A model construction method and system based on an equivalent circuit of a piezoelectric sandwich beam

Abstract

The application discloses a model construction method and system based on an equivalent circuit of a piezoelectric sandwich beam, and comprises the following steps: arranging piezoelectric sheets on a piezoelectric sandwich beam, and constructing a dynamic model of the sandwich beam; building an equivalent circuit structure of the piezoelectric sandwich beam according to the piezoelectric sheets and the assumed mode of the cantilever beam; building an electromechanical coupling model of the piezoelectric sandwich beam by using the equivalent circuit structure and the dynamic model; and performing electromechanical coupling of the piezoelectric sandwich beam according to an electromechanical coupling equation in the electromechanical coupling model to obtain an equivalent circuit model. The first equivalent circuit model of the piezoelectric sandwich beam is established, and the model represents a piezoelectric energy collector based on the sandwich beam. The equivalent circuit model method can also be generally applied to analysis of any other sandwich piezoelectric energy collector. The equivalent circuit model is helpful to integration of an advanced shunt circuit, thereby performing comprehensive system-level analysis.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of equivalent circuit construction, in particular to a model construction method and system based on a piezoelectric sandwich beam equivalent circuit. BACKGROUND

[0002] With the rapid development of wireless sensor networks and micro-electro-mechanical systems (MEMS), the problem of micro power supply is increasingly prominent. Traditional wired power supply not only limits the mobility of devices, but also increases the complexity and maintenance cost of the system. Piezoelectric energy harvesting technology converts mechanical energy in the environment into electrical energy, providing a sustainable energy supply solution for micro devices. At the same time, structural vibration control has always been the focus of the engineering field, and vibration reduction technology is of great significance to improve the safety and service life of structures.

[0003] In existing technologies, there is a gradient compression-torsion energy storage and vibration reduction structure, which realizes impact energy conversion through a compression-torsion unit cell array. The unit cell is composed of an upper panel, a compression-torsion structure, a lower panel, and a bottom plate, wherein the compression-torsion structure contains multiple layers of oblique rod assemblies. When a load is applied, the compression-torsion structure converts linear load into rotational energy of the structure itself and the counterweight through the rotation of the oblique rods. The energy storage and vibration reduction unit formed by the unit cell array can absorb energy layer by layer, and the energy absorption efficiency is significantly improved compared with traditional structures. The core advantage is that the stiffness and strength can be flexibly designed by adjusting the number of oblique rods in the unit cell, which is suitable for high energy absorption scenarios. A double-layer pyramid type lightweight vibration reduction metamaterial lattice structure is designed based on a double-layer pyramid type lattice. The unit cell is composed of upper and lower panels, 8 double-layer pyramid type sandwich circular rods, and a spherical resonance unit. The glass fiber reinforced nylon material is used. By embedding the spherical resonance unit at the intersection of the sandwich circular rods, a wide frequency band gap is generated using periodic structures to scatter and attenuate vibration waves, achieving lightweight, wide frequency vibration reduction, and load capacity without changing the external geometric characteristics of the structure.

[0004] In recent years, the progress of smart material and structure technology has promoted the development of functional integration, and piezoelectric materials have been widely used in the field of vibration energy recovery. Through the positive piezoelectric effect, mechanical vibration is converted into electrical energy, providing a new way to power micro systems.

[0005] Limitations of Patent 1: The energy conversion method relies on passive rotation energy absorption, lacks active control mechanisms, and has limited response capability for low-frequency vibrations and complex loads. The energy recovery function is not integrated, and the rotational energy is not utilized as a resource.

[0006] Limitations of Patent 2: The vibration reduction effect relies on fixed bandgap characteristics, and the frequency band adjustment flexibility is insufficient. The structure has a single function (only passive vibration reduction), and does not integrate energy recovery or active control functions, making it difficult to meet the needs of intelligent equipment for multifunctional integration.

[0007] Common defects: both do not realize the coupling design of active vibration reduction and energy recovery, the functional integration degree is low, and the adaptability to wide frequency vibration environment has technical bottlenecks (such as patent one focuses on impact energy absorption, and patent two focuses on vibration suppression within the band gap, both of which cannot cover multi-frequency active control and energy efficient utilization). SUMMARY

[0008] In view of the above problems, the present application is proposed.

[0009] To solve the above technical problems, the present application provides the following technical scheme: a model construction method based on the equivalent circuit of the piezoelectric sandwich beam, comprising:

[0010] Arranging piezoelectric sheets on the piezoelectric sandwich beam to construct a dynamic model of the sandwich beam;

[0011] According to the assumed modal of the piezoelectric sheet and the cantilever beam, an equivalent circuit structure of the piezoelectric sandwich beam is built;

[0012] Using the equivalent circuit structure and the dynamic model, an electromechanical coupling model of the piezoelectric sandwich beam is built;

[0013] According to the electromechanical coupling equation in the electromechanical coupling model, electromechanical coupling of the piezoelectric sandwich beam is carried out to obtain an equivalent circuit model;

[0014] The SECE circuit and the SSDI circuit are connected as loads to the equivalent circuit model to realize piezoelectric energy harvesting and vibration reduction effect.

[0015] As a preferred scheme of the model construction method based on the equivalent circuit of the piezoelectric sandwich beam, the piezoelectric sandwich beam is composed of upper and lower substrates and a sand hour core layer in the middle, the piezoelectric sheet is placed on the upper substrate of the sandwich beam, and the piezoelectric sheet and the substrate are connected through an adhesive layer.

[0016] As a preferred scheme of the model construction method based on the equivalent circuit of the piezoelectric sandwich beam, the dynamic model includes, according to the strain-displacement relationship, stress-strain relationship, total kinetic energy, total potential energy and electric energy stored in the piezoelectric layer of the structure, the motion control equation of the piezoelectric sandwich beam is derived by applying Hamilton principle to obtain the dynamic equation of the sandwich beam, which is expressed as:

[0017] Wherein, C represents the Rayleigh damping matrix, M represents the mass matrix, K represents the stiffness matrix, F represents the external excitation force, X(t) represents the displacement of the time window t, X(t) represents the velocity of the time window t, X(t) represents the acceleration of the time window t.

[0018] As a preferred scheme of the model construction method based on the equivalent circuit of the piezoelectric sandwich beam of the present application, wherein: the piezoelectric sheet generates voltage through displacement; in the equivalent, the generated voltage, inductance, resistance, capacitance and the primary coil of the transformer are connected in series in turn;

[0019] The assumed mode of the cantilever beam includes dividing the voltage generated by the piezoelectric sheet into six modal components: three transverse displacement modes and three angular modes; each mode is equivalent through the circuit structure of the piezoelectric sheet.

[0020] As a preferred scheme of the model construction method based on the equivalent circuit of the piezoelectric sandwich beam of the present application, wherein: the equivalent circuit structure includes, in parallel with the internal capacitance of the piezoelectric sheet and the load, forming a loop with the power supply, and then connecting the six equivalent modes through the secondary coil of the transformer in parallel across the power supply to form the circuit model.

[0021] As a preferred scheme of the model construction method based on the equivalent circuit of the piezoelectric sandwich beam of the present application, wherein: the electromechanical coupling model includes, based on kinetic energy, potential energy and piezoelectric energy, using Lagrange equation to construct electromechanical coupling control equation, coupling the piezoelectric sheet and the beam structure through the voltage term v(t), and deriving to obtain the electromechanical coupling equation:

[0022]

[0023] wherein ζ a and ζ c represent the electromechanical coupling coefficients obtained by constructing the electromechanical coupling control equation through the Lagrange equation; v(t) represents the voltage generated by the piezoelectric sheet, which is the sum of the voltages of six modes; C p represents the internal capacitance of the piezoelectric layer; represents the rate of change of voltage; T represents the transpose symbol of the matrix; f represents the external excitation force, which is the sum of the external excitation forces in six modes; R represents the load resistance;

[0024] The electromechanical coupling includes equivalent M as voltage, equivalent C as resistance, and equivalent K as capacitance, mode conversion of the electric coupling equation to obtain the coupling equation of the equivalent circuit model:

[0025]

[0026] wherein ξ n and ω n represent the modal damping ratio and the natural frequency under open circuit condition of the n-order vibration mode; ε n represents the modal electromechanical coupling coefficient; f n represents the external excitation force, and q(t) represents the modal vibration displacement after conversion, represents the modal vibration displacement velocity after conversion, represents the modal vibration acceleration after conversion; N represents the modal order, and is 6.

[0027] As a preferred scheme of the model construction method based on the equivalent circuit of the piezoelectric sandwich beam, in the equivalent circuit model, the load part is replaced by an SECE circuit to achieve the energy harvesting effect, and is replaced by an SSDI circuit to achieve the vibration reduction effect.

[0028] A model construction system based on the equivalent circuit of the piezoelectric sandwich beam, which adopts the method described in any of the present application, is characterized in that: a dynamic analysis unit is arranged on the piezoelectric sandwich beam, and a dynamic model of the sandwich beam is constructed.

[0029] A construction unit is arranged according to the assumed modal of the piezoelectric sheet and the cantilever beam, and an equivalent circuit structure of the piezoelectric sandwich beam is built; the equivalent circuit structure and the dynamic model are used to build an electromechanical coupling model of the piezoelectric sandwich beam.

[0030] A coupling unit is arranged according to the electromechanical coupling equation in the electromechanical coupling model, and the electromechanical coupling of the piezoelectric sandwich beam is carried out to obtain an equivalent circuit model; the SECE circuit and the SSDI circuit are connected as loads to the equivalent circuit model to realize the piezoelectric energy harvesting and vibration reduction effect.

[0031] A computer device comprises a memory and a processor; the memory stores a computer program, wherein the processor implements the steps of the method described in any of the present application when executing the computer program.

[0032] A computer readable storage medium stores a computer program, wherein the computer program is executed by a processor to implement the steps of the method described in any of the present application.

[0033] The model construction method based on the equivalent circuit of the piezoelectric sandwich beam provided by the present application establishes the first equivalent circuit model of the piezoelectric sandwich beam, and the model represents a piezoelectric energy collector based on the sandwich beam. This equivalent circuit model method can also be generally applied to analyze any other sandwich type piezoelectric energy collector. The equivalent circuit model is helpful to integrate advanced shunt circuits, so as to carry out comprehensive system level analysis.

[0034] Enhanced understanding and intuitiveness: The equivalent circuit model provides a clear and intuitive perspective for understanding the working principles, dynamic characteristics (such as vibration modes, resonance frequencies), and energy conversion mechanisms (such as sensing, actuation, energy harvesting) of the piezoelectric sandwich beam. The elements in the circuit (such as resistors, inductors, capacitors) can be directly related to the physical parameters of the piezoelectric sandwich beam (such as mass, stiffness, piezoelectric coupling coefficient, dielectric constant, mechanical loss, etc.), making it easier for designers to understand the impact of each parameter on overall performance.

[0035] Simplified analysis and improved efficiency: By converting the complex mechanical-electrical coupling behavior of the piezoelectric sandwich beam into an equivalent circuit model, the analysis process is greatly simplified. Compared to traditional finite element analysis (FEA) or other complex numerical methods, this method usually has smaller computational load and faster analysis speed, which can significantly shorten the product development cycle and design iteration time. Engineers can quickly evaluate the performance of the piezoelectric sandwich beam using mature circuit analysis theory and tools.

[0036] Easy integration and system-level simulation: The constructed equivalent circuit model can be easily integrated into standard circuit simulation software (such as SPICE, ADS, etc.), facilitating joint simulation and analysis of the entire mechatronic system. This is particularly important for designing sensors, actuators, energy harvesters, and related interface circuits and control systems containing piezoelectric sandwich beams, enabling overall performance evaluation and optimization from device level to system level.

[0037] Optimized design and parameter research: Based on the model construction method, parameterized research and optimization design can be efficiently conducted. By adjusting the element parameters in the equivalent circuit (which directly or indirectly correspond to the geometric dimensions, material properties, boundary conditions, etc. of the sandwich beam), the performance of different design schemes can be quickly evaluated, and the optimal combination of structural parameters can be found to meet specific application requirements (such as maximizing energy output efficiency, specific frequency response, improving sensing sensitivity, etc.).

[0038] Reduced modeling cost and technical threshold: Compared to complex numerical modeling techniques that require expensive professional software and higher professional knowledge, the model construction method proposed in this invention may be more simple and easy to operate, with more explicit steps, helping to reduce research and development costs and technical thresholds. This enables more researchers and engineers to effectively model and analyze piezoelectric sandwich beams, promoting their application in a wider range of fields.

[0039] Improved prediction accuracy and reliability (within the applicable scope): Through reasonable model simplification and accurate parameter identification, the method of this invention can establish an equivalent circuit model with high consistency with actual physical characteristics while ensuring computational efficiency. This provides a more reliable theoretical basis and tool for performance prediction, fault diagnosis, and health monitoring of piezoelectric sandwich beams.

[0040] Promote standardization and modular design: equivalent circuit model has good universality and portability. The method of the application helps to abstract the piezoelectric sandwich beam in different structures or application scenarios into a circuit module with a standard interface, facilitating modular design and system integration, and being conducive to forming a standardized design process and knowledge accumulation. BRIEF DESCRIPTION OF DRAWINGS

[0041] In order to more clearly illustrate the technical solutions of the embodiments of the application, the drawings needed to be used in the embodiment description will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of these drawings.

[0042] Figure 1 The overall flowchart of a model construction method based on piezoelectric sandwich beam equivalent circuit provided for the first embodiment of the application;

[0043] Figure 2 The structure diagram of the piezoelectric sandwich beam in the model construction method based on piezoelectric sandwich beam equivalent circuit provided for the first embodiment of the application;

[0044] Figure 3 The equivalent circuit structure diagram of the model construction method based on piezoelectric sandwich beam equivalent circuit provided for the first embodiment of the application;

[0045] Figure 4 The structure diagram after the SECE circuit is connected in the model construction method based on piezoelectric sandwich beam equivalent circuit provided for the first embodiment of the application;

[0046] Figure 5 The structure diagram after the SSDI circuit is connected in the model construction method based on piezoelectric sandwich beam equivalent circuit provided for the first embodiment of the application;

[0047] Figure 6 The comparison diagram of the energy effect of connecting the SECE circuit in the model construction method based on piezoelectric sandwich beam equivalent circuit provided for the second embodiment of the application;

[0048] Figure 7 The comparison diagram of the vibration reduction effect after connecting the SSDI circuit in the model construction method based on piezoelectric sandwich beam equivalent circuit provided for the first embodiment of the application. DETAILED DESCRIPTION

[0049] In order to make the above objectives, characteristics and advantages of the present application more obvious and easy to understand, the specific embodiments of the present application are described in detail below with reference to the drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor should belong to the protection scope of the present application.

[0050] Embodiment 1, refer to Figures 1-5 For an embodiment of the present application, a model construction method based on the equivalent circuit of the piezoelectric sandwich beam is provided, comprising:

[0051] S1: arranging a piezoelectric sheet on the piezoelectric sandwich beam to construct a dynamic model of the sandwich beam.

[0052] Further, the piezoelectric sandwich beam is composed of upper and lower substrates and a middle hourglass core layer. The piezoelectric sheet is placed on the upper substrate of the sandwich beam, and the piezoelectric sheet is connected with the substrate through an adhesive layer, as shown in Figure 2 .

[0053] According to the geometric deformation of the structure, the strain-displacement relationship, stress-strain relationship, total kinetic energy, total potential energy and electric energy stored in the piezoelectric layer of the structure are obtained. The motion control equation of the piezoelectric sandwich beam is derived by applying Hamilton's principle, and the dynamic equation of the sandwich beam is expressed as:

[0054] Wherein, C represents the Rayleigh damping matrix, M represents the mass matrix, K represents the stiffness matrix, F represents the external excitation force, X(t) represents the displacement of the time window t, represents the speed of the time window t, represents the acceleration of the time window t. (M, C, K are derived by Hamilton's principle)

[0055] S2: According to the assumed modal of the piezoelectric sheet and the cantilever beam, the equivalent circuit structure of the piezoelectric sandwich beam is built.

[0056] Wherein, the piezoelectric sheet generates voltage through displacement; in the equivalent, the generated voltage, inductance, resistance, capacitance and the primary coil of the transformer are connected in series in turn. The assumed modal of the cantilever beam includes that the voltage generated by the piezoelectric sheet is divided into six modal components (in other optional embodiments, other number of modal components can be selected for decomposition): three transverse displacement modes and three angle modes; each mode is equivalent through the circuit structure of the piezoelectric sheet. After the internal capacitance of the piezoelectric sheet and the load are connected in parallel and form a loop with the power supply, the six modes equivalent obtained are connected in parallel through the secondary coil of the transformer at both ends of the power supply, to form a circuit model.

[0057] It should be noted that, as Figure 3L1, L2, L3: Each inductor (L) is in series with a resistor (R) to form a filter module. Inductors are used in conjunction with resistors to suppress high-frequency signals or smooth current fluctuations. R1, R2, R3: Each resistor is in series with an inductor to limit current changes in the circuit and reduce surges. C1, C2, C3: Each capacitor is connected in parallel after the resistor, working together with the resistor to form an RC low-pass filter to suppress high-frequency noise. S and P are the secondary coil and primary coil (forming a transformer structure) respectively. L4, L5, L6: Also as inductance units, the functions are consistent with the previous ones, used to adjust the current waveform. R4, R5, R6: In series with the inductor, the function is to limit and adjust the current. C4, C5, C6: Capacitors and resistors form a low-pass filter to help remove high-frequency noise. Load section: Usually used to transmit the output signal of the circuit to external devices or load modules. It can be a motor, LED lamp or other types of load. The entire circuit is powered by a power supply, which drives various inductors, resistors, capacitors and loads. The positive terminal of the power supply is connected to each filter unit, while the load section is connected to the ground terminal of the power supply.

[0058] S3: Build the electromechanical coupling model of the piezoelectric sandwich beam using the equivalent circuit structure and the dynamic model.

[0059] The electromechanical coupling model includes constructing the electromechanical coupling control equation based on kinetic energy, potential energy and piezoelectric energy using Lagrange's equation, coupling the piezoelectric sheet and the beam structure through the voltage term v(t), and deriving the electromechanical coupling equation:

[0060]

[0061] where ζ a and ζ c represent the electromechanical coupling coefficients obtained by constructing the electromechanical coupling control equation using Lagrange's equation; v(t) represents the voltage generated by the piezoelectric sheet, which is the sum of the voltages of the six modes; C p represents the internal capacitance of the piezoelectric layer; represents the rate of voltage change; T represents the transpose symbol of the matrix; f represents the external excitation force, which is the sum of the external excitation forces in the six modes; R represents the load resistance.

[0062] S4: According to the electromechanical coupling equation in the electromechanical coupling model, the electromechanical coupling of the piezoelectric sandwich beam is carried out to obtain the equivalent circuit model.

[0063] Establishment of equivalent circuit model: Based on the dynamic equation of the piezoelectric sandwich beam, the equivalent circuit model is established using the electrical-mechanical analogy principle. The equivalent circuit model considers the mechanical impedance, electrical impedance and electromechanical coupling effect of the piezoelectric sandwich beam.

[0064] As can be seen, the above equations include a voltage term v(t) compared to the dynamic equations in the first step. This is the effect of coupling, which couples the piezoelectric element to the beam structure. Then, to construct the subsequent equivalent circuit model, the initially obtained equations need to be converted into modal equations. Because the M, C, and K matrices in the initially obtained equations are not diagonal matrices, it is impossible to construct an equivalent circuit model. Therefore, the purpose of our modal transformation is to convert the M, C, and K matrices into diagonal matrices. For example, initially M = [1, 2, 3; 1, 2, 3; 1, 2, 3], after transformation, M = [1, 0, 0; 0, 1, 0; 0, 0, 1]. Only M, C, and K in this form can construct an equivalent circuit model.

[0065] Specifically, by equating M to voltage, C to resistance, and K to capacitance, and performing mode transformation on the electrical coupling equations, the coupling equations of the equivalent circuit model are obtained:

[0066]

[0067] Where, ξ n and ω n ε represents the modal damping ratio and the natural frequency under open-circuit conditions of the nth vibration mode; n f represents the modal electromechanical coupling coefficient; n Let represent the external excitation force, and q(t) represent the modal vibration displacement after conversion. This represents the modal vibration displacement velocity after conversion. This represents the modal vibration acceleration after conversion; N represents the modal order, with a value of 6.

[0068] Figure 3 An established equivalent circuit model of a piezoelectric biatomic sandwich beam connected to a simple load resistor is shown. This circuit model can be easily implemented in any circuit simulation software, such as SIMetrix. The load resistor can be replaced with any other complex shunt circuit, thus facilitating a comprehensive evaluation of the energy harvesting performance of the piezoelectric biatomic sandwich beam.

[0069] S5: Connect the SECE circuit and SSDI circuit as loads to the equivalent circuit model to achieve piezoelectric energy harvesting and vibration reduction effects.

[0070] In the equivalent circuit model, the load is replaced with a SECE circuit to achieve an energy-saving effect, such as... Figure 4 The vibration reduction effect can be achieved by replacing it with an SSDI circuit, such as... Figure 5 .

[0071] It should be noted that the equivalent circuit model is established based on the dynamic characteristics of the piezoelectric sandwich beam, and is used to simulate and analyze the energy conversion and vibration characteristics of the system. The SECE energy harvesting enhancement circuit is connected to the piezoelectric layer, and improves the energy harvesting efficiency through synchronous charge extraction technology. The SSDI vibration damping circuit is connected to the piezoelectric layer, and suppresses structural vibration through synchronous switching control and inductive circuitry.

[0072] On the other hand, this embodiment also provides a model building system based on the equivalent circuit of a piezoelectric sandwich beam, which includes:

[0073] The dynamic analysis unit arranges piezoelectric sheets on the piezoelectric sandwich beam to construct a dynamic model of the sandwich beam.

[0074] The construction unit builds an equivalent circuit structure for the piezoelectric sandwich beam based on the assumed modes of the piezoelectric sheet and the cantilever beam; and uses the equivalent circuit structure and the dynamic model to build an electromechanical coupling model of the piezoelectric sandwich beam.

[0075] The coupling unit performs electromechanical coupling of the piezoelectric sandwich beam according to the electromechanical coupling equation in the electromechanical coupling model to obtain an equivalent circuit model; the SECE circuit and SSDI circuit are connected as loads to the equivalent circuit model to achieve piezoelectric energy harvesting and vibration reduction effects.

[0076] If the above functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0077] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0078] More specific examples of computer-readable media (a non-exhaustive list) include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media 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 medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0079] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0080] Example 2, refer to Figure 6 and Figure 7 As an embodiment of the present invention, a model construction method based on the equivalent circuit of a piezoelectric sandwich beam is provided. In order to verify the beneficial effects of the present invention, scientific demonstration is carried out through economic benefit calculation and simulation experiments.

[0081] To analyze the energy harvesting performance of RS and SECE circuits Figure 6A comparison of the voltage outputs of the two circuits shows that as the resistance increases, the voltage increase in the RS circuit becomes less pronounced, exhibiting a tendency to saturate. Compared to the RS circuit, the SECE circuit's voltage output can rise to a higher level, meaning it has higher efficiency even under heavy load conditions. Because the SECE circuit is load-independent, it is particularly suitable for practical applications with time-varying loads.

[0082] Figure 7 The theoretical results and simulation results from LTspiceTM were compared, and the displacement amplitude-frequency response curves of the open-circuit and SSDI circuits were obtained, respectively. In the near-resonant frequency region, SSDI exhibits a strong vibration reduction effect. Although the vibration reduction effect weakens somewhat in the non-resonant region, the vibration reduction effect of the SSDI circuit is still far superior to that of the open-circuit circuit, and no instability issues were observed.

[0083] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A model construction method based on the equivalent circuit of a piezoelectric sandwich beam, characterized in that, include: Piezoelectric sheets are arranged on the piezoelectric sandwich beam to construct a dynamic model of the sandwich beam; Based on the assumed modes of the piezoelectric sheet and the cantilever sandwich beam, the equivalent circuit structure of the piezoelectric sandwich beam is constructed. Using the equivalent circuit structure and the dynamic model, an electromechanical coupling model of the piezoelectric sandwich beam is constructed. Based on the electromechanical coupling equations in the electromechanical coupling model, the electromechanical coupling of the piezoelectric sandwich beam is performed to obtain the equivalent circuit model; By connecting the SECE circuit and SSDI circuit as loads into the equivalent circuit model, piezoelectric energy harvesting and vibration reduction effects can be achieved. The piezoelectric element generates voltage through displacement; in an equivalent configuration, the generated voltage, inductance, resistance, capacitance, and the primary coil of the transformer are connected in series. The hypothetical modes of the cantilever sandwich beam include six modal components, which divide the voltage generated by the piezoelectric element into three lateral displacement modes and three rotational modes; each mode is equivalent to the circuit structure of the piezoelectric element. The equivalent circuit structure includes a circuit model in which the internal capacitor and load of the piezoelectric element are connected in parallel and a circuit is formed with the power supply. The six equivalent modes are then connected in parallel with the power supply through the secondary coil of the transformer. The electromechanical coupling model includes, based on kinetic energy, potential energy, and piezoelectric energy, constructing electromechanical coupling control equations using the Lagrange equations, and using voltage terms... By coupling the piezoelectric element and the beam structure, the electromechanical coupling equation can be derived: ； ； in, and This represents the electromechanical coupling coefficient obtained by constructing the electromechanical coupling control equations using the Lagrange equations. This represents the voltage generated by the piezoelectric element, which is the sum of the voltages of the six modes; This indicates the internal capacitance of the piezoelectric layer; Represents the voltage change rate; T represents the transpose of the matrix; f represents the external excitation force, which is the sum of the external excitation forces under the six modes; R represents the load resistance; This represents the displacement within the time window t. The velocity represents the velocity within the time window t. The acceleration represents the acceleration within the time window t; The electromechanical coupling includes equivalently representing M as voltage, C as resistance, and K as capacitance, and performing mode transformation on the electrical coupling equation to obtain the coupling equation of the equivalent circuit model: ； ； in, and The modal damping ratio and natural frequency under open-circuit conditions represent the nth order vibration mode; Indicates the modal electromechanical coupling coefficient; Indicates external incentive force. This represents the modal vibration displacement after conversion. This represents the modal vibration displacement velocity after conversion. This represents the modal vibration acceleration after conversion; N represents the modal order, with a value of 6.

2. The model construction method based on the equivalent circuit of a piezoelectric sandwich beam as described in claim 1, characterized in that: The piezoelectric sandwich beam consists of upper and lower substrates and an hourglass core layer in the middle. The piezoelectric sheet is placed on the upper substrate of the sandwich beam, and the piezoelectric sheet is connected to the substrate through an adhesive layer.

3. The model construction method based on the equivalent circuit of a piezoelectric sandwich beam as described in claim 2, characterized in that: The dynamic model includes deriving the motion control equations of the piezoelectric sandwich beam based on the strain-displacement relationship, stress-strain relationship, total kinetic energy, total potential energy, and electrical energy stored in the piezoelectric layer, using Hamilton's principle. The resulting dynamic equations of the sandwich beam are expressed as follows: ; in, Represents the Rayleigh damping matrix. Represents the mass matrix, Represents the stiffness matrix. It represents external incentive force.

4. The model construction method based on the equivalent circuit of a piezoelectric sandwich beam as described in claim 3, characterized in that: In the equivalent circuit model, the load is replaced with a SECE circuit to achieve an energy-saving effect, and with an SSDI circuit to achieve a vibration reduction effect.

5. A model construction system based on the equivalent circuit of a piezoelectric sandwich beam using the method described in any one of claims 1-4, characterized in that: The dynamic analysis unit arranges piezoelectric sheets on the piezoelectric sandwich beam to construct a dynamic model of the sandwich beam; The construction unit builds an equivalent circuit structure for the piezoelectric sandwich beam based on the assumed modes of the piezoelectric sheet and the cantilever sandwich beam; and uses the equivalent circuit structure and the dynamic model to build an electromechanical coupling model for the piezoelectric sandwich beam. The coupling unit performs electromechanical coupling of the piezoelectric sandwich beam according to the electromechanical coupling equation in the electromechanical coupling model to obtain an equivalent circuit model; the SECE circuit and SSDI circuit are connected as loads to the equivalent circuit model to achieve piezoelectric energy harvesting and vibration reduction effects.

6. A computer device, comprising: Memory and processor; The memory stores a computer program, characterized in that: when the processor executes the computer program, it implements the steps of the method as described in any one of claims 1-4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1-4.

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