Spherical vortex-induced vibration piezoelectric energy collection device and method enhanced through base excitation

Abstract

The invention relates to a sphere vortex-induced vibration piezoelectric energy collection device and method enhanced through base excitation, and belongs to the field of energy collection. The elastic supporting sphere is used for converting wind energy into vibration energy through vortex-induced vibration, meanwhile, the piezoelectric beam receives vibration excitation of the base through the fixed end of the piezoelectric beam, the vibration energy of the base is transmitted to the sphere part, and the vortex-induced vibration effect is enhanced. And vibration energy is converted into electric energy through the piezoelectric beams, so that the output performance and the multidirectional adaptability of the collector are improved. The effective working flow speed range is widened through base excitation, and the effective working flow speed range is expanded to 2.2-7.2 m / s from 2.2-5.4 m / s when only VIV is conducted. Under the optimal frequency matching conditions (the wind speed is 4.47 m / s, fb is equal to 14.3 Hz, and fsp / fp is equal to 1.03), the maximum output voltage reaches 69.53 V, the maximum output voltage is improved by 41.62 V compared with vortex-induced vibration (VIV) only, and the maximum output voltage is improved by 61.92 V compared with base excitation only.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of energy harvesting, and particularly relates to a base excitation enhanced spherical vortex-induced vibration piezoelectric energy harvesting device and method, which is particularly suitable for powering sensor nodes in structural health monitoring. BACKGROUND

[0002] Structural health monitoring (SHM) is crucial for the maintenance of civil engineering infrastructure, enabling rapid identification of structural changes, preventing potential damage, improving safety and reliability, and reducing maintenance costs. Sensor networks (WSNs) as the core tool of SHM, by deploying sensor nodes in key structures, achieve continuous and remote monitoring of physical and environmental conditions, providing timely data support for maintenance and repair. However, WSNs face significant power supply problems in practical applications, with most nodes relying on limited-life batteries, and replacing batteries in remote, dangerous or embedded environments is often impractical and unsafe, which limits the widespread application of WSNs in SHM.

[0003] There is abundant mechanical energy on civil engineering structures (such as bridges and overpasses), including wind energy and vibration energy. In order to utilize these energies, various energy conversion mechanisms have been developed, such as piezoelectric, electromagnetic and triboelectric methods. Among them, piezoelectric energy harvesters stand out due to their simple structural design and good compatibility with micro-electro-mechanical systems (MEMS), making them particularly suitable for SHM applications.

[0004] However, traditional vortex-induced vibration energy harvesters have some limitations, such as a narrow effective working range, a weak vibration response of the energy harvester due to small vortex-induced vibration amplitude at low flow rates, and an inability to efficiently capture energy at high frequencies due to structural and material inherent frequency limitations. In addition, the structure is usually designed for single wind direction energy collection, limiting its ability to effectively capture multi-directional vibration energy. Furthermore, traditional rectangular cantilever beam-mass structures have low energy harvesting efficiency, narrow bandwidth, one-way collection, and low output voltage power. SUMMARY

[0005] The present application provides a base excitation enhanced spherical vortex-induced vibration piezoelectric energy harvesting method and device, which converts wind energy into vibration energy through vortex-induced vibration by using an elastic support sphere, while the piezoelectric beam receives base vibration excitation from its fixed end and transmits base vibration energy to the sphere part, enhancing the vortex-induced vibration effect. The vibration energy is converted into electrical energy by the piezoelectric beam, thereby improving the output performance and multi-directional adaptability of the harvester. To solve the technical problems of low energy harvesting efficiency, narrow effective working range, narrow bandwidth, one-way collection, and low output voltage power of the energy harvester in the prior art, low energy harvesting efficiency outside the resonance region, and inability to effectively capture multi-directional and varying vibration energy.

[0006] According to the first aspect of the present application, a base excitation enhanced spherical vortex-induced vibration piezoelectric energy harvesting device is provided, characterized in that it comprises an elastic support sphere, a spring, a horizontal support frame, an elastic piezoelectric beam, a vertical support frame and a rotating base; the elastic support sphere is connected to one end of the horizontal support frame and one end of the elastic piezoelectric beam through the spring, the other end of the horizontal support frame is connected to the upper end of the vertical support frame, the other end of the elastic piezoelectric beam is connected to the vertical support frame, and the lower end of the vertical support frame is movably connected to the rotating base.

[0007] Preferably, the elastic piezoelectric beam comprises a metal base beam and a piezoelectric layer, and the piezoelectric layer is located on the metal base beam.

[0008] Preferably, the metal base beam is an aluminum layer.

[0009] Preferably, the diameter of the elastic support sphere is 50mm-80mm, the stiffness of the spring is 6N / m-30N / m, and the length of the elastic piezoelectric beam is 80cm-150cm.

[0010] According to another aspect of the present application, a method for energy harvesting using a spherical vortex-induced vibration piezoelectric energy harvesting device is provided, which utilizes an elastic support sphere to convert wind energy into vibration energy through vortex-induced vibration; at the same time, an elastic piezoelectric beam receives vibration excitation from its fixed end and transmits the vibration excitation to the elastic support sphere to enhance the vortex-induced vibration of the elastic support sphere; the base excitation enhanced vortex-induced vibration is transmitted to the elastic piezoelectric beam, and the elastic piezoelectric beam is used to convert the vibration energy into electrical energy.

[0011] Preferably, the vortex-induced vibration frequency f s of the elastic support sphere is 0.8-1.3 times the overall natural frequency f n of the spherical vortex-induced vibration piezoelectric energy harvesting device.

[0012] Preferably, the base excitation frequency f b transmitted by the rotating base is 1.000-1.010 times the overall natural frequency f n of the spherical vortex-induced vibration piezoelectric energy harvesting device.

[0013] Preferably, the natural frequency f sp of the elastic support sphere is 0.56-1.28 times the natural frequency f p of the elastic piezoelectric beam.

[0014] Preferably, the size of the converted electrical energy is calculated by a set of electromechanical coupling equations, the set of electromechanical coupling equations comprising a sphere vortex-induced vibration dynamics equation, a wake oscillator equation, a piezoelectric beam displacement discrete equation, a piezoelectric beam dynamics equation, and a piezoelectric beam electrical equation.

[0015] The sphere vortex-induced vibration dynamics equation is:

[0016]

[0017] The wake oscillator equation is:

[0018]

[0019] The piezoelectric beam displacement discrete equation is:

[0020]

[0021] The piezoelectric beam dynamics equation is:

[0022]

[0023] The piezoelectric beam electrical equation is:

[0024]

[0025] wherein w s (t), respectively represent the displacement, velocity and acceleration of the sphere, k1 and k2 are the stiffness of the spring connected with the horizontal support frame and the spring connected with the elastic piezoelectric beam respectively, D is the diameter of the sphere, U is the wind speed, L b and L p are the length of the elastic piezoelectric beam and the piezoelectric layer respectively, m s and c s are the equivalent mass and structural damping of the overall structure of the sphere and the spring respectively, C L represents the steady average lift coefficient, C D represents the steady average drag coefficient, p air represents the density of air, q(t) represents the fluid-structure coupling term, and respectively represent the first and second order derivatives of q(t) with respect to time t; A represents a constant of the Van der Pol wake oscillator model, A = 23; l is a constant describing the vortex street wave, l = 0.1; w s represents the vortex shedding frequency, Z(t) represents the base excitation; w(x, t) represents the displacement of the piezoelectric beam at a point with a distance of x from the fixed end at time t, r i (t) is a mode vector, is the vibration mode amplitude of the piezoelectric beam, and ξ represents the mechanical damping ratio of the structure, wi represents the i-th order vibration frequency; θ i represents the i-th order force-electric coupling coefficient, V(t) represents the output voltage; W b and W p are the width of the elastic piezoelectric beam and the piezoelectric layer, respectively, t b and t p are the thickness of the elastic piezoelectric beam and the piezoelectric layer, respectively, p b and p p are the density of the elastic piezoelectric beam and the piezoelectric layer, respectively; C p represents the piezoelectric sheet capacitance, and R represents the load resistance;

[0026] To solve the highly coupled nonlinear differential equation system formula (1)-(5), the Runge-Kutta method is used for numerical iterative calculation; the system is reduced to a first-order differential equation system, and the state vector Y is defined as:

[0027]

[0028] Let the time step be Δt, and the discrete time point be t k =kΔt (k=0, 1, 2,...); for each time step k, the following is calculated in the following order:

[0029] K1=F(t k ,Y k )

[0030]

[0031] K4=F(t k +Δt,Y k +ΔtK3)

[0032]

[0033] where F is the right end function constructed by formula (1)-(5); let Y0=0, according to the highest frequency f max =max(ω s ,ω i ) / 2π, take Δt<1 / (20f max ) to ensure convergence; after each iteration, the spherical vibration displacement w s (t k ), the piezoelectric beam end displacement w(L b ,t k ), the output voltage V(t k ), and the output power P(t k )=V 2 (t k ) / R are extracted in turn.

[0034] Overall, compared with the prior art, the above technical solutions conceived by the present application mainly have the following technical advantages:

[0035] (1) The device in the present application converts wind energy into vibration energy through vortex-induced vibration by using an elastic support ball, at the same time, the piezoelectric beam receives base vibration excitation from its fixed end and transmits base vibration energy to the ball part, enhancing the vortex-induced vibration effect. The vibration energy is converted into electrical energy by the piezoelectric beam, thereby improving the output performance and multi-directional adaptability of the collector. To solve the technical problems of low energy collection efficiency, narrow effective working range, narrow bandwidth, one-way collection, low output voltage power, low energy collection efficiency outside the resonance region, and inability to achieve multi-directional and effective capture of changing vibration energy in the prior art.

[0036] (2) The present application establishes a coupled electromechanical model based on Euler-Lagrange equation, studies the influence of base excitation on spherical VIV energy collection, and compared with the pure VIV model, the introduction of base excitation significantly widens the effective working flow range and improves the output performance. The influence of excitation frequency on the output performance of spherical VIV is analyzed. In particular, the ratio of input excitation (base excitation frequency f b and vortex-induced vibration frequency f s ) to the natural frequency of the structure f n and the ratio of the natural frequency of the ball f sp to the natural frequency of the piezoelectric beam f p on the energy collection performance are systematically studied, revealing their key role in achieving maximum output efficiency. The results show that the base excitation significantly widens the effective working flow range from 2.2-5.4 m / s in the case of only VIV to 2.2-7.2 m / s. Under the condition of optimal frequency matching (wind speed 4.47 m / s, fb=14.3 Hz, f sp / f p =1.03), the maximum output voltage reaches 69.53 V, which is 41.62 V higher than that of only vortex-induced vibration (VIV) and 61.92 V higher than that of only base excitation. When the frequency ratio f s / f n changes, the system shows obvious soft response behavior, and when the frequency ratio f s / f n =1.007, the output performance is optimal; while changing f b / f n , the system shows linear response, and when the frequency ratio f b / f n =1.004, the structure and the input base excitation resonate. In addition, the system shows good adaptability to different flow angles, and the base excitation can significantly improve the voltage output in the range of 150°-210°.

[0037] (3) The present application enhances the vortex-induced vibration of the sphere by base excitation, significantly improving the output performance of the energy harvester. The key influencing factors are discussed, and the relationship between the input excitation frequency (vortex-induced vibration frequency f s and base excitation frequency f b ), the natural frequency of the structure f n and the output performance is systematically analyzed. The results show that base excitation significantly broadens the effective working flow rate range, from 2.2-5.4 m / s in vortex-induced vibration alone to 2.2-7.2 m / s. When the frequency ratio f s / f n changes, the system exhibits obvious soft response behavior, and when the frequency ratio f s / f n = 1.007, the output performance is optimal; while changing f b / f n , the system exhibits linear response, and when the frequency ratio f b / f n = 1.004, the structure and the input base excitation resonate.

[0038] (4) The present application discusses the optimization method of the ratio of the natural frequency of the sphere f sp and the natural frequency of the piezoelectric beam f p by adjusting the structural parameters (sphere diameter D, spring stiffness K, piezoelectric beam length L b ) on the energy harvesting performance. Under the optimal frequency matching conditions (wind speed U = 4.47 m / s, base excitation frequency f b = 14.3 Hz, f sp / f p = 1.03), the maximum output voltage reaches 69.53 V, which is 41.62 V higher than that of vortex-induced vibration alone and 61.92 V higher than that of base excitation alone.

[0039] (5) The present application improves the adaptability of the energy harvester to different flow angles by introducing base excitation, especially improving the voltage capture capability in the range of 150° to 210°, thereby improving the multi-directional characteristics of the harvester under complex flow conditions.

[0040] (6) The present application introduces a rectifier circuit, and the energy harvester can store enough energy at a wind speed of 4.47 m / s to power the temperature and humidity sensors for about 23 seconds. BRIEF DESCRIPTION OF DRAWINGS

[0041] Figure 1 is a schematic diagram of the device structure, wherein: 1 - elastic support sphere, 2 - spring, 3 - horizontal support frame, 4 - elastic piezoelectric beam, 5 - vertical support frame, 6 - rotating base.

[0042] Figure 2 For the purpose of simplifying the calculation model diagram, the mechanical model of the device under the coupling excitation of vortex vibration and base vibration is shown.

[0043] Figure 3 For the purpose of simplifying the calculation model diagram, the mechanical model of the device under the coupling excitation of vortex vibration and base vibration is shown.

[0044] Figure 4 For the purpose of simplifying the calculation model diagram, the mechanical model of the device under the coupling excitation of vortex vibration and base vibration is shown.

[0045] Figure 5 For the purpose of simplifying the calculation model diagram, the mechanical model of the device under the coupling excitation of vortex vibration and base vibration is shown.

[0046] Figure 6 For the purpose of simplifying the calculation model diagram, the mechanical model of the device under the coupling excitation of vortex vibration and base vibration is shown. s n b n

[0047] Figure 7 For the purpose of simplifying the calculation model diagram, the mechanical model of the device under the coupling excitation of vortex vibration and base vibration is shown. DETAILED DESCRIPTION

[0048] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and should not be used to limit the present application. In addition, the technical features involved in the various embodiments of the present application described below can be combined with each other as long as they do not conflict with each other.

[0049] The present application provides a kind of ball vortex excitation vibration piezoelectric energy collection device enhanced by base excitation, including elastic support ball 1, spring 2, horizontal support frame 3, elastic piezoelectric beam 4, vertical support frame 5, rotating base 6;Elastic support ball 1 is connected with the one end of horizontal support frame 3 and the one end of elastic piezoelectric beam 4 respectively by spring 2, the other end of horizontal support frame 3 is connected with the upper end of vertical support frame 5, the other end of elastic piezoelectric beam 4 is connected with vertical support frame 5, the lower end of vertical support frame 5 is connected with rotating base 6.

[0050] ​​​​The elastic support sphere 1 is used to convert wind energy into vibration energy and transmit it to the elastic piezoelectric beam 4; the elastic piezoelectric beam 4 is used to convert the vibration energy transmitted by the elastic support sphere 1 and the bottom vibration energy generated by the rotating base 6 into electrical energy; the horizontal support frame 3 is used to fix the elastic support sphere 1, and the vertical support frame 5 is used to fix the elastic piezoelectric beam 4; the rotating base 6 is used to adjust the incoming wind direction.

[0051] The spring 2 has a specific stiffness and length, and is used to adjust the vibration characteristics of the elastic support ball 1.

[0052] The elastic piezoelectric beam 4 includes a metal substrate beam and a piezoelectric layer. The piezoelectric layer is located on the metal substrate beam. The metal substrate beam is preferably an aluminum layer. The aluminum layer and the piezoelectric layer have specific dimensions and material parameters to optimize energy harvesting efficiency.

[0053] The device also includes a rotating base 6 for adjusting the angle between the elastic support sphere 1 and the wind direction, so as to improve the adaptability of the energy harvester under different wind directions.

[0054] This invention provides a method for harvesting piezoelectric energy from vortex-induced vibration of a sphere enhanced by base excitation. The method utilizes an elastically supported sphere 1 to convert wind energy into vibrational energy through vortex-induced vibration. Simultaneously, an elastic piezoelectric beam 4 receives vibrational excitation from the base at its fixed end and transmits this excitation to the sphere, thereby enhancing the vortex-induced vibration of the sphere. The vibrational energy is then transferred to the elastic piezoelectric beam 4, which converts the vibrational energy into electrical energy. This electrical energy is further enhanced by adjusting the input excitation frequency (vortex-induced vibration frequency f). s and base excitation frequency f b ) and the structure's natural frequency f n The proportional relationship, and by adjusting the structural parameters (sphere diameter D, spring stiffness K, piezoelectric beam length L) b Optimize the natural frequency f sp With the natural frequency f of the piezoelectric beam p This improves output performance. The output performance of the energy harvester is optimized by adjusting the load resistance, and the multidirectional adaptability of the energy harvester is improved by adjusting the angle between the elastic support sphere 1 and the wind direction.

[0055] The optimal energy harvesting effect is achieved by adjusting the vibration frequency of the elastic support sphere to match the natural frequency of the piezoelectric beam.

[0056] The output voltage can be improved by adjusting the basic vibration frequency and vortex-induced vibration frequency to match the natural frequency of the structure.

[0057] This invention provides a method for harvesting piezoelectric energy from vortex-induced vibration of a sphere enhanced by base excitation, and obtains a set of electromechanical coupling equations using a simplified calculation model.

[0058] The simplified computational model consists of two parts: an upper sphere and a lower piezoelectric beam. The sphere has a diameter of D and a density of ρ. s The lengths of the upper and lower connecting springs are l1 and l2, and the stiffnesses of the upper and lower springs are k1 and k2, respectively. The length of the elastic piezoelectric beam is L. b Width is W b Thickness is t b The length of the piezoelectric layer on the elastic piezoelectric beam is L. p Width is W p Thickness is t p The base vibration acceleration is Z(t) = acos(2πf) b t), where a is the amplitude and f is the oscillation frequency. b Let t be the excitation frequency and t be the time.

[0059] The electromechanical coupling equation set includes the vortex-induced vibration dynamics equation of a sphere, the wake oscillator equation, the displacement discretization equation of a piezoelectric beam, the dynamics equation of a piezoelectric beam, and the electrical equation of a piezoelectric beam.

[0060] The dynamic equation for the vortex-induced vibration of the sphere is:

[0061]

[0062] The equation for the wake oscillator is:

[0063]

[0064] The displacement discretization equation of the piezoelectric beam is as follows:

[0065]

[0066] The dynamic equation of the piezoelectric beam is:

[0067]

[0068] The electrical equation of the piezoelectric beam is as follows:

[0069]

[0070] Among them, w s (t), Let k1 and k2 represent the displacement, velocity, and acceleration of the sphere, respectively, and k1 and k2 represent the stiffness of the springs connected to the horizontal support frame and the elastic piezoelectric beam, respectively. D is the diameter of the sphere, U is the wind speed, and L is the velocity. b and L p These are the lengths of the elastic piezoelectric beam and the piezoelectric layer, respectively, in meters. s and c s These are the equivalent mass and structural damping of the overall structure of the sphere and spring, respectively, C L C represents the steady-state average lift coefficient.D C D represents the steady mean drag coefficient, p air represents the density of air, q(t) represents the fluid-structure coupling term, and represent the first and second order derivatives of q(t) with respect to time t, respectively; A represents a constant of the van der pol wake oscillator model, A = 23; l is a constant describing the vortex street oscillation, l = 0.1; w s represents the vortex shedding frequency, Z(t) represents the base excitation; w(x, t) represents the displacement of the piezoelectric beam at a point x distance from the fixed end at time t, r i (t) is the mode vector, is the mode amplitude of the piezoelectric beam, l represents the mechanical damping ratio of the structure, w i represents the i-th order vibration frequency; 0 i represents the i-th order force-electric coupling coefficient, V(t) represents the output voltage; W b and W p are the width of the elastic piezoelectric beam and the piezoelectric layer, respectively, t b and t p are the thickness of the elastic piezoelectric beam and the piezoelectric layer, respectively, p b and p p are the density of the elastic piezoelectric beam and the piezoelectric layer, respectively; C p represents the piezoelectric sheet capacitance, R represents the load resistance;

[0071] To solve the highly coupled nonlinear differential equation system (1)-(5), the Runge-Kutta method is used for numerical iterative calculation; the system is reduced to a first order differential equation system, and the state vector Y is defined as:

[0072]

[0073] Let the time step be At, and the discrete time point t k = kAt (k = 0, 1, 2,...); for each time step k, calculate in the following order:

[0074] K1 = F(t k , Y k )

[0075]

[0076] K4 = F(t k + At, Y k + AtK3)

[0077]

[0078] where F is the right end function constructed by (1)-(5); let Y0 = 0, and according to the highest frequency f max= max(ω s ,ω i ) / 2π, take Δt < 1 / (20f max ) to ensure convergence; after each iteration, the spherical vibration displacement w s (t k ), the piezoelectric beam end displacement w(L b ,t k ), the output voltage V(t k ), and the output power P(t k ) = V 2 (t k ) / R are extracted in turn.

[0079] The following are specific embodiments

[0080] Example 1

[0081] Figure 1 A base excitation enhanced spherical vortex vibration piezoelectric energy harvesting device is shown in FIG. 1, which is based on the coupling effect of vortex vibration and base vibration, and is composed of an elastic support sphere 1, a spring 2, a horizontal support frame 3, an elastic piezoelectric beam 4, a vertical support frame 5, and a rotating base 6. The elastic support sphere 1 is connected to one end of the horizontal support frame 3 and one end of the elastic piezoelectric beam 4 through the spring 2, the other end of the horizontal support frame 3 is connected to the upper end of the vertical support frame 5, the other end of the elastic piezoelectric beam 4 is also connected to the vertical support frame 5, and the lower end of the vertical support frame 5 is connected to the rotating base 6. The elastic support sphere 1 is used to convert wind energy into vibration energy and transmit it to the elastic piezoelectric beam 4; the elastic piezoelectric beam 4 includes an aluminum layer (metal base beam) and a piezoelectric layer, the piezoelectric layer is located on top of the aluminum layer, has specific size and material parameters, and can convert the vibration energy transmitted by the elastic support sphere 1 and the base vibration energy into electrical energy. The spring 2 has a specific stiffness and length, which is used to adjust the vibration characteristics of the elastic support sphere 1. The horizontal support frame 3 and the vertical support frame 5 are used to fix the elastic support sphere 1 and the elastic piezoelectric beam 4 respectively, to ensure the stability of the structure. The rotating base 6 is used to adjust the incoming wind direction and improve the adaptability of the energy harvester under different wind directions. When the wind flows through the elastic support sphere 1, it will cause vortex vibration of the sphere, and this vibration is transmitted to the elastic piezoelectric beam 4 through the spring 2. At the same time, the rotating base 6 can adjust the angle of the entire device to adapt to different wind directions, ensuring efficient energy collection in variable environments. The piezoelectric layer in the elastic piezoelectric beam 4 converts vibration energy into electrical energy, thereby achieving effective energy collection.

[0082] Example 2

[0083] Figure 2A simplified calculation model of the present application is demonstrated in FIG. 6. In the present application, the elastic support sphere generates vortex-induced vibration under the action of wind, converting wind energy into vibration energy. At the same time, the piezoelectric beam receives the base vibration excitation from its fixed end and transmits the base vibration energy to the sphere part, enhancing the vortex-induced vibration effect. Through the elastic support of the spring, the vibration energy of the sphere is transmitted to the elastic piezoelectric beam. The elastic piezoelectric beam generates piezoelectric effect under the action of vibration, converting vibration energy into electrical energy. By adjusting the diameter of the sphere, the stiffness of the spring and the length of the piezoelectric beam, the natural frequency of each part and the whole of the device can be changed. Specifically, the larger the diameter of the sphere, the smaller the stiffness, and the longer the length of the piezoelectric beam, the lower the corresponding natural frequency. Adjust the size and material parameters of the piezoelectric beam to the optimal state to improve the energy harvesting efficiency.

[0084] Example 3

[0085] Figure 3 (a) in FIG. 6 demonstrates the open-circuit voltage and its frequency captured at different wind speeds without base excitation. From the graph, it can be seen that there is very good consistency between the numerical prediction of the derived model and the experimental measurement. Obviously, the theoretical model predicts the synchronization region well, especially the starting value and the peak value. However, the average output power is low in the region above the synchronization wind speed, i.e. when the wind speed value is greater than 5.4 m / s. This result is due to the fact that the theoretical model only considers the vertical wake oscillator, while there is a lateral wake oscillator interference vibration at higher wind speeds. In contrast, Figure 3Figure (bd) illustrates the significant improvement in energy harvesting performance when both base excitation and vortex-induced vibration are present. At a wind speed U = 4.47 m / s, the maximum voltage reaches 49.2 V, indicating that base excitation increases the maximum voltage of vortex-induced vibration by 21.29 V. The voltage response curves at different base excitation frequencies show a trend of first increasing and then decreasing with increasing wind speed. Within the locked region, the sphere reaches its maximum amplitude, significantly optimizing the energy conversion efficiency of the harvester. The introduction of base excitation provides a stable source of vibrational energy for vortex-induced vibration, enabling it to maintain a high amplitude over a wider wind speed range. This results in effective energy harvesting over a wider wind speed range. The output voltage response curves to wind excitation at different base vibration frequencies show that the output voltage increases with increasing wind speed until it reaches a peak, and then decreases with further increases in wind speed. Within the locked region, the sphere achieves its maximum amplitude. Furthermore, when the wind speed exceeds 6.28 m / s, the output voltage decreases, exhibiting a rapid initial decrease followed by a slower decrease. This behavior is due to the sphere shifting to a lateral vibration mode at higher wind speeds, interfering with the longitudinal vibration of the piezoelectric beam and affecting the energy conversion process. The performance changes mentioned in the above analysis, such as voltage increase, power deviation, and the output trend with wind speed, are all quantitatively calculated based on direct calculations of experimental measurement data. Specifically, the magnitude of voltage and power increases is obtained by comparing the measured peak voltage or average power values ​​with and without base excitation under the same wind speed conditions, calculating their absolute difference and relative percentage change; the evaluation of performance optimization within the locked area relies on comparative analysis of the measured sphere amplitude and corresponding output power values ​​at a specific wind speed point (e.g., U = 4.47 m / s); and the rate of decrease in output voltage with wind speed is determined by calculating the voltage change (dV / dU) caused by a unit wind speed change within a specific range (e.g., U = 6.28 m / s to U = 6.5 m / s) based on the experimentally measured voltage-wind speed curve. The core purpose of these calculations is to quantitatively compare experimental observations with model predictions, thereby supporting the conclusions in this paper.

[0086] Example 4

[0087] like Figure 4 As shown, four wind speed conditions (0 m / s, 2.39 m / s, 4.47 m / s, and 7.35 m / s) were selected to analyze the voltage response curves of the energy harvester within the 10-18 Hz base excitation frequency range. Figure 4 As shown in (a), when the wind speed is 0 m / s, the system is only excited by base vibration. In this case, the voltage response curve reflects the energy harvesting performance caused solely by base excitation. The resonant peak occurs at 14.1 Hz, and the maximum harvest voltage at resonance is only 7.61 V. Figure 4As shown in (b), at a wind speed of 2.39 m / s, the sphere experiences weak wind excitation but does not enter the locked region of vortex-induced vibration. At this point, the sphere's vibration frequency does not match the vortex shedding frequency, resulting in minimal contribution of vortex-induced vibration to the overall structural vibration. Therefore, the voltage response curve remains similar to that under the 0 m / s condition. The resonance peak still appears at approximately 14.1 Hz, indicating that the system's resonant frequency remains around 14.1 Hz. Figure 4 As shown in (c), the sphere experiences vortex-induced vibration at a wind speed of 4.47 m / s. This condition is crucial for studying the enhancing effect of base vibration on vortex-induced vibration. Vortex-induced vibration significantly alters the dynamic characteristics of the system. Figure 4 In (c), the voltage peaks at approximately 59.35V at about 14.3Hz, indicating that the system resonates at this frequency. Figure 4 Compared to the peak voltage under windless excitation shown in (a), this represents an increase of 51.74V, highlighting the significant enhancement in the system's energy harvesting capability due to increased wind speed. Figure 4 As shown in (d), when the wind speed further increases to 7.35 m / s, the vortex-induced vibration frequency exceeds the lockout region, and the vibration frequency of the sphere no longer matches the vortex shedding frequency. The influence of vortex-induced vibration decreases, and... Figure 4 Compared to the base-excitation condition shown in (a) above, the differences in the voltage response curves become smaller. At a base excitation frequency of 14.8 Hz, the voltage response at 7.35 m / s is approximately 14.57 V, only slightly higher than the 7.61 V observed at 0 m / s. This indicates that once the wind speed exceeds the locked-in area, the contribution of vortex-induced vibration to energy harvesting decreases significantly, and base excitation becomes the primary energy source, enabling the harvester to continue collecting energy. The quantitative results regarding the changes in voltage response peak values, differences, and frequency shifts in the above analysis are all based on... Figure 4 The experimental curves shown are obtained through direct measurement and calculation. Specifically, the peak voltages under different operating conditions (e.g., 7.61V at 0 m / s and 59.35V at 4.47 m / s) are directly read from the highest point of the response curve; the absolute increase in voltage (e.g., 51.74V) is obtained by calculating the difference between the peak voltage under a specific operating condition (e.g., 4.47 m / s) and the peak voltage under a reference operating condition (e.g., 0 m / s); the relative increase is calculated by the ratio of this difference to the reference peak voltage (e.g., 51.74V / 7.61V ≈ 680%). The identification of the system resonant frequency (e.g., 14.1Hz at 0 m / s and 2.39 m / s and 14.3Hz at 4.47 m / s) is determined based on the base excitation frequency corresponding to the peak value of the voltage response curve. These calculations clearly quantify the contribution and synergistic effect of vortex-induced vibration and base excitation on the system's energy harvesting performance at different wind speeds.

[0088] Example 5

[0089] Figure 5It is shown that at low wind speeds (U = 2.39 m / s), the spherical VIV-PEH device in this invention captures higher voltages within the wind yaw angle range of 30°-120° and 240°-330°. At higher wind speeds (U = 4.47 m / s and U = 6.80 m / s), higher voltages occur within the wind yaw angle range of 0°-120° and 240°-360°. This phenomenon is related to the flow field characteristics and vortex shedding behavior. When the incoming flow angle is between 330°-360° and 0°-30°, the support post is located behind the sphere. At low wind speeds, the support post significantly affects the flow field behind the sphere as it directly disrupts the wake region, which is a critical area for vortex shedding. As the wind speed increases, the flow field dynamics change. The fluid's ability to stretch and transport vortices is enhanced, resulting in an increase in vortex shedding frequency with increasing Reynolds number. This improved vortex stretching and transport reduces the support post's hindering effect on vortex shedding, allowing the sphere's vortex-induced vibration to remain relatively unaffected. At higher wind speeds, the vortex shedding process in the flow field becomes more complex, even turbulent, which further reduces the direct impact of the support post. Under these conditions, vortex shedding occurs throughout the wake region, rather than being confined to the narrow area behind the post. This enables the sphere to capture energy more effectively over a larger range of wind yaw angles. Therefore, at higher wind speeds, the captured voltage increases when the support post is located directly in front of the sphere. This is because the complexity of the flow field reduces the support post's impact on vortex shedding, allowing the sphere to more effectively convert the energy entering the airflow. On the other hand, for all three wind speeds (U = 2.39 m / s, 4.47 m / s, and 6.80 m / s), the captured voltage significantly decreases when the incoming flow angle ranges from 150° to 210°. This is because, within this range, the support post is located in front of the sphere, altering the flow field distribution upstream of the sphere. The incoming flow first passes around the support post before reaching the sphere, resulting in the sphere being subjected to a disturbed flow rather than a uniform, steady flow. This disturbed flow weakens the aerodynamic excitation on the sphere, disrupts vortex shedding, and reduces the captured voltage. When the base excitation is introduced, a significant increase in captured voltage is observed within the 150°-210° range. It is worth noting that the base excitation effectively counteracts the interference effects of the support post when its frequency is close to the natural frequency of the harvester. This greatly enhances the multi-directionality of the energy harvester. The base excitation changes the dynamic characteristics of the flow field and the local aerodynamic behavior, significantly mitigating the interference effects of the support post. Therefore, even when the sphere is located behind the post, it can generate vortex-induced vibrations and corresponding voltage outputs. As an external force, the base excitation induces vibrations in the piezoelectric beam and the elastically supported sphere. These vibrations modulate the pressure distribution and velocity field in the airflow, affecting the mode and frequency of vortex shedding. Therefore, vortex-induced vibrations can occur even when the sphere is behind the post. Near the resonance frequency, the structure's response to base vibrations is most pronounced, producing significant vibrations with minimal external excitation.This maximizes the pressure distribution and velocity field of the flow field, and optimizes the energy harvesting performance.

[0090] Example 6

[0091] In this study, the effect of the frequency ratio between the research excitation (vortex-induced vibration frequency f s and base excitation frequency f b ) and the inherent frequency of the device (f n ) on the output voltage V is crucial for optimizing the performance of the harvester. Figure 6 The output voltage variation under vortex-induced vibration and base excitation was analyzed separately. As shown in (a) of FIG. 6, Figure 6 when the frequency ratio f s / f n is about 0.8-1.3, the output performance is better than that of single vortex-induced vibration excitation; when the frequency ratio f s / f n is about 1.007, the output voltage reaches a peak value. This indicates that when the vortex-induced vibration frequency is close to the inherent frequency of the structure, energy transfer is most effective, making the system in a state of resonance. When f s / f n deviates from 1.007, the output voltage gradually decreases. However, the rate of decline is relatively slow, showing the soft characteristics of amplitude-frequency characteristics. The vortex-induced force itself is nonlinear, and its nonlinearity is mainly reflected in the time history of the lift force. Vortex shedding is a complex fluid phenomenon, and the lift force generated is affected by flow velocity fluctuations, flow field disturbances, and other factors. Due to these nonlinear effects, the frequency and amplitude of the vortex-induced force can vary within a certain range under actual conditions. From the perspective of energy transfer, even when the frequency ratio deviates from resonance, this nonlinearity allows a portion of the energy to continue to be transferred to the piezoelectric cantilever beam.

[0092] As shown in (b) of FIG. 6, Figure 6 the output voltage shows a linear trend with respect to the frequency ratio between the base excitation and the inherent frequency of the structure (f b / f n ). When the frequency ratio f b / f n is about 1.000-1.010, the output performance is better than that of single base vibration excitation; when f b / f n is close to 1.004, the output voltage reaches a peak value.

[0093] When f s / f n is close to 1.004, and when f s / f p =1.007, the output voltage reaches a peak value of 59.35 V. In contrast to (a) of FIG. 6, Figure 6 , the output voltage under base excitation is much higher than that under vortex-induced vibration.Figure 6 (b) in Figure 4 does not show this behavior, Figure 6 (a) in Figure 4 shows a soft response characteristic under vortex-induced vibration. In contrast, once the frequency ratio deviates from 1.004, the output voltage drops sharply, and no gradual drop is observed. This indicates a more linear and narrowband response under base excitation. The cause of this phenomenon lies in the fact that under base excitation, the main input to the system is the harmonic motion of the bottom piezoelectric beam. The piezoelectric cantilever beam is mainly driven by this relatively simple and stable linear excitation with consistent frequency and amplitude. Although the sphere also moves due to the cantilever's vibration, its motion is mainly passive, caused by the deformation of the cantilever, rather than actively extracting energy from the surrounding fluid as in vortex-induced vibration. Therefore, compared with vortex excitation, the coupling between the sphere, spring, and cantilever beam has less influence on the overall dynamic behavior of the system. In this case, the dynamics of the system are relatively simple, and the motion of the cantilever is mainly controlled by the base vibration. The system response is closely related to linear vibration theory, in which the behavior of a single-degree-of-freedom system under harmonic excitation mainly depends on the closeness of the excitation frequency to the natural frequency. When the excitation frequency deviates from the natural frequency, the response amplitude (reflected in the output voltage) drops sharply. In addition, the energy transfer path in base excitation is more direct, with energy being transferred from the fixed end to the cantilever, causing vibration and generating voltage. Compared with vortex vibration, which involves complex intermediate interactions and nonlinear effects, the lack of such complexity under base excitation leads to a rapid drop in energy transfer efficiency as the frequency ratio deviates from 1.0, resulting in a more linear output voltage trend. The structural frequency is a key factor in the design of energy harvesters, as it directly determines the vibration frequency at which the device can achieve optimal energy conversion efficiency. When the external excitation frequency matches the structural frequency of the harvester, resonance occurs, resulting in the highest energy conversion efficiency. The energy harvester presented in this study is excited by both vortex vibration and base vibration. Therefore, it is necessary to adjust two structural frequencies: the natural frequency of the sphere-spring system (f s ) and the natural frequency of the piezoelectric beam (f p ). Since the sphere-spring system is connected to the piezoelectric beam, they exhibit coupled motion when excited by either vibration. Therefore, when the natural frequencies of the sphere-spring system and the piezoelectric beam match, resonance can be maximized in the energy harvester. The frequency ratio is defined as the ratio of the natural frequency of the sphere-spring system to the natural frequency of the piezoelectric cantilever beam. To study the effect of the frequency ratio on energy harvesting performance, the relevant parameters are adjusted: the diameter of the sphere (D) is varied from 50 mm to 80 mm, the stiffness of the springs (k1 and k2) is adjusted from 6 N / m to 30 N / m, and the beam length (L b ) is varied from 80 cm to 150 cm. These changes result in a range of frequency ratios (sphere natural frequency fsp to piezoelectric beam natural frequency fp) from 0.56 to 1.28, as shown in Figure 6As shown in (c) in the figure. Figure 6 Figure (c) shows the variation of the maximum output voltage of the energy harvester with respect to the frequency ratio (η) of the natural frequency fsp of the sphere to the natural frequency fp of the piezoelectric beam, which is defined as the ratio of the natural frequency of the sphere-spring system to the natural frequency of the piezoelectric cantilever beam. Figure 6 As shown in (c), the curve exhibits a single peak near η = 1.03, at which point the maximum output voltage reaches approximately 69.5V. When the frequency ratio is below 1.03, the output voltage increases rapidly with η; conversely, when η exceeds 1.03, the output voltage gradually decreases. This trend indicates that, due to the connection between the ball-spring system and the cantilever beam, both vortex excitation and base excitation act as external forces on the piezoelectric beam. When the excitation frequency matches the natural frequency of the cantilever, coupled resonance occurs, significantly improving energy transfer and conversion efficiency. Therefore, the output voltage reaches its maximum value. However, as the frequency ratio deviates from the optimal value, the coupling effect weakens, leading to a decrease in output voltage.

[0094] Example 7

[0095] Figure 7 Figure (a) shows the variation of the output voltage of a capacitor charged by an energy harvester over time at a wind speed of 4.47 m / s and a fundamental vibration frequency of 14 Hz when connected to different capacitors (10 μF, 47 μF, 100 μF, and 220 μF). Figure 7 As shown in (a), the smaller the capacitor, the faster the charging speed. For example, a 10μF capacitor can quickly reach over 10V in about 30 seconds, while a 220μF capacitor takes much longer to rise in the same time period. This indicates that under the same energy input conditions, a smaller capacitor can reach the required operating voltage more quickly. Furthermore, this reflects the difference in PEH output power under different load conditions. In this experiment, only a 100μF (10V rated voltage) capacitor enabled the temperature and humidity sensors to operate normally. When using other capacitors (16V 10μF, 25V 47μF, or 50V 220μF), the sensor failed to display any readings. This is because the capacitance and circuit requirements are mismatched. A 10V 100μF capacitor with a suitable capacitance not only charges quickly but also stores enough energy to meet the sensor's operating power requirements. In contrast, the smaller 10μF and 47μF capacitors cannot accumulate enough energy to start the sensor in a short time. Furthermore, the 10V rated voltage matches the PEH's output voltage range very well, allowing the capacitors to charge effectively close to their rated voltage, thus providing sufficient energy. In contrast, capacitors with higher rated voltages (16V, 25V, and 50V) require higher voltages to store sufficient charge. Because the PEH's output voltage is not high enough to fully charge these capacitors, they cannot provide enough energy for the sensor.Figure 7 (b) in FIG. 4 shows the charging and discharging process of a 100 pF capacitor used to power the temperature and humidity sensors under the same conditions (wind speed of 4.47 m / s, vibration frequency of 14 Hz). At the start of the experiment, the switch remained open and the PEH, capacitor, and sensors were connected according to the circuit diagram. The PEH converted the mechanical vibrations into an alternating current power source, which was then rectified into a DC power source to charge the capacitor. During the charging phase (0-57 s), the voltage across the capacitor gradually increased, reaching approximately 9.4 V at 57 s. Once this voltage was reached, the switch was closed and the discharging phase (57-80 s) began, during which the stored energy in the capacitor powered the sensors. As shown in (b) in FIG. 4, the sensors successfully operated and displayed temperature and humidity data when discharging began. The sensors remained active for approximately 23 s, during which clear readings of 12.9 °C and 49% humidity were observed. After 70 s, the capacitor voltage rapidly decreased and the displayed temperature (13.4 °C) and humidity (49%) readings became fuzzy, indicating that the stored energy was running out and the sensors were about to power off. Figure 7

[0096] It is readily understood by those skilled in the art that the above description is only preferred embodiments of the present application, and is not intended to limit the present application, and any modification, equivalent replacement and improvement made within the spirit and principle of the present application should be included in the protection scope of the present application.​

Claims

1. A base-excited enhanced sphere vortex-induced vibration piezoelectric energy harvesting device, characterized in that, The utility model relates to a wind energy conversion system, including elastic support ball (1), spring (2), horizontal support frame (3), elastic piezoelectric beam (4), vertical support frame (5) and rotating base (6), elastic support ball (1) is connected with one end of horizontal support frame (3) and one end of elastic piezoelectric beam (4) respectively through spring (2), the other end of horizontal support frame (3) is connected with the upper end of vertical support frame (5), the other end of elastic piezoelectric beam (4) is connected with vertical support frame (5), and the lower end of vertical support frame (5) is movably connected with rotating base (6).

2. The base excitation enhanced spherical vortex-induced vibration piezoelectric energy harvesting device of claim 1, wherein, The elastic piezoelectric beam (4) comprises a metal base beam and a piezoelectric layer.

3. The base-excited enhanced spherical vortex galloping piezoelectric energy harvesting device of claim 2, wherein, The metal base beam is an aluminum layer.

4. The base-excited enhanced spherical vortex vortex-induced vibration piezoelectric energy harvesting device of claim 1, wherein, The diameter of the elastic support ball (1) is 50mm-80mm, the stiffness of the spring (2) is 6N / m-30N / m, and the length of the elastic piezoelectric beam (4) is 80cm-150cm.

5. A method of energy harvesting using the piezoelectric energy harvesting device of any one of claims 1-4, characterized in that, The elastic support ball converts wind energy into vibration energy through vortex-induced vibration; at the same time, the elastic piezoelectric beam receives vibration excitation from the fixed end of the rotating base and transmits the vibration excitation to the elastic support ball to enhance the vortex-induced vibration of the elastic support ball. The vortex-induced vibration energy excited by the rotating base is transmitted to the elastic piezoelectric beam, and the elastic piezoelectric beam converts the vibration energy into electrical energy.

6. The method of energy harvesting of claim 5, wherein, The ratio of the vortex-induced vibration frequency f of the elastic support ball (1) to the natural frequency f of the whole piezoelectric energy harvesting device s The ratio of the vortex-induced vibration frequency f of the elastic support ball (1) to the natural frequency f of the whole piezoelectric energy harvesting device n is 0.8-1.

3.

7. The method of energy harvesting of claim 5, wherein, The ratio of the base excitation frequency f transmitted by the rotating base (6) to the natural frequency f of the whole piezoelectric energy harvesting device with the ball vortex-induced vibration b The ratio of the base excitation frequency f transmitted by the rotating base (6) to the natural frequency f of the whole piezoelectric energy harvesting device with the ball vortex-induced vibration n is 1.000-1.

010.

8. The method of energy harvesting of claim 5, wherein, The natural frequency f of the elastic support sphere (1) sp With the natural frequency f of the elastic piezoelectric beam (4) p The ratio is 0.56 to 1.

28.

9. The method of energy harvesting of claim 5, wherein, The size of the converted electrical energy is calculated by a set of electromechanical coupling equations, including a sphere vortex-induced vibration dynamics equation, a wake oscillator equation, a piezoelectric beam displacement discrete equation, a piezoelectric beam dynamics equation, and a piezoelectric beam electrical equation. The sphere vortex-induced vibration dynamics equation is as follows: The wake oscillator equation is as follows: The piezoelectric beam displacement discrete equation is as follows: The piezoelectric beam dynamics equation is as follows: The piezoelectric beam electrical equation is as follows: wherein w s (t), denote the displacement, velocity and acceleration of the sphere, respectively, k1 and k2 are the stiffness of the spring connected with the horizontal support frame and the spring connected with the elastic piezoelectric beam, respectively, D is the diameter of the sphere, U is the wind speed, L b and L p are the length of the elastic piezoelectric beam and the piezoelectric layer, respectively, m s and c s are the equivalent mass and structural damping of the overall structure of the sphere and the spring, respectively, C L denotes the steady average lift coefficient, C D denotes the steady average drag coefficient, p air denotes the density of air, q(t) denotes the fluid-structure coupling term, and denote the first and second order derivatives of q(t) with respect to time t, respectively; A denotes a constant of the van der pol wake oscillator model, A = 23; l is a constant describing the vortex street fluctuation, l = 0.1; w s denotes the vortex shedding frequency, Z(t) denotes the base excitation; w(x, t) denotes the displacement of the piezoelectric beam at a point with a distance of x from the fixed end at time t, r i (t) is a mode vector, is the vibration mode amplitude of the piezoelectric beam, s denotes the mechanical damping ratio of the structure, w i denotes the i-th order vibration frequency; q i denotes the i-th order force-electric coupling coefficient, V(t) denotes the output voltage; W b and W p are the width of the elastic piezoelectric beam and the piezoelectric layer, respectively, t b and t p are the thickness of the elastic piezoelectric beam and the piezoelectric layer, respectively, p b and p p are the density of the elastic piezoelectric beam and the piezoelectric layer, respectively; C p denotes the piezoelectric sheet capacitance, R denotes the load resistance; In order to solve the highly coupled nonlinear differential equation set (1)-(5), the Runge-Kutta method is used for numerical iterative calculation; the system is reduced to a first-order differential equation set, and the state vector Y is defined as follows: Let the time step be Δt, and the discrete time points be t k = kΔt (k = 0, 1, 2,...); for each time step k, compute in the following order: K1 = F(t k , Y k ) K4 = F(t k + Δt, Y k + Δt K3) where F is the right end function constructed by formula (1)-(5); set Y0=0, according to the highest frequency f max = max(ω s ,ω i ) / 2π, take Δt <1 / (20f max ) to ensure convergence; after each iteration, the spherical vibration displacement w s (t k ), the piezoelectric beam end displacement w(L b ,t k ), the output voltage V(t k ), and the output power P(t k )=V 2 (t k ) / R are extracted in turn.

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