Phononic crystal topological optimization method and device and electronic equipment

Abstract

The invention discloses a photonic crystal topological optimization method, a photonic crystal topological optimization device and electronic equipment. The method comprises the following steps: determining an objective function according to the inherent frequency of a phononic crystal structure on adjacent two-order dispersion curves; determining a preset constraint condition, wherein the preset constraint condition comprises one or more of a minimum size constraint, a static stiffness constraint and a volume constraint; determining the maximum value of the target function based on a preset constraint condition and a preset optimization function, and determining the density of each photonic crystal unit according to the maximum value; and determining unit cells of the photonic crystal according to the density of each photonic crystal unit. According to the photonic crystal topological optimization method, the manufacturability of the structure is ensured by applying the minimum size constraint, the static stiffness constraint and the volume constraint, meanwhile, the maximum band gap of the photonic crystal structure can be effectively captured by maximizing the target function by taking the band gaps of the two adjacent orders as the target function, the vibration reduction performance of the structure is improved, and the performance of the photonic crystal is improved. Therefore, the photonic crystal with collaborative design of manufacturability and vibration reduction characteristics is realized.

Description

Technical Field

[0001] The present application relates to the technical field of structural topology optimization, and in particular, to a phonon crystal topology optimization method, a phonon crystal topology optimization device, and an electronic device. Background Art

[0002] As a new type of metamaterial, a phonon crystal can effectively block the propagation of elastic waves or sound waves within a specific frequency range by virtue of the periodic structure of its unit cell, thereby achieving the functions of acoustic and vibration control. Due to its unique wave regulation ability, phonon crystals are widely used in acoustic functional devices, vibration reduction and noise reduction, sound insulation and protection, etc. In particular, they show great potential in the research and development of high-performance vibration reduction materials. With the diversification of industrial application requirements and the continuous increase in the demand for high-performance vibration reduction and sound insulation materials, the research on phonon crystal bandgap design has gradually become an important research direction in acoustics, materials science, and mechanical engineering.

[0003] However, most of the current phonon crystal topology optimization designs focus on the optimization of theoretical models and numerical methods. Although certain progress has been made in optimizing the bandgap width, bandgap position, etc., these studies usually ignore the manufacturing processes and structural manufacturability issues faced in practical engineering applications. This results in certain limitations of the existing phonon crystal topology optimization methods in practical applications, especially in the difficulty of achieving efficient manufacturing and assembly during the production process, which in turn affects their popularization and application in the engineering field. Traditional phonon crystal topology optimization methods often rely on idealized assumptions and assume that materials and structures can be perfectly realized during the optimization process. This can theoretically provide relatively ideal design results but fails to fully consider the constraints and limitations of manufacturing processes. Summary of the Invention

[0004] This application aims to solve at least one of the technical problems in the related art to some extent. To this end, the first object of this application is to propose a phonon crystal topology optimization method, which includes: determining an objective function based on the natural frequencies of the phonon crystal structure on two adjacent order dispersion curves; determining preset constraint conditions, where the preset constraint conditions include one or more of a minimum size constraint, a static stiffness constraint, and a volume constraint; determining the maximum value of the objective function based on the preset constraint conditions and a preset optimization function, and determining the density of each phonon crystal unit according to the maximum value; determining the unit cell of the phonon crystal according to the density of each phonon crystal unit. The phonon crystal topology optimization method of this application ensures the physical feasibility, engineering practicability, and manufacturability of the designed structure by imposing a minimum size constraint, a static stiffness constraint, and a volume constraint, avoids the appearance of thin rods to some extent, ensures the continuity of the phonon crystal structure and a certain amount of material usage, and at the same time uses the two adjacent order bandgaps as the objective function. By maximizing the objective function, the maximum bandgap of the phonon crystal structure can be effectively captured, improving the vibration damping performance of the structure. In this way, a phonon crystal with collaborative design of manufacturability and vibration damping characteristics is realized.

[0005] The second object of this application is to propose a phonon crystal topology optimization device.

[0006] The third object of this application is to propose an electronic device.

[0007] To achieve the above object, an embodiment of the first aspect of this application proposes a phonon crystal topology optimization method, which includes: determining an objective function based on the natural frequencies of the phonon crystal structure on two adjacent order dispersion curves; determining preset constraint conditions, where the preset constraint conditions include one or more of a minimum size constraint, a static stiffness constraint, and a volume constraint; determining the maximum value of the objective function based on the preset constraint conditions and a preset optimization function, and determining the density of each phonon crystal unit according to the maximum value; determining the unit cell of the phonon crystal according to the density of each phonon crystal unit.

[0008] According to an embodiment of this application, the minimum size constraint includes:

[0009]

[0010] where N e represents the number of discrete phonon crystal units in the finite element; L e represents the minimum size of the e-th phonon crystal unit; p represents the condensation coefficient of the P-norm; ξ represents the preset threshold of the minimum size constraint function.

[0011] According to an embodiment of this application, the static stiffness constraint includes:

[0012] κ ≤ ε

[0013] Among them, κ represents the static stiffness of the phononic crystal structure; ε represents the preset threshold of the static stiffness constraint function.

[0014] According to an embodiment of the present application, the volume constraint includes:

[0015]

[0016] Among them, ρ e represents the density of the e-th phononic crystal unit; v e represents the volume of the e-th phononic crystal unit; V is the total volume of the phononic crystal structure; V * is the volume fraction of the material usage.

[0017] According to an embodiment of the present application, determining the objective function according to the natural frequencies of the phononic crystal structure on two adjacent dispersion curves includes:

[0018]

[0019] Among them, f represents the objective function; min(ω j+1 (k)) represents the minimum value of the natural frequency of the phononic crystal structure on the (j + 1)-th dispersion curve; max(ω j (k)) represents the maximum value of the natural frequency of the phononic crystal structure on the j-th dispersion curve; k represents the wave vector.

[0020] According to an embodiment of the present application, the above preset constraint conditions further include:

[0021]

[0022]

[0023] Among them, K represents the total stiffness matrix of the phononic crystal structure; M represents the total mass matrix of the phononic crystal structure; k represents the wave vector; ω represents the characteristic frequency of the phononic crystal structure; U represents the eigenvector of the phononic crystal structure; represents the density of the phononic crystal unit of the diffusion field; represents the density of the phononic crystal unit of the intermediate field; represents the density of the phononic crystal unit of the corrosion field.

[0024] According to an embodiment of the present application, the above preset constraint conditions further include:

[0025] 0 ≤ ρ e ≤ 1 (e = 1,..., N e )

[0026] Among them, ρ e represents the density of the e-th phononic crystal unit; N eRepresents the number of discrete phonon crystal units in the finite element.

[0027] According to an embodiment of the present application, the above preset constraint conditions further include:

[0028]

[0029] Wherein, U x Τ Represents the transpose of the eigenvector of the phonon crystal structure in the x-th row; M represents the overall mass matrix of the phonon crystal structure; U y Represents the eigenvector of the phonon crystal structure in the y-th column.

[0030] To achieve the above object, an embodiment of the second aspect of the present application provides a phonon crystal topology optimization device, which includes: a first determination module for determining an objective function according to the structural natural frequencies on two adjacent dispersion curves; a second determination module for determining preset constraint conditions, where the preset constraint conditions include one or more of a minimum size constraint, a static stiffness constraint, and a volume constraint; a third determination module for determining the maximum value of the objective function based on the preset constraint conditions and a preset optimization function, and determining the density of each phonon crystal unit according to the maximum value; a fourth determination module for determining the unit cell of the phonon crystal according to the density of each phonon crystal unit.

[0031] To achieve the above object, an embodiment of the third aspect of the present application provides an electronic device, including a memory, a processor, and a phonon crystal topology optimization program stored in the memory and executable on the processor. When the processor executes the phonon crystal topology optimization program, the foregoing phonon crystal topology optimization method is implemented.

[0032] According to the phonon crystal topology optimization method, device, and electronic device of the embodiments of the present application, an objective function is determined according to the structural natural frequencies of the phonon crystal on two adjacent dispersion curves; preset constraint conditions are determined, where the preset constraint conditions include one or more of a minimum size constraint, a static stiffness constraint, and a volume constraint; the maximum value of the objective function is determined based on the preset constraint conditions and a preset optimization function, and the density of each phonon crystal unit is determined according to the maximum value; the unit cell of the phonon crystal is determined according to the density of each phonon crystal unit. The phonon crystal topology optimization method of the present application, by imposing a minimum size constraint, a static stiffness constraint, and a volume constraint, ensures the physical feasibility, engineering practicability, and manufacturability of the designed structure, avoids the appearance of thin rods to a certain extent, ensures the continuity of the phonon crystal structure and a certain amount of material usage, and at the same time uses two adjacent band gaps as the objective function. By maximizing the objective function, the maximum band gap of the phonon crystal structure can be effectively captured, improving the vibration damping performance of the structure. In this way, a phonon crystal with collaborative design of manufacturability and vibration damping characteristics is realized. Description of the Drawings

[0033] Figure 1 A flowchart of a phonon crystal topology optimization method according to some embodiments of the present application;

[0034] Figure 2 A schematic diagram of a unit cell of a phonon crystal after phonon crystal topology optimization according to some embodiments of the present application;

[0035] Figure 3 A schematic diagram of a dispersion curve after phonon crystal topology optimization according to some embodiments of the present application;

[0036] Figure 4 A schematic block diagram of a phonon crystal topology optimization device according to some embodiments of the present application;

[0037] Figure 5 A schematic block diagram of an electronic device according to some embodiments of the present application. Detailed implementation manners

[0038] The embodiments of the present application will be described in detail below. The examples of the embodiments are shown in the accompanying drawings, where the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to explain the present application, and should not be construed as a limitation to the present application.

[0039] The phonon crystal topology optimization method, device, and electronic device of the embodiments of the present application will be described in detail below with reference to the accompanying drawings.

[0040] Figure 1 A flowchart of a phonon crystal topology optimization method according to some embodiments of the present application. Referring to Figure 1 , the phonon crystal topology optimization method of the embodiments of the present application may include the following steps:

[0041] S110, determining an objective function according to the natural frequencies of the phonon crystal structure on two adjacent orders of dispersion curves.

[0042] Specifically, the two adjacent orders of dispersion curves may be the j-th order dispersion curve and the (j + 1)-th order dispersion curve. Determine the maximum value of the natural frequency of the phonon crystal structure on the j-th order dispersion curve and the minimum value of the natural frequency of the phonon crystal structure on the (j + 1)-th order dispersion curve. The frequency range between the maximum value of the natural frequency of the phonon crystal structure on the j-th order dispersion curve and the minimum value of the natural frequency of the phonon crystal structure on the (j + 1)-th order dispersion curve is the bandgap between two adjacent orders, and the bandgap between two adjacent orders is used as the objective function. By maximizing the objective function, the maximum bandgap range of the phonon crystal structure can be effectively captured, and the vibration damping performance of the phonon crystal structure can be improved.

[0043] S120. Determine the preset constraint conditions, which include one or more of the minimum size constraint, static stiffness constraint, and volume constraint.

[0044] Specifically, to improve the manufacturability of the phononic crystal, one or more of the minimum size constraint, static stiffness constraint, and volume constraint can be imposed. Among them, by imposing the minimum size constraint, the generation of thin rods can be avoided to a certain extent. By imposing the static stiffness constraint, the continuity of the phononic crystal structure can be ensured to a certain extent. By imposing the volume constraint, a certain amount of material usage can be ensured to a certain extent.

[0045] S130. Based on the preset constraint conditions and the preset optimization function, determine the maximum value of the objective function, and determine the density of each phononic crystal unit according to the maximum value.

[0046] Specifically, integrate the objective function and various preset constraint conditions into the dynamic topology optimization model, and use the preset optimization function, such as the MMA (Method of Moving Asymptotes, a topology optimization algorithm) solver, to solve the dynamic topology optimization model to maximize the objective function, and determine the density of each phononic crystal unit after the objective function converges.

[0047] S140. Determine the unit cell of the phononic crystal according to the density of each phononic crystal unit.

[0048] Specifically, the phononic crystal structure is composed of multiple identical phononic crystal unit cells, and each phononic crystal unit cell is divided into multiple phononic crystal units. By solving the above dynamic topology optimization model, the density of each phononic crystal unit can be determined. According to the density of each phononic crystal unit, the phononic crystal unit cell can be determined, and the phononic crystal can be determined according to the phononic crystal unit cell.

[0049] The phononic crystal topology optimization method of the present application, by imposing the minimum size constraint, static stiffness constraint, and volume constraint, ensures the physical feasibility, engineering practicability, and manufacturability of the designed structure, avoids the appearance of thin rods to a certain extent, ensures the continuity of the phononic crystal structure and a certain amount of material usage, and at the same time takes the adjacent two-order band gaps as the objective function. By maximizing the objective function, the maximum band gap of the phononic crystal structure can be effectively captured, and the vibration damping performance of the structure is improved. In this way, a phononic crystal with collaborative design of manufacturability and vibration damping characteristics is realized.

[0050] In some embodiments, the minimum size constraint includes:

[0051]

[0052] Among them, N e represents the number of discrete phononic crystal units in the finite element; L eDenote the minimum size of the $e$-th phononic crystal unit; $p$ represents the aggregation coefficient of the $P$-norm; $\xi$ represents the preset threshold of the minimum size constraint function.

[0053] Specifically, the generation of thin rods can be avoided to a certain extent by imposing the minimum size constraint. The preset threshold of the minimum size constraint function and the aggregation coefficient of the $P$-norm can be determined according to the actual situation. For example, the preset threshold of the minimum size constraint function can be 0.01, and the aggregation coefficient of the $P$-norm can be 40. There is no specific limitation here.

[0054] In some embodiments, the static stiffness constraint includes:

[0055] $\kappa\leq\varepsilon$

[0056] where $\kappa$ represents the static stiffness of the phononic crystal structure; $\varepsilon$ represents the preset threshold of the static stiffness constraint function.

[0057] Specifically, the continuity of the phononic crystal structure can be ensured to a certain extent by imposing the static stiffness constraint. The preset threshold of the static stiffness constraint function can be determined according to the actual situation. For example, the preset threshold of the static stiffness constraint function can be $6.6\times10^{7}$. There is no specific limitation here.

[0058] In some embodiments, the volume constraint includes:

[0059]

[0060] where $\rho$ e represents the density of the $e$-th phononic crystal unit; $v$ e represents the volume of the $e$-th phononic crystal unit; $V$ is the total volume of the phononic crystal structure; $V$ * is the volume fraction of the material usage.

[0061] Specifically, a certain amount of material usage can be ensured to a certain extent by imposing the volume constraint. The volume fraction of the material usage can be determined according to the actual situation. For example, the volume fraction of the material usage can be 0.6. There is no specific limitation here.

[0062] In some embodiments, determining the objective function according to the natural frequencies of the phononic crystal structure on two adjacent dispersion curves includes:

[0063]

[0064] where $f$ represents the objective function; $\min(\omega$ j+1 $(k))$ represents the minimum value of the natural frequency of the phononic crystal structure on the $(j + 1)$-th dispersion curve; $\max(\omega$ j $(k))$ represents the maximum value of the natural frequency of the phononic crystal structure on the $j$-th dispersion curve; $k$ represents the wave vector.

[0065] Specifically, numerical methods (such as the finite element method, plane wave expansion method) can be used to calculate the j-th order dispersion curve, and the wave vector k is scanned in the Brillouin zone to calculate the corresponding frequency ω j (k). In the calculated frequency data, an optimization algorithm (such as the gradient descent method or genetic algorithm) can be used to optimize the wave vector k to determine a wave vector point that maximizes ω j (k), and then determine the maximum value of the natural frequency of the phononic crystal structure on the j-th order dispersion curve. Similarly, the above method can also be used to determine the minimum value of the natural frequency of the phononic crystal structure on the (j + 1)-th order dispersion curve. According to the minimum value of the natural frequency of the phononic crystal structure on the (j + 1)-th order dispersion curve and the maximum value of the natural frequency of the phononic crystal structure on the j-th order dispersion curve, the objective function is determined by the following formula:

[0066]

[0067] where f represents the objective function; min(ω j+1 (k)) represents the minimum value of the natural frequency of the phononic crystal structure on the (j + 1)-th order dispersion curve; max(ω j (k)) represents the maximum value of the natural frequency of the phononic crystal structure on the j-th order dispersion curve; k represents the wave vector.

[0068] In some embodiments, the above preset constraint conditions further include:

[0069]

[0070] where K represents the overall stiffness matrix of the phononic crystal structure; M represents the overall mass matrix of the phononic crystal structure; k represents the wave vector; ω represents the characteristic frequency of the phononic crystal structure; U represents the eigenvector of the phononic crystal structure; represents the density of the phononic crystal unit of the diffusion field; represents the density of the phononic crystal unit of the intermediate field; represents the density of the phononic crystal unit of the corrosion field.

[0071] Specifically, the finite element method is used to perform finite element analysis on the elastic wave control equation of the phononic crystal to obtain the characteristic equation of the phononic crystal, and its expression is:

[0072] (K(k) - ω 2 M)U = 0

[0073] where K represents the overall stiffness matrix of the phononic crystal structure; M represents the overall mass matrix of the phononic crystal structure; k represents the wave vector; ω represents the characteristic frequency of the phononic crystal structure; U represents the eigenvector of the phononic crystal structure.

[0074] The solutions of the characteristic equation of the phononic crystal directly determine the bandgap characteristics of the phononic crystal. By taking the characteristic equation as a constraint condition, it can be ensured that the optimization process always focuses on the bandgap characteristics, thereby achieving the goal of vibration reduction or sound insulation. The characteristic equation is a mathematical description of the vibration characteristics of the phononic crystal, and its solutions must satisfy physical laws (such as the elastic wave equation). Taking the characteristic equation as a constraint condition can ensure that the structures generated during the optimization process are physically feasible and avoid designs that do not conform to physical laws.

[0075] In practical engineering, the design of phononic crystals needs to consider factors such as manufacturing errors and material property variations. By taking the characteristic equation as a constraint condition and combining the element density constraints of the diffusion field, intermediate field, and corrosion field, the robustness of the optimization results can be improved, making it have better stability and reliability in practical applications.

[0076] In some embodiments, the above preset constraint conditions further include:

[0077] 0 ≤ ρ e ≤ 1 (e = 1,..., N e )

[0078] where ρ e represents the density of the e-th phononic crystal unit; N e represents the number of discretized phononic crystal units in the finite element.

[0079] Specifically, when the density of the e-th phononic crystal unit is 1, it is considered that the e-th phononic crystal unit has material, and when the density of the e-th phononic crystal unit is 0, it is considered that the e-th phononic crystal unit has no material. By setting 0 ≤ ρ e ≤ 1 (e = 1,..., N e ) it can be ensured that the optimization process proceeds within a reasonable range and avoid unrealistic density values. In this way, the optimal material distribution can be effectively searched, thereby realizing the optimization of the bandgap characteristics of the phononic crystal.

[0080] In some embodiments, the above preset constraint conditions further include:

[0081]

[0082] where represents the transpose of the eigenvector of the phononic crystal structure in the x-th row; M represents the overall mass matrix of the phononic crystal structure; U y represents the eigenvector of the phononic crystal structure in the y-th column.

[0083] Specifically, the overall mass matrix of the phononic crystal structure can be normalized through the following formula:

[0084]

[0085] Among them, represents the transpose of the eigenvector of the phonon crystal structure in the x-th row; M represents the overall mass matrix of the phonon crystal structure; U y represents the eigenvector of the phonon crystal structure in the y-th column.

[0086] In this way, by normalizing the overall mass matrix of the phonon crystal structure using the eigenvectors of the phonon crystal structure, the calculation can be simplified and the numerical stability can be improved.

[0087] As a specific example, the unit cell size of the phonon crystal can be set to 100 mm × 100 mm, and its material composition is epoxy resin (elastic modulus E = 4.35 GPa). The unit cell is meshed and boundary conditions are added according to the actual working conditions. The density ρ e (e = 1, …, 10000) of each phonon crystal unit in the design domain is the design variable. Calculate the stiffness matrix K e (e = 1, …, 10000) of the phonon crystal unit and the mass matrix M e (e = 1, …, 10000) of the phonon crystal unit, and establish the overall stiffness matrix K of the phonon crystal structure and the overall mass matrix M of the phonon crystal structure. According to the preset constraint conditions and objective function (taking j = 3 as an example for illustration, but not as a limitation to this application), apply the commonly used Robust formulation in the art, adopt the corrosion field, the intermediate field, and the diffusion field to ensure the robustness of the optimization result, and establish the topology optimization model as follows:

[0088]

[0089] Adopt a preset optimization function, such as the MMA solver, to solve the above topology optimization model, complete the optimization design of the phonon crystal structure, and obtain the unit cell of the phonon crystal after topology optimization of the phonon crystal as Figure 2 shown, where the density of the black phonon crystal unit is 1 and the density of the white phonon crystal unit is 0. The minimum bar meets the predetermined minimum size, and the structure is continuous and has a certain load-bearing capacity. The dispersion curve diagram of the phonon crystal after topology optimization is as Figure 3 shown, and an elastic wave / sonic wave maximized band gap is generated within the range of the 3-4th order dispersion curve, thus verifying the accuracy of the phonon crystal topology optimization method considering the collaborative design of manufacturability and vibration reduction.

[0090] In summary, for the phonon crystal topology optimization method of the present application, in terms of manufacturability design, by imposing a minimum size constraint, the generation of thin rods is avoided to a certain extent; by imposing a static stiffness constraint, the continuity of the structure is ensured to a certain extent; by imposing a volume constraint, a certain amount of material usage is ensured to a certain extent. In terms of vibration damping characteristic design, maximizing the adjacent two-order band gaps is used as the objective function to capture the maximum band gap range of the structure on the premise of meeting manufacturability. Finally, the objective function and various constraint functions are integrated into the dynamic topology optimization model, and the Robust formulation is introduced to establish a solution method that meets the generality and robustness required for optimization iteration, realizing a phonon crystal with collaborative design considering manufacturability and vibration damping characteristics.

[0091] Thus, for the topology optimization method of the present application, by imposing a minimum size constraint, a static stiffness constraint, and a volume constraint, the physical feasibility, engineering practicability, and manufacturability of the designed structure are ensured. The appearance of thin rods is avoided to a certain extent, the continuity of the phonon crystal structure and a certain amount of material usage are ensured. At the same time, using the adjacent two-order band gaps as the objective function, the maximum band gap of the phonon crystal structure can be effectively captured by maximizing the objective function, improving the vibration damping performance of the structure, and realizing the collaborative optimization of manufacturability and vibration damping characteristics.

[0092] The present application also integrates the objective function and various preset constraint conditions into the dynamic topology optimization model, and introduces the Robust formulation to construct a general optimization model with strong robustness. Combining with the MMA solver, a set of solution methods that meet the generality and robustness required for optimization iteration are established. In this way, the uncertainty and numerical errors in the optimization process can be effectively handled, ensuring the stability and reliability of the optimization results.

[0093] The present application also uses maximizing the adjacent two-order band gaps as the objective function, which can effectively design a phonon crystal structure with wide band gap characteristics. This wide band gap can better hinder the propagation of elastic waves in a specific frequency range, thus significantly improving the vibration damping performance of the structure and playing a better noise reduction and vibration damping effect in practical engineering applications.

[0094] The present application also integrates the manufacturability constraint and vibration damping performance optimization into a topology optimization model, simplifies the design process, and avoids the steps of multiple iterations and adjustments in the traditional method. This significantly improves the design efficiency and makes the design of the phonon crystal more convenient and fast.

[0095] Corresponding to the above embodiments, the present application also proposes a phonon crystal topology optimization device.

[0096] Refer to Figure 4, the phonon crystal topology optimization device 200 includes: a first determination module 210, a second determination module 220, a third determination module 230, and a fourth determination module 240.

[0097] Among them, the first determination module 210 is configured to determine an objective function according to the structural natural frequencies on two adjacent order dispersion curves. The second determination module 220 is configured to determine preset constraint conditions, and the preset constraint conditions include one or more of a minimum size constraint, a static stiffness constraint, and a volume constraint. The third determination module 230 is configured to determine the maximum value of the objective function based on the preset constraint conditions and a preset optimization function, and determine the density of each phonon crystal unit according to the maximum value. The fourth determination module 240 is configured to determine the unit cell of the phonon crystal according to the density of each phonon crystal unit.

[0098] According to an embodiment of the present application, the second determination module 220 determines the minimum size constraint through the following formula:

[0099]

[0100] where N e represents the number of discrete phonon crystal units in the finite element; L e represents the minimum size of the e-th phonon crystal unit; p represents the condensation coefficient of the P-norm; ξ represents a preset threshold of the minimum size constraint function.

[0101] According to an embodiment of the present application, the second determination module 220 determines the static stiffness constraint through the following formula:

[0102] κ ≤ ε

[0103] where κ represents the static stiffness of the phonon crystal structure; ε represents a preset threshold of the static stiffness constraint function.

[0104] According to an embodiment of the present application, the second determination module 220 determines the volume constraint through the following formula:

[0105]

[0106] where ρ e represents the density of the e-th phonon crystal unit; v e represents the volume of the e-th phonon crystal unit; V is the total volume of the phonon crystal structure; V * is the volume fraction of the material usage.

[0107] According to an embodiment of the present application, the first determination module 210 determines the objective function through the following formula:

[0108]

[0109] where f represents the objective function; min(ωj+1 (k)) represents the minimum value of the natural frequency of the phononic crystal structure on the (j + 1)-th order dispersion curve; max(ω j (k)) represents the maximum value of the natural frequency of the phononic crystal structure on the j-th order dispersion curve; k represents the wave vector.

[0110] According to an embodiment of the present application, the second determination module 220 determines the preset constraint conditions through the following formula:

[0111]

[0112] where K represents the overall stiffness matrix of the phononic crystal structure; M represents the overall mass matrix of the phononic crystal structure; k represents the wave vector; ω represents the characteristic frequency of the phononic crystal structure; U represents the eigenvector of the phononic crystal structure; represents the density of the phononic crystal unit in the diffusion field; represents the density of the phononic crystal unit in the intermediate field; represents the density of the phononic crystal unit in the corrosion field.

[0113] According to an embodiment of the present application, the second determination module 220 determines the preset constraint conditions through the following formula:

[0114] 0 ≤ ρ e ≤ 1 (e = 1,..., N e )

[0115] where ρ e represents the density of the e-th phononic crystal unit; N e represents the number of discrete phononic crystal units in the finite element.

[0116] According to an embodiment of the present application, the second determination module 220 determines the preset constraint conditions through the following formula:

[0117]

[0118] where represents the transpose of the eigenvector of the x-th row of the phononic crystal structure; M represents the overall mass matrix of the phononic crystal structure; U y represents the eigenvector of the y-th column of the phononic crystal structure.

[0119] It should be noted that the above explanations of the embodiments and beneficial effects of the phononic crystal topology optimization method are also applicable to the phononic crystal topology optimization device of the embodiments of the present application. To avoid redundancy, no detailed elaboration is made here.

[0120] Corresponding to the above embodiments, the present application also proposes an electronic device.

[0121] See Figure 5As shown in the figure, the electronic device 300 of the present application includes a memory 310, a processor 320, and a phononic crystal topology optimization program stored on the memory 310 and executable on the processor 320. When the processor executes the phononic crystal topology optimization program, the above-mentioned phononic crystal topology optimization method is implemented.

[0122] It should be noted that the above explanations of the embodiments and beneficial effects of the phononic crystal topology optimization method are also applicable to the electronic device of the embodiments of the present application. To avoid redundancy, they will not be elaborated in detail here.

[0123] It should be noted that the logic and / or steps represented in the flowchart or described in other ways herein, for example, can be considered as a definite sequence list of executable instructions for implementing logical functions, and can be specifically implemented in any computer-readable medium for use by an instruction execution system, apparatus, or device (such as a computer-based system, a system including a processor, or other systems that can fetch and execute instructions from the instruction execution system, apparatus, or device), or in combination with these instruction execution systems, apparatus, or devices. For the purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. More specific examples (non-exhaustive list) of computer-readable media include the following: an electrical connection part with one or more wirings (electronic device), a portable computer diskette (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). Additionally, the computer-readable medium can even be paper or other suitable media on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other media, followed by editing, interpretation, or other appropriate processing as necessary, and then stored in a computer memory.

[0124] It should be understood that each part of the present application can be implemented by hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, any one or a combination of the following techniques well known in the art can be used: discrete logic circuits with logic gate circuits for implementing logical functions on data signals, application-specific integrated circuits with suitable combinational logic gate circuits, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0125] In the description of this specification, the descriptions referring to terms such as "one embodiment", "some embodiments", "example", "specific example", or "some examples", etc. mean that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of this application. In this specification, the schematic expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in a suitable manner in any one or more embodiments or examples.

[0126] In addition, the terms "first" and "second" are used only for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include at least one of such features. In the description of this application, the meaning of "a plurality" is at least two, such as two, three, etc., unless otherwise specifically and clearly defined.

[0127] In this application, unless otherwise clearly specified and defined, terms such as "install", "connect", "link", "fix", etc. shall be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or integrated; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the communication inside two elements or the interaction relationship between two elements, unless otherwise clearly defined. For those of ordinary skill in the art, the specific meanings of the above terms in this application can be understood according to specific circumstances.

[0128] Although the embodiments of this application have been shown and described above, it can be understood that the above embodiments are exemplary and cannot be understood as a limitation to this application. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of this application.

Claims

1. A phonon crystal topology optimization method, characterized in that The method includes: Determining an objective function based on the natural frequencies of the phononic crystal structure on two adjacent orders of dispersion curves; Determining preset constraint conditions, where the preset constraint conditions include one or more of a minimum size constraint, a static stiffness constraint, and a volume constraint; Determining the maximum value of the objective function based on the preset constraint conditions and a preset optimization function, and determining the density of each phononic crystal unit according to the maximum value; Determining the unit cell of the phononic crystal according to the density of each phononic crystal unit.

2. The phonon crystal topology optimization method according to claim 1, characterized in that The minimum size constraint includes: Among them, N e represents the number of discrete phonon crystal units in the finite element; L e represents the minimum size of the e-th phonon crystal unit; p represents the condensation coefficient of the P-norm; ξ represents the preset threshold of the minimum size constraint function.

3. The phonon crystal topology optimization method according to claim 1, characterized in that The static stiffness constraint includes: κ ≤ ε where κ represents the static stiffness of the phononic crystal structure; ε represents the preset threshold of the static stiffness constraint function.

4. The phonon crystal topology optimization method according to claim 1, characterized in that The volume constraint includes: Among them, ρ e represents the density of the e-th phononic crystal unit; v e represents the volume of the e-th phononic crystal unit; V is the total volume of the phononic crystal structure; V * is the volume fraction of the material usage.

5. The phonon crystal topology optimization method according to claim 1, characterized in that Determining an objective function based on the natural frequencies of the phononic crystal structure on two adjacent orders of dispersion curves includes: where f represents the objective function; min(ω j+1 (k)) represents the minimum value of the natural frequency of the phononic crystal structure on the (j + 1)-th order dispersion curve; max(ω j (k)) represents the maximum value of the natural frequency of the phononic crystal structure on the j-th order dispersion curve; k represents the wave vector.

6. The phonon crystal topology optimization method according to claim 1, wherein The preset constraint conditions further include: Among them, K represents the overall stiffness matrix of the phononic crystal structure; M represents the overall mass matrix of the phononic crystal structure; k represents the wave vector; ω represents the characteristic frequency of the phononic crystal structure; U represents the eigenvector of the phononic crystal structure; The density of the phononic crystal unit representing the diffusion field; The density of the phononic crystal unit representing the intermediate field; The density of the phononic crystal unit representing the corrosion field.

7. The phonon crystal topology optimization method according to claim 1, wherein The preset constraint conditions further include: 0 ≤ ρ e ≤ 1 (e = 1, ..., N e ) Among them, ρ e represents the density of the e-th phononic crystal unit; N e represents the number of discrete phononic crystal units in the finite element.

8. The phonon crystal topology optimization method according to claim 1, characterized in that The preset constraint conditions further include: Among them, represents the transpose of the eigenvector of the phononic crystal structure in the x-th row; M represents the overall mass matrix of the phononic crystal structure; U y represents the eigenvector of the phononic crystal structure in the y-th column.

9. A phonon crystal topology optimization device, characterized in that, The device includes: A first determination module for determining an objective function based on the natural frequencies of the structure on two adjacent orders of dispersion curves; A second determination module for determining preset constraint conditions, where the preset constraint conditions include one or more of a minimum size constraint, a static stiffness constraint, and a volume constraint; A third determination module for determining the maximum value of the objective function based on the preset constraint conditions and a preset optimization function, and determining the density of each phononic crystal unit according to the maximum value; A fourth determination module for determining the unit cell of the phononic crystal according to the density of each phononic crystal unit.

10. An electronic device, characterized in that, It includes a memory, a processor, and a phononic crystal topology optimization program stored in the memory and executable on the processor. When the processor executes the phononic crystal topology optimization program, it implements the phononic crystal topology optimization method according to any one of claims 1-8.

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