Calculation method and device for effective elastic wave amplitude range of nonlinear acoustic metamaterials

Abstract

The present application relates to a method and device for calculating the effective elastic wave amplitude range of a nonlinear acoustic metamaterial, which includes: obtaining the unit cell structure of the nonlinear acoustic metamaterial, performing a force analysis on the unit cell structure to obtain the motion relationship of the unit cell structure; determining the bandgap characteristics of the nonlinear acoustic metamaterial based on the motion relationship and the perturbation method; determining the effective elastic wave amplitude range of the nonlinear acoustic metamaterial according to the bandgap characteristics of the nonlinear acoustic metamaterial, so as to re-determine the bandgap characteristics of the nonlinear acoustic metamaterial according to the effective elastic wave amplitude range and determine the use environment of the nonlinear acoustic metamaterial. The present application can improve the calculation accuracy of the bandgap characteristics of the nonlinear acoustic metamaterial, and determine the use environment of the nonlinear acoustic metamaterial according to the effective elastic wave amplitude range, so as to achieve vibration reduction and noise reduction and improve the performance of structural components.

Description

Technical Field

[0001] The present application relates to the technical field of metamaterials. Specifically, it relates to a method for calculating the effective elastic wave amplitude range of a nonlinear acoustic metamaterial, a device for calculating the effective elastic wave amplitude range of a nonlinear acoustic metamaterial, a computer storage medium, and an electronic device. Background Art

[0002] Structural vibration problems widely exist in various fields such as aerospace, ships, and vehicle traffic. Suppressing the harmful vibrations of structures and the radiated noise has always been an urgent problem to be solved in engineering technology. Essentially, both vibrations and noises in structures propagate in the medium in the form of elastic waves. To suppress harmful vibrations, it is necessary to conduct in-depth research on the propagation and regulation of elastic waves in structures.

[0003] Currently, the research on acoustic metamaterials mainly focuses on their linear effects. However, in the face of extremely harsh environments and high-precision analysis requirements, the nonlinear effect will become a key factor affecting the analysis of structures. In the process of studying the bandgap characteristics of nonlinear metamaterials, the perturbation method is usually used based on the small parameter assumption, and the nonlinear bandgap characteristics are obtained by perturbing the linear bandgap results. However, in this process, the influence of the elastic wave amplitude range on the nonlinear bandgap characteristics is usually ignored, resulting in obvious errors in the calculation results of the nonlinear bandgap characteristics.

[0004] Therefore, it is necessary to study a new method for calculating the effective elastic wave amplitude range of nonlinear acoustic metamaterials.

[0005] It should be noted that the information disclosed in the above background art section is only used to enhance the understanding of the background of the present application, and thus may include information that does not constitute the prior art known to those of ordinary skill in the art. Summary of the Invention

[0006] The purpose of the present application is to overcome the deficiencies of the above-mentioned prior art, and provide a method for calculating the effective elastic wave amplitude range of a nonlinear acoustic metamaterial, a device for calculating the effective elastic wave amplitude range of a nonlinear acoustic metamaterial, a computer storage medium, and an electronic device. This method can obtain the effective elastic wave amplitude range of the nonlinear acoustic metamaterial, and improve the calculation accuracy of the bandgap characteristics of the nonlinear acoustic metamaterial under the limitation of the effective elastic wave amplitude range, thereby improving the vibration reduction and noise reduction performance of the nonlinear acoustic metamaterial.

[0007] According to the first aspect of the present application, there is provided a method for calculating the effective elastic wave amplitude range of a nonlinear acoustic metamaterial, including:

[0008] Obtain the unit cell structure of the nonlinear acoustic metamaterial, and perform a force analysis on the unit cell structure to obtain the motion relationship of the unit cell structure;

[0009] Determine the bandgap characteristics of the nonlinear acoustic metamaterial based on the motion relationship and the perturbation method;

[0010] Determine the effective elastic wave amplitude range of the nonlinear acoustic metamaterial according to the bandgap characteristics of the nonlinear acoustic metamaterial, so as to determine the usage environment of the nonlinear acoustic metamaterial according to the effective elastic wave amplitude range.

[0011] In an exemplary embodiment of the present application, the nonlinear acoustic metamaterial is a one-dimensional nonlinear acoustic metamaterial with an inertial amplification mechanism; the unit cell structure includes a first basic mass block, a second basic mass block, a first inertial amplification mass block, a second inertial amplification mass block, a first resonant mass block and a second resonant mass block. The first basic mass block and the second basic mass block are connected by a first spring. The first inertial amplification mass block and the second inertial amplification mass block are connected by a second spring. The first basic mass block and the first resonant mass block are connected by a third spring. The second basic mass block and the second resonant mass block are connected by a fourth spring. The first basic mass block and the second basic mass block are respectively connected to the first inertial amplification mass block and the second inertial amplification mass block through rigid connecting rods.

[0012] In an exemplary embodiment of the present application, the force analysis of the unit cell structure to obtain the motion relationship of the unit cell structure includes:

[0013] Perform a force analysis on the unit cell structure according to the degrees of freedom corresponding to each mass block in the unit cell structure to obtain a force model corresponding to the unit cell structure;

[0014] Obtain the motion relationship based on the force model. The motion relationship includes a displacement relationship, an internal force relationship of the rigid connecting rod, and a resultant force relationship in the horizontal axis. The resultant force relationship in the horizontal axis is the resultant force acting on the basic mass block in the unit cell structure along the horizontal axis direction.

[0015] In an exemplary embodiment of the present application, the determining the bandgap characteristics of the nonlinear acoustic metamaterial based on the motion relationship and the perturbation method includes:

[0016] Obtain the nonlinear restoring force generated by the nonlinear spring connecting the resonant mass block and the basic mass block in the unit cell structure;

[0017] Based on the nonlinear restoring force and the lumped mass method, determine the dynamic equation corresponding to the bandgap characteristics of the nonlinear acoustic metamaterial;

[0018] Solve the dynamic equation by introducing a small parameter through the perturbation method to obtain the bandgap characteristics of the nonlinear acoustic metamaterial.

[0019] In an exemplary embodiment of the present application, determining the effective elastic wave amplitude range of the nonlinear acoustic metamaterial according to the bandgap characteristics of the nonlinear acoustic metamaterial includes:

[0020] Determining the effective elastic wave amplitude range according to the boundary conditions and the bandgap characteristics of the nonlinear acoustic metamaterial.

[0021] In an exemplary embodiment of the present application, the effective elastic wave amplitude range is [0, A], where A is the minimum value of the function A(μ);

[0022] where, μ is the wave number, Ω0 is the linear frequency, α, γ, and Γ are all normalized parameters, m is the mass of the basic mass block in the unit cell structure, k is the stiffness of the spring connecting the two basic mass blocks in the unit cell structure, m r is the mass of the resonant mass block in the unit cell structure, k r is the nonlinear stiffness of the spring connecting the resonant mass block and the basic mass block in the unit cell structure, k NL is the nonlinear stiffness.

[0023] In an exemplary embodiment of the present application, the method further includes:

[0024] Obtaining a finite one-dimensional nonlinear acoustic metamaterial, moving the finite one-dimensional nonlinear acoustic metamaterial with a preset elastic wave amplitude until it is stable, and obtaining the time-domain information of the basic mass at the central position in the finite one-dimensional nonlinear acoustic metamaterial;

[0025] Performing a Fourier transform on the time-domain information to obtain the bandgap characteristics to be compared;

[0026] Using the effective elastic wave amplitude range as the boundary condition, obtaining the bandgap characteristics corresponding to different target amplitudes by the perturbation method;

[0027] Comparing the bandgap characteristics with the bandgap characteristics to be compared to evaluate the bandgap characteristics of the nonlinear acoustic metamaterial.

[0028] In an exemplary embodiment of the present application, the method further includes:

[0029] When the target amplitude is within the effective elastic wave amplitude range, the bandgap characteristics match the bandgap characteristics to be compared;

[0030] When the target amplitude is outside the effective elastic wave amplitude range, the bandgap characteristics do not match the bandgap characteristics to be compared.

[0031] According to a second aspect of the present application, there is provided an apparatus for calculating the effective elastic wave amplitude range of a nonlinear acoustic metamaterial, including:

[0032] A force analysis module, configured to obtain the unit cell structure of the nonlinear acoustic metamaterial, perform a force analysis on the unit cell structure to obtain the motion relationship of the unit cell structure;

[0033] A bandgap characteristic determination module, configured to determine the bandgap characteristics of the nonlinear acoustic metamaterial based on the motion relationship and the perturbation method;

[0034] An amplitude range determination module, configured to determine the effective elastic wave amplitude range of the nonlinear acoustic metamaterial according to the bandgap characteristics of the nonlinear acoustic metamaterial, so as to determine the usage environment of the nonlinear acoustic metamaterial according to the effective elastic wave amplitude range.

[0035] According to a third aspect of the present application, there is provided a computer storage medium, on which a computer program is stored, characterized in that when the computer program is executed by a processor, the method for calculating the effective elastic wave amplitude range of the nonlinear acoustic metamaterial as described above is implemented.

[0036] According to a fourth aspect of the present application, there is provided an electronic device, characterized by including:

[0037] A processor; and

[0038] A memory, configured to store executable instructions of the processor;

[0039] Wherein, the processor is configured to execute the method for calculating the effective elastic wave amplitude range of the nonlinear acoustic metamaterial as described above by executing the executable instructions.

[0040] It can be seen from the above technical solutions that the method for calculating the effective elastic wave amplitude range of the nonlinear acoustic metamaterial, the apparatus for calculating the effective elastic wave amplitude range of the nonlinear acoustic metamaterial, the computer storage medium, and the electronic device in the exemplary embodiments of the present application at least have the following advantages and positive effects:

[0041] The method for calculating the effective elastic wave amplitude range of the nonlinear acoustic metamaterial in this application obtains the motion relationship of the unit cell structure of the nonlinear acoustic metamaterial through force analysis of the unit cell structure, determines the bandgap characteristics of the nonlinear acoustic metamaterial based on this motion relationship and the perturbation method, and determines the effective elastic wave amplitude range of the nonlinear acoustic metamaterial based on the bandgap characteristics of the nonlinear acoustic metamaterial. This effective elastic wave amplitude range can be used to re-determine the bandgap characteristics of the nonlinear acoustic metamaterial and determine the usage environment of the nonlinear acoustic metamaterial. The method for calculating the effective elastic wave amplitude range of the nonlinear acoustic metamaterial in the embodiments of this application can improve the calculation accuracy of the bandgap characteristics of the nonlinear acoustic metamaterial by determining the effective elastic wave amplitude range, and determine the usage environment of the nonlinear acoustic metamaterial according to the effective elastic wave amplitude range, so as to achieve vibration reduction and noise reduction through this nonlinear acoustic metamaterial and improve the performance of structural components.

[0042] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit this application. Brief Description of the Drawings

[0043] The drawings here are incorporated into the specification and form a part of this specification, showing embodiments consistent with this application, and are used together with the specification to explain the principles of this application. Obviously, the drawings in the following description are only some embodiments of this application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0044] Figure 1 The structural schematic diagram of the system architecture applying the method for calculating the effective elastic wave amplitude range of the nonlinear acoustic metamaterial in the embodiments of this application is schematically shown.

[0045] Figure 2 The flowchart of the method for calculating the effective elastic wave amplitude range of the nonlinear acoustic metamaterial in the embodiments of this application is schematically shown.

[0046] Figure 3 The structural schematic diagram of the one-dimensional nonlinear acoustic metamaterial with an inertia amplification mechanism in the embodiments of this application is schematically shown.

[0047] Figure 4 The degrees of freedom of movement of each mass block in the unit cell structure 301 in the embodiments of this application are schematically shown.

[0048] Figure 5 The force model corresponding to the unit cell structure in the embodiments of this application is schematically shown.

[0049] Figure 6 The effective elastic wave amplitude range diagram in the embodiments of this application is schematically shown.

[0050] Figure 7 Schematically shows a flowchart for evaluating the bandgap characteristics of a nonlinear acoustic metamaterial in an embodiment of the present application.

[0051] Figure 8 Schematically shows the position-displacement diagram of the unit cell structure in a finite one-dimensional nonlinear acoustic metamaterial in an embodiment of the present application.

[0052] Figures 9A - 9B Schematically shows the bandgap characteristics of a nonlinear acoustic metamaterial at different elastic wave amplitudes in an embodiment of the present application.

[0053] Figure 10 Schematically shows the structural block diagram of a device for calculating the effective elastic wave amplitude range of a nonlinear acoustic metamaterial in the present application.

[0054] Figure 11 Schematically shows the computer system structural block diagram of an electronic device suitable for implementing the embodiments of the present application. Detailed implementation manners

[0055] Now, example embodiments will be described more fully with reference to the accompanying drawings. However, the example embodiments can be implemented in various forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this application will be more thorough and complete, and will fully convey the concept of the example embodiments to those skilled in the art.

[0056] In addition, the described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to give a thorough understanding of the embodiments of the present application. However, those skilled in the art will realize that the technical solutions of the present application can be practiced without one or more of the specific details, or other methods, components, devices, steps, etc. may be used. In other cases, well-known methods, devices, implementations, or operations are not shown or described in detail to avoid obscuring aspects of the present application.

[0057] As used in this specification, the terms "a", "an", "the", and "said" are used to denote the presence of one or more elements / components / etc.; the terms "comprising" and "having" are used to mean an open inclusion and mean that in addition to the listed elements / components / etc., there may be additional elements / components / etc.; the terms "first" and "second", etc. are only used as labels and are not a limitation on the quantity of their objects.

[0058] The block diagrams shown in the accompanying drawings are only functional entities and do not necessarily correspond to physically independent entities. That is, these functional entities can be implemented in software form, or implemented in one or more hardware modules or integrated circuits, or implemented in different networks and / or processor devices and / or microcontroller devices.

[0059] The flowcharts shown in the accompanying drawings are only exemplary illustrations, and do not necessarily include all contents and operations / steps, nor do they necessarily need to be executed in the described order. For example, some operations / steps can be decomposed, while some operations / steps can be combined or partially combined, so the actual execution order may change according to the actual situation.

[0060] In the related art, the methods for calculating the nonlinear bandgap characteristics mainly include the perturbation method, the harmonic balance method, and the homotopy analysis method. Taking the perturbation method as an example, in the process of studying the bandgap characteristics of nonlinear acoustic metamaterials, the perturbation method is based on the small parameter assumption, and the nonlinear bandgap characteristics are obtained by perturbing the linear bandgap results. However, related studies usually ignore the influence of the effective elastic wave amplitude range on the nonlinear bandgap characteristics, resulting in obvious errors in the subsequent calculation results of the bandgap characteristics, and also unable to accurately guide the use environment of nonlinear acoustic metamaterials.

[0061] After introducing the technical terms that may be involved in the embodiments of the present application, the method for calculating the effective elastic wave amplitude range of the nonlinear acoustic metamaterials in the present application will be described in detail.

[0062] Figure 1 An exemplary system architecture block diagram applying the technical solution of the present application is schematically shown.

[0063] As Figure 1 shown, the system architecture 100 may include a terminal device 101, a server 102, and a network 103. Among them, the terminal device 101 may include various devices with a display screen such as a smart phone, a tablet computer, a notebook computer, a desktop computer, a smart TV, and a smart vehicle terminal. The server 102 may be an independent physical server, or a server cluster or a distributed system composed of multiple physical servers, or a cloud server providing cloud computing services. The network 103 may be a communication medium of various connection types capable of providing a communication link between the terminal device 101 and the server 102, for example, it may be a wired communication link or a wireless communication link.

[0064] In an exemplary embodiment of the present application, the terminal device 101 may send the unit cell structure of the nonlinear acoustic metamaterial to the server 102 via the network 103. After receiving the unit cell structure, the server 102 performs a force analysis on it to obtain the corresponding motion relationship, then determines the bandgap characteristics of the nonlinear acoustic metamaterial based on the motion relationship and the perturbation method, and then determines the effective elastic wave amplitude range according to the bandgap characteristics of the nonlinear acoustic metamaterial. Finally, the bandgap characteristics and the usage environment of the nonlinear acoustic metamaterial can be re-determined according to the effective elastic wave amplitude range.

[0065] Of course, the method for calculating the effective elastic wave amplitude range of the nonlinear acoustic metamaterial in the embodiment of the present application may also be executed by the terminal device 101. After obtaining the unit cell structure, the terminal device 101 performs a force analysis on it to obtain the corresponding motion relationship, then determines the bandgap characteristics of the nonlinear acoustic metamaterial based on the motion relationship and the perturbation method, and then determines the effective elastic wave amplitude range according to the bandgap characteristics of the nonlinear acoustic metamaterial. Finally, the bandgap characteristics and the usage environment of the nonlinear acoustic metamaterial can be re-determined according to the effective elastic wave amplitude range.

[0066] According to the implementation requirements, the system architecture in the embodiment of the present application may have any number of terminal devices, networks, and servers. For example, the server may be a server group composed of multiple server devices.

[0067] The following will make a detailed description of the technical solutions such as the method for calculating the effective elastic wave amplitude range of the nonlinear acoustic metamaterial, the device for calculating the effective elastic wave amplitude range of the nonlinear acoustic metamaterial, the computer-readable medium, and the electronic device provided by the present application in combination with the specific implementation manners.

[0068] Figure 2 The flowchart of the method for calculating the effective elastic wave amplitude range of the nonlinear acoustic metamaterial is shown. As Figure 2 shown, the method for calculating the effective elastic wave amplitude range of the nonlinear acoustic metamaterial includes:

[0069] Step S210: Obtain the unit cell structure of the nonlinear acoustic metamaterial, and perform a force analysis on the unit cell structure to obtain the motion relationship of the unit cell structure;

[0070] Step S220: Determine the bandgap characteristics of the nonlinear acoustic metamaterial based on the motion relationship and the perturbation method;

[0071] Step S230: Determine the effective elastic wave amplitude range of the nonlinear acoustic metamaterial according to the bandgap characteristics of the nonlinear acoustic metamaterial, so as to re-determine the bandgap characteristics of the nonlinear acoustic metamaterial and determine the usage environment of the nonlinear acoustic metamaterial according to the effective elastic wave amplitude range.

[0072] The method for calculating the effective elastic wave amplitude range of the nonlinear acoustic metamaterial in this application obtains the motion relationship of the unit cell structure of the nonlinear acoustic metamaterial through force analysis of the unit cell structure, determines the bandgap characteristics of the nonlinear acoustic metamaterial based on this motion relationship and the perturbation method, and determines the effective elastic wave amplitude range of the nonlinear acoustic metamaterial based on the bandgap characteristics of the nonlinear acoustic metamaterial. This effective elastic wave amplitude range can be used to re-determine the bandgap characteristics of the nonlinear acoustic metamaterial and determine the usage environment of the nonlinear acoustic metamaterial. The method for calculating the effective elastic wave amplitude range of the nonlinear acoustic metamaterial in the embodiments of this application can improve the calculation accuracy of the bandgap characteristics of the nonlinear acoustic metamaterial by determining the effective elastic wave amplitude range, and determine the usage environment of the nonlinear acoustic metamaterial based on the effective elastic wave amplitude range, so as to achieve vibration reduction and noise reduction through this nonlinear acoustic metamaterial and improve the performance of structural components.

[0073] The following Figure 2 will detail each step of the method for calculating the effective elastic wave amplitude range of the nonlinear acoustic metamaterial shown.

[0074] In step S210, the unit cell structure of the nonlinear acoustic metamaterial is obtained, and force analysis is performed on the unit cell structure to obtain the motion relationship of the unit cell structure.

[0075] In the exemplary embodiments of this application, a metamaterial refers to a class of artificial materials with special properties that do not exist in nature and have some special properties, such as enabling light and electromagnetic waves to change their normal properties, and such effects cannot be achieved by traditional materials. An acoustic metamaterial refers to a material / structure with the characteristic of sub-wavelength ultra-long elastic waves. A nonlinear acoustic metamaterial refers to an acoustic metamaterial with nonlinear dynamic effects. Metamaterials have an important vibration characteristic, namely the bandgap characteristic. When elastic waves propagate in a periodic structure, elastic waves in certain frequency ranges cannot pass through, which is called the bandgap, while elastic waves in certain frequency ranges can propagate, which is called the passband. A large number of studies have shown that in the face of extremely harsh environments and high-precision analysis requirements, the nonlinear effect will become a key factor affecting the analysis results. During the study of the nonlinear effect, the elastic wave amplitude range has an impact on the nonlinear bandgap characteristics. Therefore, it is necessary to determine the effective elastic wave amplitude range of the nonlinear acoustic metamaterial to determine the bandgap characteristics of the nonlinear acoustic metamaterial based on this effective elastic wave amplitude range.

[0076] In an exemplary embodiment of the present application, the effective elastic wave amplitude range can be calculated based on the structure of the nonlinear acoustic metamaterial. In the embodiments of the present application, the nonlinear acoustic metamaterial can specifically be a one-dimensional nonlinear acoustic metamaterial, a two-dimensional nonlinear acoustic metamaterial, or of course other types of nonlinear acoustic metamaterials. Different types of nonlinear acoustic metamaterials have different structures and specific calculation formulas will vary, but the overall idea is the same. Next, taking the one-dimensional nonlinear acoustic metamaterial as an example, the calculation method of the effective elastic wave amplitude range of the nonlinear acoustic metamaterial in the embodiments of the present application will be described.

[0077] In an exemplary embodiment of the present application, the one-dimensional nonlinear acoustic metamaterial is a one-dimensional nonlinear acoustic metamaterial with an inertial amplification mechanism. Figure 3 The structural schematic diagram of the one-dimensional nonlinear acoustic metamaterial with an inertial amplification mechanism is schematically shown, as Figure 3 shown. The one-dimensional nonlinear acoustic metamaterial with an inertial amplification mechanism is formed by connecting multiple unit cell structures 301, and there is a shared mass block between two adjacent unit cell structures. Specifically, the unit cell structure 301 includes a first basic mass block 302, a second basic mass block 303, a first inertial amplification mass block 304, a second inertial amplification mass block 305, a first resonant mass block 306, and a second resonant mass block 307. The first basic mass block 302 and the second basic mass block 303 are connected by a first spring 308. The first inertial amplification mass block 304 and the second inertial amplification mass block 305 are connected by a second spring 309. The first basic mass block 302 and the first resonant mass block 306 are connected by a third spring 310. The second basic mass block 303 and the second resonant mass block 307 are connected by a fourth spring 311. The first basic mass block 302 and the second basic mass block 303 are respectively connected to the first inertial amplification mass block 304 and the second inertial amplification mass block 305 through rigid connecting rods L. Among them, the first inertial amplification mass block 304 and the second inertial amplification mass block 305 are the mass blocks that provide the inertial amplification mechanism for the one-dimensional nonlinear acoustic metamaterial. Further, between the (n - 1)th unit cell and the nth unit cell, a basic mass block and the resonant mass block connected to the basic mass block are shared. This basic mass block is the second basic mass block in the (n - 1)th unit cell and also the first basic mass block in the nth unit cell. This resonant mass block is the second resonant mass block in the (n - 1)th unit cell and also the first resonant mass block in the nth unit cell, where n is a positive integer greater than 1.

[0078] In an exemplary embodiment of the present application, each mass block has its corresponding degree of freedom of motion. Figure 4 The degrees of freedom of motion of the mass blocks in the unit cell structure 301 are schematically shown, as Figure 4As shown, the first base mass block 302 and the second base mass block 303 both have a degree of freedom of movement u in the horizontal direction. The first resonant mass block 306 and the second resonant mass block 307 both have a degree of freedom of movement q in the horizontal direction. The first inertial amplification mass block 304 and the second inertial amplification mass block 305 both have a degree of freedom of movement v, and the direction of the degree of freedom of movement of the first inertial amplification mass block 304 is in the vertical direction, and the direction of the degree of freedom of movement of the second inertial amplification mass block 305 is in the opposite direction of the vertical direction.

[0079] Furthermore, based on Figure 4 the degrees of freedom of movement of each mass block shown, a force analysis is performed on the unit cell structure, and a force model corresponding to the unit cell structure can be obtained. Then, based on this force model, a motion relationship corresponding to the unit cell structure can be obtained. This motion relationship specifically includes a displacement relationship, an internal force relationship of the rigid link, and a resultant force relationship in the horizontal axis. The resultant force relationship in the horizontal axis is the resultant force acting on the base mass block in the unit cell structure in the horizontal axis direction.

[0080] Since the movement of the resonant mass block is related to the base mass block, there is no force corresponding to the resonant mass block in the force model. Only the base mass block and the inertial amplification mass block are subject to forces. Figure 5 Schematically shows the force model corresponding to the unit cell structure, as Figure 5 shown. When the mass blocks in the unit cell structure move, there is an internal force Fn in the rigid link between the base mass block and the inertial amplification mass block, and the resultant force of this internal force in the horizontal direction exists

[0081] Based on Figure 5 the force model shown, the following motion relationships can be calculated. The displacement relationship is shown in formula (1). Based on formula (1), the internal force relationship of the rigid link can be obtained, as shown in formula (2). Then, based on formula (2), the resultant force relationship in the horizontal axis can be obtained, as shown in formula (3). Specifically:

[0082]

[0083]

[0084]

[0085] where v n is the displacement of the inertial amplification mass block in the nth unit cell, u n+1 is the displacement of the second base mass block in the nth unit cell, u n is the displacement of the first base mass block in the nth unit cell, θ is the angle between the rigid link L and the horizontal direction, F n is the internal force received by the rigid link in the nth unit cell, m vis the mass of the inertial amplification mass block in the nth unit cell, is the acceleration of the second basic mass block in the nth unit cell, is the acceleration of the first basic mass block in the nth unit cell, k v is the stiffness of the spring connecting the inertial amplification mass block, is the horizontal component of the internal force on the rigid connecting rod in the nth unit cell.

[0086] In step S220, based on the motion relationship and the perturbation method, the bandgap characteristics of the nonlinear acoustic metamaterial are determined.

[0087] In an exemplary embodiment of the present application, after obtaining the motion relationship, the bandgap characteristics of the nonlinear acoustic metamaterial can be determined based on the motion relationship and the perturbation method. The nonlinear effect in the nonlinear acoustic metamaterial is introduced by the nonlinear spring connecting the resonant mass block and the basic mass block. First, the nonlinear restoring force generated by the nonlinear spring connecting the resonant mass block and the basic mass block in the unit cell structure can be obtained. The expression of the nonlinear restoring force is shown in formula (4):

[0088] F NL = k r Δx + εk NL (Δx) 3 (4)

[0089] where F NL is the nonlinear restoring force, k r is the nonlinear stiffness of the spring connecting the resonant mass block and the basic mass block, Δx is the relative displacement, ε is a small parameter, and k NL is the nonlinear stiffness.

[0090] Then, based on the nonlinear restoring force and the lumped mass method, the dynamic equation corresponding to the bandgap characteristics of the nonlinear acoustic metamaterial can be determined, as shown in formula (5):

[0091]

[0092] where m is the mass of the basic mass block, k is the stiffness of the spring connecting the basic mass block, u n-1 is the displacement of the first basic mass block in the (n - 1)th unit cell, is the horizontal component of the internal force on the rigid connecting rod in the (n - 1)th unit cell, q n is the displacement of the first resonant mass block in the nth unit cell, m r is the mass of the resonant mass block, is the displacement of the first resonant mass block in the nth unit cell.

[0093] Finally, a small parameter ε is introduced by the perturbation method to obtain the corresponding dynamic equation, as shown in Equation (6):

[0094]

[0095]

[0096]

[0097] wherein, is the 0th order term of the displacement of the first basic mass block in the nth unit cell, is the 1st order term of the displacement of the first basic mass block in the nth unit cell, is the 0th order term of the displacement of the first resonant mass block in the nth unit cell, is the 1st order term of the displacement of the first resonant mass block in the nth unit cell, Ω is the nonlinear frequency, Ω (0) is the 0th order term of the nonlinear frequency Ω, Ω (1) is the 1st order term of the nonlinear frequency Ω, ε 0 is the 0th order small parameter, τ is the normalized time, Q is the inertia amplification coefficient, H is the inertia amplification frequency ratio, is the 0th order term of the displacement of the second basic mass block in the nth unit cell, is the 0th order term of the displacement of the first basic mass block in the nth unit cell, is the 1st order term of the displacement of the second basic mass block in the nth unit cell, is the 0th order term of the displacement of the first basic mass block in the nth unit cell, Ω0 is the linear frequency, Ω1 is the perturbation frequency calculated by the perturbation method, ε 1 is the 1st order small parameter, ε 2 is the 2nd order small parameter, α, γ, and Γ are all normalized parameters,

[0098] Solving Equation (6) gives the bandgap characteristics of the one-dimensional nonlinear metamaterial, as shown in Equation (7):

[0099]

[0100] wherein, A is the amplitude of the elastic wave, and μ is the wave number.

[0101] Analyzing Equation (7), it can be seen that Ω0 is the bandgap characteristic of the linear system, and the latter term is the perturbation result of the perturbation method on the bandgap characteristic of the linear system.

[0102] In step S230, the effective elastic wave amplitude range of the nonlinear acoustic metamaterial is determined according to the bandgap characteristics of the nonlinear acoustic metamaterial, so as to re-determine the bandgap characteristics of the nonlinear acoustic metamaterial and determine the usage environment of the nonlinear acoustic metamaterial according to the effective elastic wave amplitude range.

[0103] In an exemplary embodiment of the present application, according to Equation (6), it can be seen that the bandgap characteristics of the one-dimensional nonlinear acoustic metamaterial need to satisfy corresponding boundary conditions, and the specific boundary conditions are shown in Equation (8):

[0104]

[0105] Based on the small parameter assumption of the perturbation method, the amplitude of the elastic wave in the nonlinear system is bounded. To make Equation (8) hold, the relationship should be satisfied. Then, combined with Ω = Ω (0) + εΩ (1) + O(ε 2 ) in Equation (6) and Equation (7), the relational expression shown in Equation (9) can be obtained:

[0106]

[0107] Since the small parameter ε in the small parameter assumption can be equivalent to << 1, the maximum value of the effective elastic wave amplitude can be obtained as A, and where

[0108]

[0109] Since the larger the elastic wave amplitude, the more inaccurate the calculated bandgap characteristics of the nonlinear acoustic metamaterial. Therefore, in the embodiment of the present application, the minimum value among different A values can be used as the maximum value in the effective elastic wave amplitude range. That is to say, through the small parameter assumption based on the perturbation method, the effective elastic wave amplitude range can be obtained as [0, A], where A is the minimum value of the function A(μ).

[0110] Figure 6 Schematically shows the effective elastic wave amplitude range diagram, as Figure 6 shown. In the effective elastic wave amplitude range diagram, there are three pairs of curves corresponding to different nonlinear stiffnesses. Among them, (a, a') is the pair of curves corresponding to the nonlinear stiffness of 1, (b, b') is the pair of curves corresponding to the nonlinear stiffness of 0.5, and (c, c') is the pair of curves corresponding to the nonlinear stiffness of 1.5. For the same nonlinear stiffness, two curves a and b can be obtained under different wave vector conditions. When determining the effective elastic wave amplitude range, the minimum amplitude corresponding to the tangent of each curve is used as the maximum value in the effective elastic wave amplitude range. Specifically, the minimum amplitude corresponding to the tangent of curve a is 0.2, and the minimum amplitude corresponding to the tangent of curve b is 0.6. Therefore, it can be determined that under this nonlinear stiffness, the effective elastic wave amplitude range of the nonlinear acoustic metamaterial is [0, 0.2].

[0111] In an exemplary embodiment of the present application, after obtaining the effective elastic wave amplitude range, the bandgap characteristics of the nonlinear acoustic metamaterial can be re-determined based on this effective elastic wave amplitude range. Specifically, this effective elastic wave amplitude range can be used as a constraint condition in the process of perturbing the linear bandgap result by the perturbation method to obtain the nonlinear bandgap characteristics, thereby improving the accuracy of calculating the bandgap characteristics of the nonlinear acoustic metamaterial.

[0112] Furthermore, the usage environment of the nonlinear acoustic metamaterial can also be determined according to this effective elastic wave amplitude range. Specifically, the structural member prepared from the nonlinear acoustic metamaterial can be applied to an environment where the environmental elastic wave amplitude is within the effective elastic wave amplitude range. For example, when the effective elastic wave amplitude range is [0, 0.5 nm], only when the structural member prepared from the nonlinear acoustic metamaterial is applied to an environment where the environmental elastic wave amplitude is within [0, 0.5 nm], can the elastic waves in this structural member be absorbed by the nonlinear acoustic metamaterial and not be propagated, thereby achieving the effect of vibration reduction and noise reduction.

[0113] In an exemplary embodiment of the present application, after obtaining the effective elastic wave amplitude range corresponding to the nonlinear acoustic metamaterial, the bandgap characteristics of the nonlinear acoustic metamaterial determined by the perturbation method at different elastic wave amplitudes can be evaluated through the time-domain method, that is, to judge the accuracy of the nonlinear acoustic metamaterial determined by the perturbation method when using the effective elastic wave amplitude range as a constraint condition. The reason for using the time-domain method for evaluation in the embodiments of the present application is that by analyzing the vibration modes of each mass block in the nonlinear acoustic metamaterial from the time-domain perspective, the bandgap characteristics of the nonlinear acoustic metamaterial can be accurately obtained.

[0114] Figure 7 A schematic diagram showing the process of evaluating the bandgap characteristics of the nonlinear acoustic metamaterial is schematically shown, as Figure 7 shown, this process at least includes step S701 - step S704, specifically:

[0115] In step S701, a finite one-dimensional nonlinear acoustic metamaterial is obtained, and the finite one-dimensional nonlinear acoustic metamaterial is moved until it is stable with the preset elastic wave amplitude, and the time-domain information of the basic mass at the central position in the finite one-dimensional nonlinear acoustic metamaterial is obtained.

[0116] In an exemplary embodiment of the present application, a finite one-dimensional nonlinear acoustic metamaterial refers to a one-dimensional nonlinear acoustic metamaterial having a finite number of unit cell structures. For example, a finite one-dimensional nonlinear acoustic metamaterial can be formed according to the number of unit cell structures such as 400, 800, etc. After obtaining the finite one-dimensional nonlinear acoustic metamaterial, at the moment of t = 0, an initial motion state can be set for each mass block therein, that is, a preset elastic wave amplitude is set for the degrees of freedom of each mass block, and then each mass block is released. Under the action of the preset elastic wave amplitude, each mass block moves. After a period of movement, the finite one-dimensional nonlinear acoustic metamaterial reaches a stable state. At this time, the time-domain information of the basic mass block located at the middle position can be obtained, and the bandgap characteristics of the nonlinear acoustic metamaterial can be determined according to the time-domain information. Figure 8 Schematically shows the position-displacement diagram of the unit cell structure in the finite one-dimensional nonlinear acoustic metamaterial, as Figure 8 shown. The finite one-dimensional nonlinear acoustic metamaterial includes 800 unit cell structures. It can be seen from this position-displacement diagram that there will be some perturbations at the leftmost and rightmost sides of the diagram. Therefore, the results closer to the ends are less credible, and it is necessary to take the unit cell structures processed at the middle position for research. Further, since both the inertia amplification mass block and the resonant mass block act on the basic mass block, the time-domain information of the basic mass block in the unit cell structure at the middle position can be used as the time-domain information of the unit cell structure at the middle position.

[0117] In step S702, perform a Fourier transform on the time-domain information to obtain the bandgap characteristics to be compared.

[0118] In an exemplary embodiment of the present application, after obtaining the time-domain information of the basic mass block at the middle position, a Fourier transform can be performed on it to obtain the bandgap characteristics of the nonlinear acoustic metamaterial, and the bandgap characteristics can be used as the bandgap characteristics to be compared for evaluating the accuracy of the bandgap characteristics of the nonlinear acoustic metamaterial determined by the perturbation method.

[0119] In step S703, use the effective elastic wave amplitude range as a boundary condition, and obtain the bandgap characteristics corresponding to different target amplitudes by the perturbation method.

[0120] In an exemplary embodiment of the present application, after obtaining the effective elastic wave amplitude range, it can be used as a boundary condition to determine the bandgap characteristics of the nonlinear acoustic metamaterial by the perturbation method. Since the purpose of the evaluation is to evaluate the accuracy rate of the bandgap characteristics of the nonlinear acoustic metamaterial under the action of the effective elastic wave amplitude range, an elastic wave amplitude can be selected from the effective elastic wave amplitude range, and at the same time, an elastic wave amplitude can be selected outside the effective elastic wave amplitude range, and then the bandgap characteristics corresponding to the two elastic wave amplitudes are compared with the bandgap characteristics of the nonlinear acoustic metamaterial determined by the time-domain method.

[0121] In step S704, the bandgap characteristic and the bandgap characteristic to be compared are compared to evaluate the bandgap characteristic of the nonlinear acoustic metamaterial.

[0122] In an exemplary embodiment of the present application, Figures 9A - 9B schematically shows the bandgap characteristics of the nonlinear acoustic metamaterial at different elastic wave amplitudes, as Figure 9A shown. The bandgap characteristic of this nonlinear acoustic metamaterial is the bandgap characteristic determined corresponding to the elastic wave amplitude within the effective elastic wave amplitude range. Among them, the solid line represents the bandgap characteristic determined by the perturbation method, and the pentagram represents the bandgap characteristic determined by the time-domain method. By comparison, it can be seen that under the limitation of the effective elastic wave amplitude range, the bandgap characteristic of the nonlinear acoustic metamaterial determined by the perturbation method is basically consistent and matched with the bandgap characteristic to be compared of the nonlinear acoustic metamaterial determined by the time-domain method, and the error is less than or equal to 5%; as Figure 9B shown. The bandgap characteristic of this nonlinear acoustic metamaterial is the bandgap characteristic determined corresponding to the elastic wave amplitude outside the effective elastic wave amplitude range. Among them, the solid line represents the bandgap characteristic determined by the perturbation method, and the pentagram represents the bandgap characteristic determined by the time-domain method. By comparison, it can be seen that for the elastic wave amplitude in the non-effective elastic wave amplitude range, the bandgap characteristic of the nonlinear acoustic metamaterial determined by the perturbation method does not match the bandgap characteristic to be compared of the nonlinear acoustic metamaterial determined by the time-domain method, and the error is greater than 5%.

[0123] By comparing Figure 9A and Figure 9B it can be seen that under the action of the effective elastic wave amplitude range, the accuracy of the bandgap characteristic of the nonlinear acoustic metamaterial can be improved.

[0124] The calculation method of the effective elastic wave amplitude range of the nonlinear acoustic metamaterial in the present application obtains the motion relationship of the unit cell structure by analyzing the force on the unit cell structure of the nonlinear acoustic metamaterial, determines the bandgap characteristic of the nonlinear acoustic metamaterial based on this motion relationship and the perturbation method, and determines the effective elastic wave amplitude range of the nonlinear acoustic metamaterial based on the bandgap characteristic of the nonlinear acoustic metamaterial. This effective elastic wave amplitude range can be used to re-determine the bandgap characteristic of the nonlinear acoustic metamaterial and determine the use environment of the nonlinear acoustic metamaterial. The calculation method of the effective elastic wave amplitude range of the nonlinear acoustic metamaterial in the embodiment of the present application can improve the calculation accuracy of the bandgap characteristic of the nonlinear acoustic metamaterial by determining the effective elastic wave amplitude range, and determine the use environment of the nonlinear acoustic metamaterial according to the effective elastic wave amplitude range, so as to achieve vibration reduction and noise reduction through this nonlinear acoustic metamaterial and improve the performance of the structural member.

[0125] The present application also provides a calculation device for the effective elastic wave amplitude range of a nonlinear acoustic metamaterial,Figure 10 The structural schematic diagram of a calculation device for the effective elastic wave amplitude range of a nonlinear acoustic metamaterial is shown, as Figure 10 shown, the calculation device 1000 for the effective elastic wave amplitude range of the nonlinear acoustic metamaterial may include a force analysis module 1001, a bandgap characteristic determination module 1002, and an amplitude range determination module 1003. Among them:

[0126] The force analysis module 1001 is configured to obtain the unit cell structure of the nonlinear acoustic metamaterial, perform a force analysis on the unit cell structure to obtain the motion relationship of the unit cell structure;

[0127] The bandgap characteristic determination module 1002 is configured to determine the bandgap characteristics of the nonlinear acoustic metamaterial based on the motion relationship and the perturbation method;

[0128] The amplitude range determination module 1003 is configured to determine the effective elastic wave amplitude range of the nonlinear acoustic metamaterial according to the bandgap characteristics of the nonlinear acoustic metamaterial, and determine the usage environment of the nonlinear acoustic metamaterial according to the effective elastic wave amplitude range.

[0129] In an exemplary embodiment of the present application, the nonlinear acoustic metamaterial is a one-dimensional nonlinear acoustic metamaterial with an inertial amplification mechanism; the unit cell structure includes a first basic mass block, a second basic mass block, a first inertial amplification mass block, a second inertial amplification mass block, a first resonant mass block, and a second resonant mass block. The first basic mass block and the second basic mass block are connected by a first spring, the first inertial amplification mass block and the second inertial amplification mass block are connected by a second spring, the first basic mass block and the first resonant mass block are connected by a third spring, the second basic mass block and the second resonant mass block are connected by a fourth spring, and the first basic mass block and the second basic mass block are respectively connected to the first inertial amplification mass block and the second inertial amplification mass block through rigid connecting rods.

[0130] In an exemplary embodiment of the present application, the force analysis module 1001 is configured as:

[0131] Perform a force analysis on the unit cell structure according to the degrees of freedom corresponding to each mass block in the unit cell structure to obtain a force model corresponding to the unit cell structure;

[0132] Obtain the motion relationship based on the force model. The motion relationship includes a displacement relationship, an internal force relationship of the rigid connecting rod, and a resultant force relationship in the horizontal axis. The resultant force relationship in the horizontal axis is the resultant force acting on the basic mass block in the unit cell structure along the horizontal axis direction.

[0133] In an exemplary embodiment of the present application, the bandgap characteristic determination module 1002 is configured to:

[0134] Obtain the nonlinear restoring force generated by the nonlinear spring connecting the resonant mass block and the base mass block in the unit cell structure;

[0135] Based on the nonlinear restoring force and the lumped mass method, determine the dynamic equation corresponding to the bandgap characteristics of the nonlinear acoustic metamaterial;

[0136] Solve the dynamic equation by introducing a small parameter through the perturbation method to obtain the bandgap characteristics of the nonlinear acoustic metamaterial.

[0137] In an exemplary embodiment of the present application, the amplitude range determination module 1003 is configured to:

[0138] Determine the effective elastic wave amplitude range according to the boundary conditions and the bandgap characteristics of the nonlinear acoustic metamaterial.

[0139] In an exemplary embodiment of the present application, the effective elastic wave amplitude range is [0, A], where A is the minimum value of the function A(μ);

[0140] Where μ is the wave number, Ω0 is the linear frequency, α, γ, and Γ are all normalized parameters, m is the mass of the base mass block in the unit cell structure, k is the stiffness of the spring connecting the two base mass blocks in the unit cell structure, m r is the mass of the resonant mass block in the unit cell structure, k r is the nonlinear stiffness of the spring connecting the resonant mass block and the base mass block in the unit cell structure, k NL is the nonlinear stiffness.

[0141] In an exemplary embodiment of the present application, the effective elastic wave amplitude range calculation device 1000 of the nonlinear acoustic metamaterial further includes:

[0142] An evaluation module, configured to evaluate the bandgap characteristics of the nonlinear acoustic metamaterial by a time-domain method after obtaining the effective elastic wave amplitude range.

[0143] In an exemplary embodiment of the present application, the evaluation module is configured to:

[0144] Obtain a finite one-dimensional nonlinear acoustic metamaterial, move the finite one-dimensional nonlinear acoustic metamaterial with the preset elastic wave amplitude until it is stable, and obtain the time-domain information of the base mass block located at the middle position in the finite one-dimensional nonlinear acoustic metamaterial;

[0145] Perform a Fourier transform on the time-domain information to obtain the bandgap characteristics to be compared.

[0146] Use the effective elastic wave amplitude range as the boundary condition, and obtain the bandgap characteristics corresponding to different target amplitudes through the perturbation method.

[0147] Compare the bandgap characteristics with the bandgap characteristics to be compared to evaluate the bandgap characteristics of the nonlinear acoustic metamaterial.

[0148] In an exemplary embodiment of the present application, the comparing the bandgap characteristics with the bandgap characteristics to be compared to evaluate the bandgap characteristics of the nonlinear acoustic metamaterial is configured as follows:

[0149] When the target amplitude is within the effective elastic wave amplitude range, the bandgap characteristics match the bandgap characteristics to be compared.

[0150] When the target amplitude is outside the effective elastic wave amplitude range, the bandgap characteristics do not match the bandgap characteristics to be compared.

[0151] It should be noted that although several modules or units of the device for action execution are mentioned in the above detailed description, this division is not mandatory. In fact, according to the embodiments of the present application, the features and functions of the two or more modules or units described above can be embodied in one module or unit. Conversely, the features and functions of one module or unit described above can be further divided and embodied by multiple modules or units.

[0152] In addition, although the steps of the method in the present application are described in a specific order in the drawings, this does not require or imply that these steps must be executed in this specific order, or that all the steps shown must be executed to achieve the desired result. Additionally or alternatively, some steps may be omitted, multiple steps may be combined into one step for execution, and / or one step may be decomposed into multiple steps for execution, etc.

[0153] Through the description of the above embodiments, those skilled in the art can easily understand that the exemplary embodiments described herein can be implemented by software, or by a combination of software and necessary hardware. Therefore, the technical solutions according to the embodiments of the present application can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, mobile hard disk, etc.) or on the network, including several instructions to enable a computing device (such as a personal computer, server, mobile terminal, or network device, etc.) to execute the method according to the embodiments of the present application.

[0154] Figure 11A computer system block diagram of an electronic device for implementing the embodiments of the present application is schematically shown. The electronic device may be disposed in a terminal device or a server.

[0155] It should be noted that Figure 11 The computer system 1100 of the shown electronic device is only an example and should not impose any limitation on the functions and usage scope of the embodiments of the present application.

[0156] As Figure 11 shown, the computer system 1100 includes a central processing unit 1101 (Central Processing Unit, CPU), which can execute various appropriate actions and processes according to the program stored in the read-only memory 1102 (Read-Only Memory, ROM) or the program loaded from the storage section 1108 into the random access memory 1103 (Random Access Memory, RAM). In the random access memory 1103, various programs and data required for system operation are also stored. The central processing unit 1101, the read-only memory 1102, and the random access memory 1103 are connected to each other via a bus 1104. The input / output interface 1105 (Input / Output interface, i.e., I / O interface) is also connected to the bus 1104.

[0157] In some embodiments, the following components are connected to the input / output interface 1105: an input section 1106 including a keyboard, a mouse, etc.; an output section 1107 including, for example, a cathode ray tube (Cathode Ray Tube, CRT), a liquid crystal display (Liquid Crystal Display, LCD), etc. and a speaker, etc.; a storage section 1108 including a hard disk, etc.; and a communication section 1109 including a network interface card such as a local area network card, a modem, etc. The communication section 1109 performs communication processing via a network such as the Internet. A drive 1110 is also connected to the input / output interface 1105 as required. A removable medium 1111, such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, etc., is installed on the drive 1110 as required so that the computer program read from it can be installed into the storage section 1108 as required.

[0158] In particular, according to embodiments of the present application, the processes described in each method flowchart can be implemented as computer software programs. For example, embodiments of the present application include a computer program product that includes a computer program carried on a computer-readable medium, and the computer program contains program code for performing the methods shown in the flowcharts. In such an embodiment, the computer program can be downloaded and installed from the network through the communication part 1109, and / or installed from the removable medium 1111. When the computer program is executed by the central processing unit 1101, various functions defined in the system of the present application are performed.

[0159] It should be noted that the computer-readable medium shown in the embodiments of the present application can be a computer-readable signal medium, a computer-readable medium, or any combination of the two. The computer-readable medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the above. More specific examples of the computer-readable medium can include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM), a flash memory, an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present application, the computer-readable medium can be any tangible medium that contains or stores a program, and the program can be used by or in combination with an instruction execution system, apparatus, or device. In the present application, the computer-readable signal medium can include a data signal propagated in a baseband or as part of a carrier wave, which carries computer-readable program code. Such a propagated data signal can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. The computer-readable signal medium can also be any computer-readable medium other than the computer-readable medium, and the computer-readable medium can send, propagate, or transmit a program for use by or in combination with an instruction execution system, apparatus, or device. The program code contained on the computer-readable medium can be transmitted by any suitable medium, including but not limited to: wireless, wired, etc., or any suitable combination of the above.

[0160] The flowcharts and block diagrams in the accompanying drawings illustrate the possible architectures, functions, and operations of systems, methods, and computer program products according to various embodiments of the present application. In this regard, each block in the flowchart or block diagram may represent a module, a segment of a program, or a portion of code that contains one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than that marked in the accompanying drawings. For example, two consecutive blocks shown may actually be executed substantially in parallel, and they may sometimes be executed in the reverse order, depending on the functions involved. It should also be noted that each block in the block diagram or flowchart, as well as combinations of blocks in the block diagram or flowchart, can be implemented by a dedicated hardware-based system that performs the specified functions or operations, or can be implemented by a combination of dedicated hardware and computer instructions.

[0161] It should be noted that although several modules or units of devices for action execution are mentioned in the above detailed description, such a division is not mandatory. In fact, according to the embodiments of the present application, the features and functions of the two or more modules or units described above can be embodied in one module or unit. Conversely, the features and functions of one module or unit described above can be further divided and embodied by multiple modules or units.

[0162] From the description of the above embodiments, those skilled in the art can easily understand that the example embodiments described herein can be implemented by software, or can be implemented by a combination of software and necessary hardware. Therefore, the technical solutions according to the embodiments of the present application can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a USB flash drive, a mobile hard disk, etc.) or on a network, and includes several instructions to enable an electronic device to execute the method according to the embodiments of the present application.

[0163] It should be understood that the present application is not limited to the exact structures described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the present application is only limited by the appended claims.

Claims

1. A method for calculating the effective elastic wave amplitude range of a nonlinear acoustic metamaterial, characterized in that The method includes: Obtaining the unit cell structure of the nonlinear acoustic metamaterial, performing a force analysis on the unit cell structure to obtain the motion relationship of the unit cell structure; Determining the bandgap characteristics of the nonlinear acoustic metamaterial based on the motion relationship and the perturbation method; Determining the effective elastic wave amplitude range of the nonlinear acoustic metamaterial according to the bandgap characteristics of the nonlinear acoustic metamaterial, and re-determining the bandgap characteristics of the nonlinear acoustic metamaterial and determining the usage environment of the nonlinear acoustic metamaterial according to the effective elastic wave amplitude range; Among them, the determining the bandgap characteristics of the nonlinear acoustic metamaterial based on the motion relationship and the perturbation method includes: Obtaining the nonlinear restoring force generated by the nonlinear spring connecting the resonant mass block and the base mass block in the unit cell structure; Determining the dynamic equation corresponding to the bandgap characteristics of the nonlinear acoustic metamaterial based on the nonlinear restoring force and the lumped mass method; Solving the dynamic equation by introducing a small parameter through the perturbation method to obtain the bandgap characteristics of the nonlinear acoustic metamaterial.

2. The method according to claim 1, characterized in that The nonlinear acoustic metamaterial is a one-dimensional nonlinear acoustic metamaterial with an inertia amplification mechanism; the unit cell structure includes a first base mass block, a second base mass block, a first inertia amplification mass block, a second inertia amplification mass block, a first resonant mass block and a second resonant mass block. The first base mass block and the second base mass block are connected by a first spring, the first inertia amplification mass block and the second inertia amplification mass block are connected by a second spring, the first base mass block and the first resonant mass block are connected by a third spring, the second base mass block and the second resonant mass block are connected by a fourth spring, and the first base mass block and the second base mass block are respectively connected to the first inertia amplification mass block and the second inertia amplification mass block through rigid connecting rods.

3. The method according to claim 1 or 2, characterized in that, The performing a force analysis on the unit cell structure to obtain the motion relationship of the unit cell structure includes: Performing a force analysis on the unit cell structure according to the degrees of freedom corresponding to each mass block in the unit cell structure to obtain a force model corresponding to the unit cell structure; Obtaining the motion relationship based on the force model. The motion relationship includes a displacement relationship, an internal force relationship of the rigid connecting rod, and a transverse resultant force relationship. The transverse resultant force relationship is the resultant force acting on the base mass block in the unit cell structure along the transverse axis direction.

4. The method according to claim 1, characterized in that, The determining the effective elastic wave amplitude range of the nonlinear acoustic metamaterial according to the bandgap characteristics of the nonlinear acoustic metamaterial includes: Determining the effective elastic wave amplitude range according to the boundary conditions and the bandgap characteristics of the nonlinear acoustic metamaterial.

5. The method according to claim 4, characterized in that, The effective elastic wave amplitude range is [0, A], and A is the minimum value of the function A(μ); Among them, μ is the wave number, Ω0 is the linear frequency, and α, γ, and Γ are all normalized parameters, m is the mass of the basic mass block in the unit cell structure, k is the stiffness of the spring connecting the two basic mass blocks in the unit cell structure, m r is the mass of the resonant mass block in the unit cell structure, k r is the nonlinear stiffness of the spring connecting the resonant mass block and the basic mass block in the unit cell structure, k NL is the nonlinear stiffness.

6. The method according to claim 1 or 5, characterized in that, After obtaining the effective elastic wave amplitude range, the method further includes: Obtaining a finite one-dimensional nonlinear acoustic metamaterial, moving the finite one-dimensional nonlinear acoustic metamaterial with a preset elastic wave amplitude until it is stable, and obtaining the time-domain information of the base mass block located at the middle position in the finite one-dimensional nonlinear acoustic metamaterial. Perform a Fourier transform on the time-domain information to obtain the bandgap characteristics to be compared. Use the effective elastic wave amplitude range as a boundary condition, and obtain the bandgap characteristics corresponding to different target amplitudes by the perturbation method. Compare the bandgap characteristics with the bandgap characteristics to be compared to evaluate the bandgap characteristics of the nonlinear acoustic metamaterial.

7. The method according to claim 6, wherein The step of comparing the bandgap characteristics with the bandgap characteristics to be compared to evaluate the bandgap characteristics of the nonlinear acoustic metamaterial includes: When the target amplitude is within the effective elastic wave amplitude range, the bandgap characteristics match the bandgap characteristics to be compared. When the target amplitude is outside the effective elastic wave amplitude range, the bandgap characteristics do not match the bandgap characteristics to be compared.

8. An apparatus for calculating the effective elastic wave amplitude range of a nonlinear acoustic metamaterial, characterized in that It includes: A force analysis module for obtaining the unit cell structure of the nonlinear acoustic metamaterial, performing a force analysis on the unit cell structure to obtain the motion relationship of the unit cell structure. A bandgap characteristic determination module for determining the bandgap characteristics of the nonlinear acoustic metamaterial based on the motion relationship and the perturbation method. An amplitude range determination module for determining the effective elastic wave amplitude range of the nonlinear acoustic metamaterial according to the bandgap characteristics of the nonlinear acoustic metamaterial, and determining the usage environment of the nonlinear acoustic metamaterial according to the effective elastic wave amplitude range. The step of determining the bandgap characteristics of the nonlinear acoustic metamaterial based on the motion relationship and the perturbation method includes: obtaining the nonlinear restoring force generated by the nonlinear spring connecting the resonant mass block and the base mass block in the unit cell structure; determining the dynamic equation corresponding to the bandgap characteristics of the nonlinear acoustic metamaterial based on the nonlinear restoring force and the lumped mass method; introducing a small parameter by the perturbation method to solve the dynamic equation to obtain the bandgap characteristics of the nonlinear acoustic metamaterial.

9. An electronic device, characterized in that, It includes: A processor; and A memory for storing executable instructions of the processor; wherein, the processor is configured to execute the method for calculating the effective elastic wave amplitude range of the nonlinear acoustic metamaterial according to any one of claims 1 to 7 by executing the executable instructions.

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