High-power-density broadband vibration energy taking method
By optimizing the output of electrostatic components through electret-piezoelectric coupling array and variable cross-section beam design, the problems of low vibration energy harvesting power density and narrow frequency domain in low-frequency environments are solved, achieving efficient wide-frequency vibration energy harvesting with strong adaptability.
Patent Information
- Application Number
- CN202610206852.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-02-12
- Publication Date
- 2026-05-15
AI Technical Summary
Existing vibration energy harvesting methods have low power density in low-frequency environments and narrow operating frequency domains. They do not fully consider the synergistic and complementary optimization between coupled structures, making it difficult to meet the continuous power supply needs of smart devices.
A low-frequency vibration energy harvesting array with electret-piezoelectric coupling was adopted. The operating frequency domain of vibration energy harvesting was broadened by the design of a variable cross-section coupling beam. The output power of the electrostatic components was optimized by arranging electrets with interval polarity. A distributed parameter finite element simulation model of multi-physics electromechanical coupling was built for optimization design.
It achieves high power density and wide-frequency vibration energy harvesting. The piezoelectric component outputs high power density during resonance and the electrostatic component outputs stably during non-resonance, significantly widening the operating frequency domain and enhancing adaptability to low-frequency random excitation in the natural environment.
Smart Images
Figure CN122052593A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of vibration energy harvesting technology and relates to a high power density broadband vibration energy harvesting method. Background Technology
[0002] With the rapid development of smart grids, the energy harvesting devices of transmission lines that power smart devices need to be optimized to meet the requirements of durability, stability, and efficiency. Among them, the integrated and complementary coupling energy harvesting method shows significant advantages in terms of strong adaptability. However, the working mechanism often changes after integration, and the optimized design of the output capacity of the new coupling structure has gradually become a research focus.
[0003] Piezoelectric and electrostatic vibration energy harvesting components come in various forms, which is beneficial for miniaturization and non-contact design. Furthermore, the wide range of vibration energy sources has made them a key focus of research in low-power, small-space integrated energy harvesting. The coupling of various energy harvesting methods with distinct characteristics with different energy harvesting components to complement each other's advantages and disadvantages has become a research hotspot. However, the vibration frequencies in natural environments are highly random, resulting in relatively low power densities for vibration energy harvesting methods. Many existing coupling methods are simply combinations, failing to fully consider the synergistic and complementary optimization between coupling structures. Improvements and designs for practical applications, such as increasing power density in low-frequency environments and broadening the vibration operating frequency domain, are also relatively incomplete.
[0004] Some studies have designed energy harvesting methods using electromagnetic-triboelectric coupling, complementing the advantages of both at high and low frequencies to achieve a wideband design that broadens the operating frequency range of vibration energy harvesting. However, the contact separation process of the triboelectric components inevitably leads to structural wear and motion obstruction. Other studies have proposed vibration energy harvesting methods using piezoelectric and electrostatic coupling, optimizing the resonant output characteristics of the piezoelectric components and demonstrating the potential for coupling applications; however, the power density still needs optimization. Considering the changes in structure and operating mechanism after coupling, it is necessary to conduct in-depth analysis of the new structure to obtain applicable optimization methods. Therefore, further optimizing the design of strongly coupled integrated vibration energy harvesting structures to achieve high power density and wideband design is an urgent technical problem to be solved. Summary of the Invention
[0005] In view of this, the purpose of this invention is to provide a high power density broadband vibration energy harvesting method. To achieve the above objectives, the present invention provides the following technical solution: A high power density broadband vibration energy harvesting method includes the following steps: S1: Construct an electret-piezoelectric coupled low-frequency vibration energy harvesting array; S2: The coupling beam that vibrates in coordination with the modulation array, which broadens the working frequency domain of vibration energy harvesting; S3: Using electrets that permanently retain polarized charges as electrostatic field sources, and based on the near-field assumption, optimizing the output power of electrostatic components by arranging electrets with alternating polarities.
[0006] Furthermore, in step S2, the coupling beams in the variable cross-section fine-tuning array are made to have certain differences in their natural frequencies. Then, taking advantage of the relatively large deformation of the beams near the resonance frequency, an array design is carried out to superimpose the working frequency domains of each beam, thereby broadening the resonant and non-resonant working frequency domains.
[0007] Furthermore, the coupled beams in the modulation array described in step S2, which vibrate in tandem, broaden the operating frequency domain for vibration energy harvesting, including: Arbitrary cross-section beam x Equivalent moment of inertia at the location I total The result obtained by integration using the equivalent stiffness method is:
[0008] In the formula, b ( x () is a variable cross-section beam with arbitrary length direction x The width of the cross section at that location, h This is the thickness of the cross section; b ( x ) by fixed end width b 1. Width of the active end b 2, and the length of the elastic section of the cantilever beam. L The equivalent mass of the composite variable cross-section beam is expressed using the equal area method and obtained using the distributed kinetic energy formula. m eff :
[0009] In the formula, ρ eff The equivalent density of the composite beam; A ( x )for x Cross-sectional area; For the velocity distribution of the beam, v max The maximum speed of the beam, n ( x From the modal functions of the beam Normalization yields:
[0010] For low-frequency conditions, the first-order mode shape function is applicable. 1( x ); Substituting the stiffness and equivalent mass of the coupled variable cross-section beam into the first-order characteristic frequency formula for a single-degree-of-freedom linear elastic small deformation system, the natural frequencies are obtained. expression:
[0011] When the thickness and material are determined E eff It is considered a constant.
[0012] Furthermore, in step S3, the upper surface charge and potential of the unipolar electret film are 0, the lower surface has a uniform surface charge, and the charge density of adjacent electret surfaces is... Equal polarity and opposite polarity; output parameters of electrostatic components, including short-circuit current. I sc and open circuit voltage U oc It satisfies the formula:
[0013] The coupled beam resonates at its natural frequency. The system exhibits periodic symmetrical vibration, with the electrostatic component at the moving end following its regular displacement; where, The inter-electrode capacitance is constant once the structure is determined. S e The area of the electrode plate is the key factor; increasing the area helps to increase the total amount of induced charge. When the vibration of the coupled beam is normalized to the maximum value z Directional displacement function, let x = L ; This represents the charge density on the lower surface of a positively charged electret thin film. It is a negative polarity thin film; d The distance between the electret and the electrode plate. h e Electret thickness; and The dielectric constants of electret and air; From the above, we can see that the electrical output parameters of the paired plates are positively correlated with the difference in induced charge between the plates and the amplitude of the change in induced charge on the plates. If the frequency remains constant, but the amplitude of the cantilever beam and the relative displacement of the plates increase, the amplitude of the change in induced charge on the plates will increase, which will help improve the output capability. If only electret films of the same polarity are used, the difference in induced charge between the two plates is extremely small, and the plate potential does not meet the conditions for charge to flow in the circuit.
[0014] Furthermore, in step S3, an electret assembly is constructed using alternating positive and negative polarities to increase the difference in induced charge between paired copper electrode plates and the amplitude of induced charge changes during movement, thereby optimizing the output electrical performance of the electret electrostatic assembly.
[0015] Furthermore, it also includes building a distributed parameter finite element simulation model of multi-physics electromechanical coupling and completing the optimized design of the variable cross-section coupled beam.
[0016] Furthermore, in the finite element simulation model, the boundary conditions are that the left base of the cantilever beam is fixed and the potential of the inner surface of the upper and lower piezoelectric layers is 0; the model is constrained to be a linear elastic small deformation model under low frequency conditions, and the excitation acceleration of the base is set to 0.4g.
[0017] The beneficial effects of this invention are as follows: This invention can more efficiently harvest low-frequency environmental vibration energy, and its operating frequency range and power density are more considerable compared to other beam-type low-frequency vibration energy harvesting methods; the arrayed and stacked variable cross-section coupling beams significantly broaden the resonant operating frequency domain, while also broadening the non-resonant frequency domain to a certain extent; the optimized piezoelectric power density is considerable during resonance, while the optimized electrostatic component provides stable voltage and higher output power during non-resonance, and the complementary output characteristics of the two further broaden the operating frequency domain; the output power density of the electret electrostatic component with optimized spacing polarity arrangement under the near-field assumption is significantly improved, and the theoretical optimization model is correct and feasible; this invention provides a high-power-density broadband vibration energy harvesting approach.
[0018] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description
[0019] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1 Design block diagram for high power density broadband vibration energy harvesting method; Figure 2 This is a schematic diagram of the optimization of a variable cross-section beam; Figure 3 An optimization model for the induced charge and polarity arrangement of the electret plates in a coupled structure; Figure 4 The model is a simulation and optimization model of the coupled structure, where (a) is the piezoelectric component and (b) is the electrostatic component; Figure 5 The simulation results are for the open-circuit voltage and short-circuit current of the structural electrostatic components. Figure 6 Simulation calculations and optimization results of induced charge in structural electrostatic components; Figure 7The coupled structure output optimization test includes (a) variable cross-section frequency modulation test, (b) polarity arrangement optimized output power test, and (c) applicability of optimization method under different spacing conditions. Detailed Implementation
[0020] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.
[0021] It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Therefore, the drawings only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.
[0022] In the following description, numerous details are explored to provide a more thorough explanation of embodiments of the invention. However, it will be apparent to those skilled in the art that embodiments of the invention may be practiced without these specific details. In other embodiments, well-known structures and devices are shown in block diagram form rather than in detail to avoid obscuring embodiments of the invention.
[0023] Example 1: This invention provides a high-power-density, wide-band vibration energy harvesting method based on a complementary coupling low-frequency vibration energy harvesting array of electret (electrostatic) and piezoelectric components. The method optimizes the synergistic motion and vibration of the piezoelectric and electret electrostatic components in the coupling structure. The arrayed, superimposed variable-section coupling beam design broadens the overall resonant frequency domain, while achieving a higher overall power density after optimization. Furthermore, the near-field assumption-based method for optimizing the polarity arrangement of electret components enables the electrostatic components to achieve a more considerable power density and better complements the output when the voltage and power of the piezoelectric components drop sharply in the non-resonant state, further broadening the operating frequency domain and enhancing adaptability to low-frequency random excitation in natural environments.
[0024] Specifically, this invention addresses the issue that many existing coupling designs are merely simple combinations, failing to fully consider the synergistic complementarity between coupling structures and the optimization required for practical application environments. This method designs a coupling energy harvesting structure with coordinated motion and optimization methods, and optimizes the component power density and operating frequency domain for low-frequency vibration energy harvesting. To address the problem of the narrow operating frequency domain of piezoelectric components and the randomness of low-frequency vibration excitation in natural environments, this method broadens the resonant frequency domain and the overall operating frequency domain through the design of arrayed superimposed variable cross-section coupling beams. Simultaneously, it employs electret electrostatic components to complement the output capability in non-resonant states, further broadening the operating frequency domain and enhancing adaptability to low-frequency random excitation in natural environments. To address the issues of low power density and unstable field source of electrostatic components, this method uses electrets that persistently maintain polarization charge as the electrostatic field source. Furthermore, based on the near-field assumption, it optimizes the output power of the electrostatic components by arranging electrets with alternating polarities, resulting in a higher overall array power density.
[0025] Efficient and stable vibration energy harvesting methods are beneficial for meeting the continuous power supply requirements of transmission line monitoring devices. However, the adaptability of existing methods to the energy of highly random vibration environments still needs improvement. This patent proposes a high-power-density broadband vibration energy harvesting method based on an electret-piezoelectric coupling structure. The overall design block diagram of the high-power-density broadband vibration energy harvesting method is shown below. Figure 1 As shown.
[0026] This design, based on the vibration modulation of a variable cross-section coupled beam array and an electret electrostatic component model under the near-field assumption, yields a wide-frequency domain design and power density optimization method for low-frequency vibration energy harvesting. By constructing an electret-piezoelectric multiphysics coupling simulation model to calculate key parameters, the design optimizes the component's operating frequency domain and power density output.
[0027] First, the coupled beams vibrating in the modulation array are used to broaden the operating frequency domain for vibration energy harvesting. Besides increasing the mass to lower the natural frequency, the design of a piezoelectric cantilever beam with a variable cross-section can affect the beam's natural frequency and piezoelectric output. Furthermore, even with a slight deviation from the resonant frequency during excitation, the beam will still exhibit relatively large deformation, such as... Figure 2 As shown.
[0028] Assume the beam is only for z A single-degree-of-freedom system that vibrates in a specific direction, where the piezoelectric layer and the metal layer are tightly integrated rather than bearing load independently. The beam is composed of a linearly elastic material with a uniform distribution, and even in the resonant state, it remains constrained by small linear elastic deformations, with the deformation curve showing little difference from the initial state. Based on these assumptions, arbitrary cross-section beams... x Equivalent moment of inertia at the location I total It can be obtained by integration using the equivalent stiffness method:
[0029] In the formula, b( x () is a variable cross-section beam with arbitrary length direction x The width of the cross section at that location, h The thickness of the cross section is given. b ( x ) by fixed end width b 1. Width of the active end b 2, and the length of the elastic section of the cantilever beam. L Represented by the equal area method. When the thickness and material are determined, E eff It can be considered a constant. Due to the homogeneity and tight bonding of the material, the equivalent mass of the composite variable cross-section beam can be obtained using the distributed kinetic energy formula. m eff As shown in the formula.
[0030]
[0031] In the formula, ρ eff The equivalent density of the composite beam; A ( x )for x Cross-sectional area; For the velocity distribution of the beam, v max The maximum speed of the beam, n ( x From the modal functions of the beam Normalization yields:
[0032] This structural design is for low-frequency conditions and applies a first-order mode shape function. 1( x Substituting the stiffness and equivalent mass of the coupled variable cross-section beam into the first-order characteristic frequency formula for a single-degree-of-freedom linear elastic small deformation system, the natural frequencies of the designed structure are obtained. expression:
[0033] Both equivalent mass and cross-sectional width changes will affect f This has an impact. Using higher density or larger area mass blocks can effectively reduce the natural frequency of cantilever beams, while the elastic segment of a composite beam with variable cross-section design is used to fine-tune the natural frequency. Because the denominator of the formula includes a normalization function term, f and b ( xThe relationship is mainly positively correlated. Arraying causes the working frequency domains of each beam to be superimposed, while the variable cross-section design causes slight differences in the natural frequencies of each coupled beam in the energy harvesting array. Subsequently, taking advantage of the large beam deformation in the range near the resonance frequency, the variable cross-section beams are arrayed and superimposed to broaden the overall resonance frequency domain of coupled and coordinated vibration energy harvesting.
[0034] Piezoelectric components exhibit considerable output power density at resonance, but the sudden drop in open-circuit voltage at non-resonance hinders their output to the energy management circuit, resulting in a narrow operating frequency range. Coupled with a co-moving electret electrostatic component, this approach optimizes the non-resonant output capability while maintaining a high resonant power density. The energy conversion model of the electrostatic component is based on an equivalent capacitance model similar to that of a piezoelectric component. The working principle of the electrostatic component is as follows: Figure 3 As shown.
[0035] The electrostatic model is based on the near-field assumption. Under the premise that the distance between the electret and the plate is extremely small relative to the plate surface area, it mainly considers the interaction between the plate and the electret directly opposite it, and the electric field intensity in the gap is uniformly distributed and perpendicular to the plate surface. Assuming that the electret and air are linear homogeneous media with constant dielectric constant, the electric field inside the medium is uniformly distributed in the direction perpendicular to its surface, and the electric field is discontinuous on both sides of the surface.
[0036] The upper surface of the unipolar electret thin film has zero charge and potential, while the lower surface carries a uniform surface charge. The surface charge density of adjacent electret surfaces is... Equal polarity, opposite polarity. Output parameters of the electrostatic discharge (ESD) component, including short-circuit current. I sc and open circuit voltage U oc It satisfies the formula:
[0037] The coupled beam resonates at its natural frequency. The system exhibits periodic symmetrical vibration, with the electrostatic component at the moving end following its regular displacement. In the formula, The inter-electrode capacitance is constant once the structure is determined. S e The area of the electrode plate is the key factor; increasing the area helps to increase the total amount of induced charge. When the vibration of the coupled beam is normalized to the maximum value z Directional displacement function, let x = L ; This represents the charge density on the lower surface of a positively charged electret thin film. It is a negative polarity thin film; d The distance between the electret and the electrode plate. h e Electret thickness; and is the dielectric constant of electret and air.
[0038] It is evident that the electrical output parameters of the paired plates are positively correlated with the difference in induced charge between the plates and the amplitude of the change in induced charge on the plates. If the frequency remains constant, but the amplitude of the cantilever beam and the relative displacement of the plates increase, the amplitude of the change in induced charge on the plates will increase, which will help improve the output capability. Furthermore, if only electret films of the same polarity are used, the difference in induced charge between the two plates is extremely small, and the plate potential does not meet the conditions for charge flow in the circuit. Compared to the electret configuration with empty spaces of the same polarity used in other studies, the electret configuration with alternating positive and negative polarities designed in this paper increases the difference in induced charge between the paired copper electrode plates and the amplitude of the change in induced charge during movement, thereby optimizing the output electrical performance of the electret electrostatic assembly.
[0039] Example 2: This embodiment constructs a distributed parameter finite element simulation model of multiphysics electromechanical coupling to complete the optimized design of a variable cross-section coupled beam. The finite element simulation software used is COMSOL 6.2. The boundary conditions are: the left base of the cantilever beam is fixed, and the potential of the inner surfaces of the upper and lower piezoelectric layers is 0. The model is constrained to a linear elastic small deformation model under low-frequency conditions, with the base excitation acceleration set to 0.4g. The coupling model simulation is as follows: Figure 4 As shown in (a) and (b), the piezoelectric component includes a base, a cantilever beam, and a pointed mass. One end of the cantilever beam is fixed and connected to the base, while the other end is movable and connected to the pointed mass. The cross-sectional area of the cantilever beam gradually decreases from the fixed end to the movable end, exhibiting a variable cross-section design. A metal electrode plate is located at the center of the cantilever beam, and piezoelectric layers are connected in parallel on both sides of the metal electrode plate. The electrostatic component includes a copper electrode plate and an electret film. The copper electrode plate is fixedly connected to the pointed mass. The copper electrode plate and the electret film are positioned opposite each other but do not contact each other. The electret film is unipolar. Multiple electret films are arranged alternately with positive and negative polarities to form the electrostatic component.
[0040] The natural frequencies of the slender coupled beam with a large, pointed mass attached occur in the low-frequency range. The variable cross-section design causes the resonant frequency of the coupled beam to change as expected. Different cross-sectional widths in the array... b The superposition of coupled beams (1) can broaden the resonant operating range and increase the absolute output. In the initial state of the electrostatic component, the copper electrode plate and the electret film are centered and directly opposite each other, and the polarity distribution of the induced charge on the plates conforms to the theoretical model. The equivalent capacitance of the three pairs of parallel plates in the electrostatic component is calculated to be 18.76 pF using an electrostatic simulation model. The simulation results of the output parameters are as follows: Figure 5 , 6 As shown.
[0041] Simulation results show that although the alternating positive and negative polarity electret arrangement reduces the amplitude of induced charge when the electret is directly opposite the plate due to the superposition and weakening of opposing electric fields, it significantly improves the charge difference between paired plates and the amplitude of induced charge change during movement. Ultimately, the open-circuit voltage and short-circuit current of the electrostatic component increase, demonstrating the correctness of the optimization theory.
[0042] To verify the correctness of the high power density broadband vibration energy harvesting optimization theory for electret-piezoelectric coupling structures, the array output performance and optimization effect were tested, and the results are as follows: Figure 7 As shown in (a)-(c). Experimental results show that, with the fixed end width b The increase in cross-sectional width (1) of the cantilever beam leads to a gradual increase in the natural frequency of the variable cross-section cantilever beam in the coupled structure, demonstrating the correctness of the variable cross-section optimization theory. Vibration excitation within a small range near the resonant frequency of the designed coupled structure can also produce a relatively large deformation response. The natural frequencies of the four cantilever beams under variable cross-section fine-tuning are very close, with an average interval of 1.17 Hz. Forming an array allows for the superposition of the working frequency domain with larger deformations, thereby widening the overall working range, consistent with the array optimization theory. A single, unarrayed component achieves low-frequency resonance design, but its average working frequency width is only 7.22 Hz. In contrast, the arrayed piezoelectric components have an average working frequency width of 4.17 Hz compared to a single component, achieving low-frequency triggered resonance and wide-frequency optimization design.
[0043] Compared to a single-polarity electret arrangement, an alternating polarity arrangement increases the rate of change of electrostatic induced charge and the inter-electrode charge difference, thereby increasing the maximum output power density at resonance by 1.52 mW / cm². 3 This demonstrates the correctness of the optimization theory and simulation results.
[0044] Spacing refers to the distance between the electrode and the electret. Under resonant conditions, the output power is inversely proportional to the spacing. When the spacing is too large, the near-field assumption no longer applies, and the influence of each electret must be fully considered, rather than assuming that the nearest electret dominates electrostatic induction. The electric field generated by electrets of opposite polarities weakens as the electrode moves further away, becoming increasingly significant and drastically reducing the total induced charge on the electrode. Alternating polarity electret arrangements no longer offer a significant advantage. Under non-resonant conditions, when the piezoelectric component output is limited, the optimized array maintains a high output from the electrostatic component, ultimately widening the array's operating frequency domain by nearly 13Hz.
[0045] Finally, 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 present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.
Claims
1. A high power density broadband vibration energy harvesting method, characterized in that: Includes the following steps: S1: Construct an electret-piezoelectric coupled low-frequency vibration energy harvesting array; S2: The coupling beam that vibrates in coordination with the modulation array, which broadens the working frequency domain of vibration energy harvesting; S3: Using electrets that permanently retain polarized charges as electrostatic field sources, and based on the near-field assumption, optimizing the output power of electrostatic components by arranging electrets with alternating polarities.
2. The high power density broadband vibration energy harvesting method according to claim 1, characterized in that: In step S2, the coupling beams in the variable cross-section fine-tuning array are made to have certain differences in their natural frequencies. Then, the characteristic that the beams near the resonant frequency have relatively large deformations is used to perform array design, so that the working frequency domains of each beam are superimposed, thereby broadening the resonant and non-resonant working frequency domains.
3. The high power density broadband vibration energy harvesting method according to claim 2, characterized in that: The coupled beams in the modulation array described in step S2, which vibrate in tandem, broaden the operating frequency domain for vibration energy harvesting, include: Arbitrary cross-section beam x Equivalent moment of inertia at the location I total The result obtained by integration using the equivalent stiffness method is: In the formula, b ( x () is a variable cross-section beam with arbitrary length direction x The width of the cross section at that location, h This is the thickness of the cross section; b ( x ) by fixed end width b 1. Width of the active end b 2, and the length of the elastic section of the cantilever beam. L The equivalent mass of the composite variable cross-section beam is expressed using the equal area method and obtained using the distributed kinetic energy formula. m eff : In the formula, ρ eff The equivalent density of the composite beam; A ( x )for x Cross-sectional area; For the velocity distribution of the beam, v max The maximum speed of the beam, n ( x From the modal functions of the beam Normalization yields: For low-frequency conditions, the first-order mode shape function is applicable. 1( x ); Substituting the stiffness and equivalent mass of the coupled variable cross-section beam into the first-order characteristic frequency formula for a single-degree-of-freedom linear elastic small deformation system, the natural frequencies are obtained. expression: When the thickness and material are determined E eff It is considered a constant.
4. The high power density broadband vibration energy harvesting method according to claim 1, characterized in that: In step S3, the upper surface charge and potential of the unipolar electret film are 0, the lower surface has a uniform surface charge, and the surface charge density of adjacent electrets is... Equal polarity and opposite polarity; output parameters of electrostatic components, including short-circuit current. I sc and open circuit voltage U oc It satisfies the formula: The coupled beam resonates at its natural frequency. The system exhibits periodic symmetrical vibration, with the electrostatic component at the moving end following its regular displacement; where, The inter-electrode capacitance is constant once the structure is determined. S e The area of the electrode plate is the key factor; increasing the area helps to increase the total amount of induced charge. When the vibration of the coupled beam is normalized to the maximum value z Directional displacement function, let x = L ; This represents the charge density on the lower surface of a positively charged electret thin film. It is a negative polarity thin film; d The distance between the electret and the electrode plate. h e Electret thickness; and The dielectric constants of electret and air; From the above, we can see that the electrical output parameters of the paired plates are positively correlated with the difference in induced charge between the plates and the amplitude of the change in induced charge on the plates. If the frequency remains constant, but the amplitude of the cantilever beam and the relative displacement of the plates increase, the amplitude of the change in induced charge on the plates will increase, which will help improve the output capability. If only electret films of the same polarity are used, the difference in induced charge between the two plates is extremely small, and the plate potential does not meet the conditions for charge to flow in the circuit.
5. The high power density broadband vibration energy harvesting method according to claim 1, characterized in that: In step S3, an electret assembly is constructed using alternating positive and negative polarities to increase the difference in induced charge between paired copper electrode plates and the amplitude of induced charge changes during movement, thereby optimizing the output electrical performance of the electret electrostatic assembly.
6. The high power density broadband vibration energy harvesting method according to claim 1, characterized in that: It also includes building a distributed parameter finite element simulation model of multiphysics electromechanical coupling and completing the optimized design of variable cross-section coupled beams.
7. The high power density broadband vibration energy harvesting method according to claim 6, characterized in that: In the finite element simulation model, the boundary conditions are that the left base of the cantilever beam is fixed and the potential of the inner surface of the upper and lower piezoelectric layers is 0; the model is constrained to be a linear elastic small deformation model under low frequency conditions, and the excitation acceleration of the base is set to 0.4g.