present invention will be further described in detail below according to the specific embodiments of the present invention in conjunction with the drawings.

[0081] Figure 1 is the flowchart of the method of the present invention;

[0082] Figure 2 is a schematic diagram of a piezoelectric energy harvesting structure (piezoelectric cantilever beam model) under the action of a harmonic excitation source (harmonic inertial force) in an embodiment of the present invention;

[0083] Figure 3 is a schematic diagram of the frequency response characteristics of the output voltage and output electric power under different substrate thicknesses in an embodiment of the present invention;

[0084] Figure 4It is the output power optimization result diagram of the piezoelectric energy harvesting structure under a fixed load resistor in the embodiment of the present invention;

[0085] Figure 5 It is the output power iteration history curve diagram of different load resistors in the embodiment of the present invention;

[0086] Figure 6 It is the characteristic frequency iteration history curve diagram of different load resistors in the embodiment of the present invention;

[0087] Figure 7 It is the collaborative optimization result diagram of the substrate structure topology and the load resistor impedance matching in the embodiment of the present invention;

[0088] Figure 8 It is the iteration curve of the output power under the collaborative optimization of the substrate structure topology and the load resistor impedance matching in the embodiment of the present invention.

[0089] Figure 9 It is the iteration curve of the load resistor under the collaborative optimization of the substrate structure topology and the load resistor impedance matching in the embodiment of the present invention. Detailed implementation manners

[0090] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present invention and be able to implement it, but the specific embodiments cited are not intended to limit the present invention.

[0091] Embodiment 1

[0092] Refer to Figure 1 As shown, the present invention relates to a design method of a piezoelectric energy harvesting structure for maximizing output power, including:

[0093] Step S1: Discretize the design domain of the piezoelectric energy harvesting structure to be designed into N finite elements. For each finite element, construct a multi-phase material interpolation model representing the substrate material, piezoelectric material, and air material structure distribution in the piezoelectric energy harvesting structure, and construct an interpolation model of the external load resistor of the piezoelectric energy harvesting structure, where the design domain is the two-dimensional cross-section of the piezoelectric energy harvesting structure;

[0094] Step S2: Construct an objective function for the external load resistor of the piezoelectric energy harvesting structure. Based on the multi-phase material interpolation model, the interpolation model of the load resistor, and the objective function, construct a topology optimization model with the maximum output power of the external load resistor;

[0095] Step S3: Solve the topology optimization model to obtain the designed piezoelectric energy harvesting structure.

[0096] The following is a detailed introduction to this embodiment:

[0097] Please refer to Figure 1 and Figure 2, the present invention mainly includes the following steps:

[0098] In step S1, the method for constructing a multi-phase material interpolation model representing the substrate material and the air material structure distribution in the piezoelectric energy harvesting structure includes: for the dynamic response topology optimization design considering the action of harmonic inertial force, the RAMP model is used for the density and constitutive matrix interpolation of the multi-phase material. The multi-phase material interpolation model can be written as:

[0099]

[0100] Among them, each finite element of the piezoelectric energy harvesting structure is represented by design variables ρ E and ρ P . The design variable ρ E is used to judge whether there is material in this finite element, and the design variable ρ P is used to discriminate what kind of material is filled in this finite element. ρ represents the density of the multi-phase material after interpolation, and ρ pzt and ρ nonpzt are the mass densities of the piezoelectric material and the substrate material respectively. q1, q2, q3, and q4 are penalty factors, and their values are generally between 5 and 120 to push the design variables to extreme values close to 0 or 1. In the multi-phase material interpolation model, the physical meanings of the design variable values are as follows:

[0101]

[0102] Among them, C, e, and κ are the effective property matrices of the interpolated material. C pzt and C nonpzt are the elastic matrices of the piezoelectric material and the substrate material respectively. e pzt and κ pzt represent the piezoelectric coupling matrix and the dielectric matrix of the piezoelectric material respectively. ρ E,e is used to judge whether the material is filled in element e. If it is filled, it is the piezoelectric material or the substrate material or a mixture of both; if not, it is the air material. If there is no air material in element e, then ρ P,e is used to distinguish the piezoelectric material and the substrate material in this element. It can effectively avoid the convergence problem caused by the influence of gravity-related loads during the structural optimization process.

[0103] In this embodiment, an external load resistor R L is connected to the piezoelectric energy harvesting structure, and then the piezoelectric energy harvesting structure is equivalent to an equivalent current source model. This equivalent current source model includes a series-connected equivalent voltage V eq , an equivalent resistor R eq and an equivalent capacitor C eq . Finally, the output power of the piezoelectric energy harvesting structure is the electric power consumed on the external load resistor R L , and when , the load resistor RL Power consumption P L is maximum and satisfies the formula From the formula P Lmax it is not difficult to find that the external resistance R L has a direct impact on the output power. When the external load circuit is equivalent to a pure resistor, in this embodiment, the external resistance is used as the optimized design variable, and a non-linear interpolation function is adopted, and its expression is as follows:

[0104]

[0105] where, J power is the electric power output by the external load resistor, R represents the resistor load in the external circuit, Φ is the global electric potential vector, is the complex conjugate vector of Φ, L dummy is a symmetric angular matrix.

[0106] The objective function of the external load resistor of the piezoelectric energy harvesting structure constructed in step S2 is specifically as follows:

[0107] By restricting the amount of substrate material used, while finding the optimal structural layout of the substrate material and the impedance matching of the external resistor, the maximization of the structural output electric power is achieved. The final output performance of the piezoelectric energy harvesting structure is measured by the electric power output across the external load resistor, and its defined formula can be expressed as:

[0108]

[0109] where, R represents the resistor load in the external circuit, Φ is the global electric potential vector, is the complex conjugate vector of Φ, L dummy is a symmetric angular matrix (specifying that the position component corresponding to the output voltage node is 1, while other components are 0).

[0110] The specific topological optimization model for maximizing the output power of the external load resistor of the piezoelectric energy harvesting structure constructed in step S2 is as follows:

[0111]

[0112] where, K 11 、K 12 、K 21 and K 22 The four sub-module matrices are respectively expressed as:

[0113]

[0114] where, the mechanical response of the piezoelectric energy harvesting structure is described by the matrix K 11 and it changes with the layout of the material and the layout method of the structure; the matrix K 12 and K21 is a piezoelectric coupling matrix, which is used to couple the structure and the electrical response and varies with the layout and polarization direction of the piezoelectric material; the matrix K 22 The dynamic characteristics in are determined by the inductance matrix R in the circuit matrix of the external circuit of the piezoelectric energy harvesting structure (the external circuit for the piezoelectric energy harvesting structure in this embodiment is an RLC circuit with a series resistor R, an inductor L, and a capacitor C) L , the resistance matrix R R , the capacitance matrix R C , the dielectric matrix K φφ and the conductance matrix Z of the electrodes; the dielectric matrix K φφ varies with the layout of the material, and the conductance matrix Z varies with the conductivity and topology of the electrodes.

[0115] However, in this embodiment, only the damping and an external pure resistor are considered. Therefore, finally, K 11 , K 12 , K 21 and K 22 matrices are respectively expressed as:[[]]

[0116]

[0117] wherein, the components of the resistance tensor R I satisfy And when the external circuit of the piezoelectric energy harvesting structure (i.e., C = 0, L = 0) has only a resistor, the formula is further simplified to:[[]]

[0118] In this embodiment, the static compliance constraint of the piezoelectric energy harvesting structure is also introduced into formula (5), and the following constraint conditions are specifically added:[[]]

[0119]

[0120] wherein, C s is the static compliance, is the constraint value of the static compliance. Numerical design shows that the additionally considered strain energy constraint will also accelerate the convergence speed of the optimization.[[]]

[0121] Please refer to Figure 3 for the frequency response characteristics of the output electric power at different substrate thicknesses in this embodiment. It can be seen that reducing the substrate thickness reduces the first-order bending frequency of the structure, but the output power is increased. The maximum output power appears near the resonance frequency, that is, there are two peaks in the output electric power, which respectively correspond to the vicinity of the first-order bending characteristic frequency of their respective structures.[[]]

[0122] When solving the topology optimization model (i.e., formula (5)) in step S3, the design variable ρ E,eand ρ R,e The derivation process is optimized as follows:

[0123] Before optimizing the derivation process of the design variables, the coupled balance equation of the whole system of the piezoelectric energy harvesting structure is introduced. Since the piezoelectric energy harvesting structure has an external circuit (as described above), the present embodiment uses the system charge conservation equation q piezo +q electrode +q circuit = 0 as the target, the charge equation generated by the piezoelectric material Electrode charge equation and the charge equation in the equivalent external circuit (-ω 2 R L +iωR R +R C )Φ=q circuit , the final coupling equation of the whole system of piezoelectric energy harvesting structure is obtained as:

[0124] The topology optimization problem of maximizing the output power needs to be solved using a gradient-based mathematical programming method, so it is necessary to calculate the sensitivity of the objective function and constraint function relative to the design variables (including the sensitivity of the output power to the design variables, and the sensitivity of the strain energy constraint to the design variables). Due to the large number of design variables, it is difficult to directly derive, so the adjoint variable method is used. For the problem studied in this embodiment, especially the harmonic response analysis system with complex values, the coupled equilibrium equation of the piezoelectric energy harvesting structure is It can be written as a complex system equation:

[0125]

[0126] Among them, the global system matrix By K 11 , K 12 , K 21 and K 22 The four submodule matrices are assembled. S is the total system stiffness matrix, X is the system response vector, and F is the external load vector. When considering complex numbers and their conjugate complex numbers, the real and imaginary parts can be separated as follows:

[0127]

[0128] in,(·) r and(·) i denote the real and imaginary parts respectively, represents the conjugate of the complex number. The complex number system equation (Formula (8)) can be equivalently rewritten as:

[0129]

[0130] Express \(z(\rho i ) = z(\rho i , X(\rho i ))\) in the general form with respect to the design variable \(\rho i \). Using the chain rule, rewrite its gradient with respect to the design variable \(\rho i \) as:

[0131]

[0132] Adopt the adjoint method to obtain the augmented objective function \(z_0(\rho i )\) containing the design variable \(\rho i \) as:

[0133]

[0134] where \(\lambda_1\) and \(\lambda_2\) are complex Lagrange multiplier vectors. According to the additional term (i.e., ) of the rewritten complex system equation (Equation (10)) being equal to zero, the augmented objective function (Equation (12)) is equivalent to \(z(\rho i ) = z(\rho i , X(\rho i ))\). Differentiate Equation (12) with respect to the \(i\)-th design variable, and we can get:

[0135]

[0136] After arranging Equation (13), we get:

[0137]

[0138] Let the adjoint vector in Equation (14) satisfy the following equation:

[0139]

[0140] Considering the arbitrariness of the stiffness matrix \(S\) and , by comparing \((\lambda_1) T S\) and (i.e., Equations (15) and (16)), we can obtain Therefore, only need to solve one of the above two adjoint equations to determine the adjoint vector in Equation (14). After arranging Equation (14), we get:

[0141]

[0142] where the adjoint vector \(\lambda\) satisfies the following equation:

[0143]

[0144] The objective function in the mathematical model (formula (5)) of the topology optimization problem for maximizing output power can be rewritten as a minimization problem:

[0145]

[0146] By taking the derivative of formula (19), we can obtain:

[0147]

[0148] Substituting formula (20) into formula (18), the adjoint vector solution equation is:

[0149]

[0150] Finally, the derivative of the objective function with respect to the design variable ρ i is:

[0151]

[0152] Among them, the relevant partial derivative expressions are as follows:

[0153]

[0154] Among them, and are the index intervals of the base material design variable and the resistance design variable respectively.

[0155]

[0156] Among them, g is the acceleration due to gravity and M is the global mass matrix.

[0157] Please refer to Figure 4 , in this embodiment, the designed piezoelectric energy harvesting structure base material is mainly distributed at the fixed end and the free end, while the intermediate material forms the connection of different topological implementation structures (the base material and the blank part are empty materials).

[0158] After each optimization iteration, it is necessary to determine whether the optimization process has converged. Usually, the convergence criterion can be set by the change in the objective function or the change in the design variable. If the change in the design variable is less than the preset convergence threshold, or the improvement of the objective function has reached the desired accuracy, it is considered that the optimization process has converged and the next step can be entered. If it has not converged, continue to iterate to further optimize the design.

[0159] Please refer to Figure 5 , the output power iteration curves under different fixed load resistances, and finally the objective function and the characteristic frequency tend to be stable, that is, both converge.

[0160] Please refer toFigure 6 The iterative curves of the characteristic frequency under different fixed load resistances are shown. Eventually, the characteristic frequency tends to be stable, that is, it converges.

[0161] Once the optimization process converges, the finally obtained design scheme will be used as the optimal topological configuration of the piezoelectric energy harvesting structure. To clearly display the shape of the structure, an image binaryzation algorithm that satisfies the volume constraint can be used to convert the optimized material distribution into a binary image, in which the material region (substrate material) and the blank region (void material) are clearly marked. The finally output image shows the optimal material distribution of the piezoelectric energy harvesting structure and generates a distribution map of the substrate material, which serves as the basis for subsequent actual manufacturing and experimental verification.

[0162] Please refer to Figure 7 which shows the iterative history curve of the structural static compliance and the corresponding structural evolution process. As the iteration progresses, the topological configuration gradually becomes clear, and the static compliance of the final structure meets the constraint conditions.

[0163] Please refer to Figure 8 which shows the iterative history curve of the output power and the iterative curve of the output power. In the first 30 steps of the iteration, the output power gradually increases; between 30 and 120 steps, the output power oscillates; and after 120 steps, the output power tends to be stable, with a maximum output power of 100.44 mW.

[0164] Please refer to Figure 9 which shows the iterative curve of the load resistance as shown in the figure. The resistance rapidly drops to 2.51×10 4 Ω in the first 10 steps, and then the resistance also oscillates. Although the resistance has a slight oscillation after 120 steps, it has basically no effect on the output power, and the optimal resistance is 6.20×104 Ω.

[0165] Embodiment 2

[0166] This embodiment provides a piezoelectric energy harvesting structure design system for maximizing the output power, including:

[0167] A discretization module: used to discretize the design domain of the piezoelectric energy harvesting structure to be designed into N finite elements. For each finite element, a multi-phase material interpolation model representing the structural distributions of the substrate material, piezoelectric material, and void material in the piezoelectric energy harvesting structure is constructed, and an interpolation model of the external load resistance of the piezoelectric energy harvesting structure is constructed, where the design domain is the two-dimensional cross-section of the piezoelectric energy harvesting structure;

[0168] A construction module: used to construct the objective function of the external load resistance of the piezoelectric energy harvesting structure, and based on the multi-phase material interpolation model, the interpolation model of the load resistance, and the objective function, construct a topological optimization model with the maximum output power of the external load resistance;

[0169] Solution module: used to solve the topology optimization model to obtain the designed piezoelectric energy harvesting structure.

[0170] Embodiment III

[0171] This embodiment provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the piezoelectric energy harvesting structure design method for maximizing the output power described in Embodiment I.

[0172] Embodiment IV

[0173] This embodiment provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements the steps of the piezoelectric energy harvesting structure design method for maximizing the output power described in Embodiment I.

[0174] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of the present application can be implemented in various computer languages, for example, object-oriented programming languages such as Java and interpreted scripting languages such as JavaScript.

[0175] The present application is described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, as well as the combination of flows and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate a device for implementing the specified functions in Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.

[0176] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory generate a manufactured article including an instruction device, and the instruction device implements the specified functions in Figure 1 one process or multiple processes and / or blocks Figure 1The functions specified in one or more boxes.

[0177] These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process. Thus, the instructions executed on the computer or other programmable device provide for implementing the steps of the functions specified in one Figure 1 process or more processes and / or boxes Figure 1 step of the functions specified in one box or more boxes.

[0178] Although the preferred embodiments of the present application have been described, those skilled in the art can make additional changes and modifications to these embodiments once they learn the basic creative concepts. Therefore, the appended claims are intended to be construed to include the preferred embodiments as well as all changes and modifications falling within the scope of the present application.

[0179] Obviously, the above embodiments are merely examples for clear illustration and not limitations on the implementation manners. For those of ordinary skill in the art, other different forms of changes or variations can be made based on the above description. It is not necessary and impossible to enumerate all the implementation manners here. And the obvious changes or variations derived therefrom are still within the protection scope of the present invention.

Claims

1. A piezoelectric energy harvesting structure design method for maximizing output power, characterized in that: include: Step S1: discretize the design domain of the piezoelectric energy harvesting structure to be designed into N finite elements. For each finite element, construct a multiphase material interpolation model representing the distribution of the substrate material, piezoelectric material and empty material structure in the piezoelectric energy harvesting structure, and construct an interpolation model of the external load resistance of the piezoelectric energy harvesting structure, wherein the design domain is a two-dimensional cross-section of the piezoelectric energy harvesting structure; Step S2: constructing an objective function of an external load resistor of the piezoelectric energy harvesting structure, and constructing a topology optimization model for maximizing the output power of the external load resistor based on a multiphase material interpolation model, an interpolation model of the load resistor, and the objective function; Step S3: Solve the topology optimization model to obtain the designed piezoelectric energy harvesting structure.

2. The method for designing a piezoelectric energy harvesting structure for maximizing output power according to claim 1, characterized in that: The method for constructing a multiphase material interpolation model representing the distribution of the substrate material and the empty material structure in the piezoelectric energy harvesting structure in step S1 includes: The multiphase material interpolation model of piezoelectric energy harvesting structure is constructed based on RAMP model, which is expressed as: Among them, the design variable ρ E Used to determine whether the finite element has material, design variable ρ P It is used to determine what material the finite element is filled with. C, e and κ are the effective attribute matrices of the interpolated material. pzt and C nonpzt are the elastic matrices of the piezoelectric material and the substrate material, respectively, and e pzt and κ pzt denote the piezoelectric coupling matrix and dielectric matrix of the piezoelectric material, ρ denotes the density of the multiphase material after interpolation, and ρ pzt and ρ nonpzt are the mass densities of piezoelectric material and substrate material, respectively, q1, q2, q3 and q4 are penalty factors; When the external load resistance of the piezoelectric energy harvesting structure is used as the optimized design variable, a nonlinear interpolation function is constructed, which is expressed as: Where R represents the resistance load in the external circuit of the piezoelectric energy harvesting structure after interpolation, ρ R,e is the resistance variable, R min and R max are the minimum and maximum allowable values ​​of the resistor, respectively.

3. The method for designing a piezoelectric energy harvesting structure for maximizing output power according to claim 1, characterized in that: The objective function of the external load resistance of the piezoelectric energy harvesting structure constructed in step S2 is as follows: Among them, J power is the electric power output by the external load resistor, R represents the resistive load in the external circuit, Φ is the global potential vector, is the complex conjugate vector of Φ, L dummy is a symmetric corner matrix.

4. The method for designing a piezoelectric energy harvesting structure for maximizing output power according to claim 3, characterized in that: The step S2 constructs a topology optimization model for maximizing the output power of the external load resistor of the piezoelectric energy harvesting structure, including: find:r i =[ρ E,e ,r R,e ] subject to: V(r E,e ) / V0≤θ E 0≤ρ R,e ≤1,e=1 0≤ρ E,e ≤1,e=1,…,N Among them, K 11 , K 12 , K 21 and K 22 Respectively expressed as: The mechanical response of the structure is given by the matrix K 11 Description; Matrix K 12 and K 21 is the piezoelectric coupling matrix, used to couple the structure and electrical response; the matrix K 22 The dynamic characteristics of the piezoelectric energy harvesting structure are determined by the resistance matrix R connected to the external load resistor R. R , dielectric matrix K φφ Combination.

5. The method for designing a piezoelectric energy harvesting structure for maximizing output power according to claim 4, characterized in that: When the topology optimization model is solved in step S3, the design variable ρ E,e and ρ R,e The derivation process is optimized, specifically: The topology optimization model Written as a complex system of equations: Among them, S is the total system stiffness matrix, X is the system response vector, and F is the external load vector. Separating the real and imaginary parts of S, X, and F yields: in,(·) r and(·) i denote the real and imaginary parts respectively, represents the conjugate of the complex number, then the complex number system equation is equivalently rewritten as: z(ρ i )=z(ρ i ,X(ρ i )) is expressed as the design variable ρ i The general form of z(ρ i ) relative to the design variable ρ i The gradient of is rewritten as: Using the adjoint method, we get i The augmented objective function z0 is: Among them, λ1 and λ2 are complex Lagrange multiplier vectors; according to the rewritten complex system equation, the additional term is equal to zero, and the augmented objective function z0(ρ i ) is equivalent to z(ρ i )=z(ρ i ,X(ρ i )); The augmented objective function z0 is differentiated with respect to the i-th design variable to obtain: After rearranging the above formula, we get: Let the adjoint vector satisfy the following equation: Since the stiffness matrix S and The arbitrariness of (λ1) T S and get Therefore, we only need to solve (λ1) T S and After any one of the The companion vector in get: Among them, the adjoint vector λ satisfies the equation: Will Rewritten as a minimization problem: By i ,R(ρ i ),X(p i )) Taking the derivative, we get: z(ρ i ,R(ρ i ),X(ρ i )) is derived into The adjoint vector solution equation is: Finally, the derivative of the objective function with respect to the design variables is calculated as: in, Among them, ρE and ρR are the index intervals of substrate material design variables and resistor design variables, respectively; Where g is the acceleration due to gravity and M is the global mass matrix.

6. The method for designing a piezoelectric energy harvesting structure for maximizing output power according to claim 1, characterized in that: The step S2 further includes: introducing the static compliance of the piezoelectric energy harvesting structure into the constraint condition of the topology optimization model, the formula is: Among them, C s It is quietness and softness. is the constraint value of static flexibility.

7. The method for designing a piezoelectric energy harvesting structure for maximizing output power according to claim 1, characterized in that: When the step S3 solves the topology optimization model, it also includes determining whether the external load resistance is variable; if so, the MMA algorithm is used to adjust the substrate design variable ρ E and the resistance design variable ρ R If not, only the base design variable ρ E to update.

8. A piezoelectric energy harvesting structure design system for maximizing output power, characterized in that: include: Discrete module: used to discretize the design domain of the piezoelectric energy harvesting structure to be designed into N finite elements. For each finite element, a multiphase material interpolation model representing the distribution of the substrate material, piezoelectric material and empty material structure in the piezoelectric energy harvesting structure is constructed, and an interpolation model of the external load resistance of the piezoelectric energy harvesting structure is constructed, wherein the design domain is a two-dimensional cross-section of the piezoelectric energy harvesting structure; Construction module: It is used to construct the objective function of the external load resistor of the piezoelectric energy harvesting structure. Based on the multiphase material interpolation model, the interpolation model of the load resistor and the objective function, a topology optimization model with the maximum output power of the external load resistor is constructed; Solution module: used to solve the topology optimization model to obtain the designed piezoelectric energy harvesting structure.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the steps of the method for designing a piezoelectric energy harvesting structure for maximizing output power as claimed in any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for designing a piezoelectric energy harvesting structure for maximizing output power as claimed in any one of claims 1 to 7 are implemented.

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