CN-122021412-A - Random response analysis method of piezoelectric-electromagnetic hybrid energy collector under pulsating wind excitation

CN122021412ACN 122021412 ACN122021412 ACN 122021412ACN-122021412-A

Abstract

The invention particularly relates to a random response analysis method of a piezoelectric-electromagnetic hybrid energy collector under pulsating wind excitation, which comprises the steps of establishing a mechanical vibration equation comprising a relaxation aerodynamic force item and a time-lag feedback control item, forming an initial electromechanical coupling equation set by being combined with a piezoelectric voltage state equation and an electromagnetic current state equation, simultaneously representing mechanical end dynamics and two-branch energy conversion effects in the same model, introducing dimensionless pulsating wind speed into the relaxation aerodynamic force and carrying out equivalent modeling by multiplicative noise, so as to explicitly map the pulsating wind speed into a state-related random excitation item, adopting harmonic transformation to equivalent the algebraic items of voltage and current variable into displacement and speed, obtaining an equivalent decoupling system, realizing model variable transformation and improving analysis solving efficiency, and finally obtaining a steady probability density function based on energy envelope random average and calculating a random response analysis result according to the steady probability density function, thereby providing a reliable basis for control parameter and energy harvesting performance evaluation.

Inventors

ZHANG YING
Qin Ruobing
ZHENG KAIXIN
ZHANG JINGWEN
QIN QIANQIAN

Assignees

西北工业大学

Dates

Publication Date: 20260512
Application Date: 20260109

Claims (9)

1. A method for random response analysis of a piezoelectric-electromagnetic hybrid energy harvester under pulsating wind excitation, the method comprising: Constructing a mechanical vibration equation based on a mechanical end dynamic balance relation of the relaxation type hybrid energy collector; Combining a mechanical vibration equation, a voltage state equation of a piezoelectric branch of a relaxation type hybrid energy collector and a current state equation of an electromagnetic branch to construct an initial electromechanical coupling equation set; carrying out pulsating wind equivalent modeling on the initial electromechanical coupling equation set by utilizing dimensionless pulsating wind speed analytic type and multiplicative noise to obtain a random electromechanical coupling equation set under the excitation of pulsating wind; Decoupling the random electromechanical coupling equation set based on harmonic transformation to obtain an equivalent electromechanical decoupling equation; and solving an equivalent machine decoupling equation based on an energy envelope random average method to obtain a random response analysis result of the relaxation type hybrid energy collector.
2. The method of claim 1, wherein constructing a mechanical vibration equation based on a mechanical end dynamic balance relationship of the relaxation hybrid energy harvester comprises: Constructing a structural dynamics item of a mechanical vibration equation according to an inertia item of a blunt body in the relaxation type hybrid energy collector, a damping item and a rigidity item of the relaxation type hybrid energy collector and an electromechanical coupling item formed by the combined action of a piezoelectric branch output voltage and an electromagnetic branch output current of the relaxation type hybrid energy collector, wherein the structural dynamics item takes dimensionless transverse displacement of the blunt body as an independent variable; and determining an external excitation term of the mechanical vibration equation based on the relaxation aerodynamic term and the time lag feedback control term.
3. The method of claim 1, wherein the combining the mechanical vibration equation, the voltage state equation of the piezoelectric branch and the current state equation of the electromagnetic branch of the relaxation hybrid energy harvester to construct the initial set of electromechanical coupling equations comprises: taking the dimensionless transverse speed of the blunt body as the driving input of the piezoelectric branch, and determining a voltage state equation of the piezoelectric branch based on an equivalent first-order circuit dynamic model of the piezoelectric branch and the dimensionless time constant ratio of the piezoelectric branch; the method comprises the steps of taking the dimensionless transverse speed of a blunt body as the driving input of an electromagnetic branch, and determining a current state equation of the electromagnetic branch based on an equivalent first-order circuit dynamic model of the electromagnetic branch and the dimensionless collector constant ratio of the electromagnetic branch; and (3) combining the mechanical vibration equation, the voltage state equation and the current state equation to construct an initial electromechanical coupling equation set.
4. The method according to claim 2, wherein the performing pulsating wind equivalent modeling on the initial set of electromechanical coupling equations using dimensionless pulsating wind speed analytic and multiplicative noise to obtain a random electromechanical coupling equation under pulsating wind excitation comprises: determining a dimensionless fluctuating wind speed analytic expression based on a dimensionless average wind speed and a wind speed fluctuation term; Substituting the dimensionless pulsating wind speed analysis formula into a relaxation aerodynamic term of a mechanical vibration equation, performing Taylor expansion on the dimensionless pulsating wind speed analysis formula, and substituting the dimensionless pulsating wind speed analysis formula into the mechanical vibration equation to obtain a wind speed fluctuation additional term; and (5) the wind speed fluctuation additional term is equivalent to multiplicative noise, and a random electromechanical coupling equation set under the excitation of pulsating wind is obtained.
5. A method according to claim 3, wherein decoupling the set of random electromechanical coupling equations based on harmonic transformation results in an equivalent electromechanical decoupling equation, comprising: Integrating the piezoelectric branch voltage state equation and the electromagnetic branch current state equation respectively to obtain convolution analysis type of piezoelectric output voltage and electromagnetic output current respectively; Constructing a harmonic hypothesis solution based on harmonic transformation, wherein the harmonic hypothesis solution is a combination form of amplitude items and phase items of the dimensionless lateral displacement of the blunt body, which change with time; The convolution analytic expression is converted into a first equivalent algebraic analytic expression and a second equivalent algebraic analytic expression according to harmonic hypothesis solution respectively, wherein the first equivalent algebraic analytic expression is an equivalent algebraic analytic expression of the non-dimensional transverse response of the piezoelectric output voltage relative to the blunt body; Substituting the harmonic hypothesis solution and the first equivalent algebraic analytic expression and the second equivalent algebraic analytic expression into a mechanical vibration equation of the random electromechanical coupling equation set to obtain an equivalent electromechanical decoupling equation.
6. The method of claim 5, wherein the solving the equivalent machine decoupling equation based on the stochastic average method of the energy envelope to obtain the stochastic response analysis result of the relaxation type hybrid energy harvester comprises: obtaining a potential energy function, an energy function and a vibration periodic function according to an equivalent machine decoupling equation, and carrying out variable transformation on the equivalent machine decoupling equation by combining an energy envelope variable to obtain an energy random differential equation of the equivalent machine decoupling equation; Performing random average based on the energy envelope on the energy random differential equation to obtain an Islamic differential equation of the energy random differential equation; Obtaining a drift coefficient and a diffusion coefficient based on the Isaria differential equation, and determining a probability density partial differential equation by using the drift coefficient and the diffusion coefficient; solving a steady-state solution of a probability density partial differential equation under a steady-state condition, and determining a steady-state probability density function; a random response analysis result is calculated based on the steady state probability density function, the first equivalent algebraic analysis formula, and the second equivalent algebra.
7. The method of claim 6, wherein the steady state probability density functions include a displacement velocity joint density function, a displacement edge density function, and a velocity edge density function; the random response analysis result comprises a mean square voltage function, a mean square current function and an average output power function; the calculating the random response analysis result based on the steady-state probability density function, the first equivalent algebra analysis result and the second equivalent algebra comprises the following steps: integrating the displacement speed joint density function, the displacement edge density function and the speed edge density function respectively to obtain a corresponding displacement speed joint distribution function, a displacement accumulated distribution function and a speed accumulated distribution function; squaring the first equivalent algebraic analysis formula and taking mathematical expectations to obtain a second moment analysis formula of the mean square voltage, substituting the displacement speed joint distribution function, the displacement accumulated distribution function and the speed accumulated distribution function into the second moment analysis formula of the mean square voltage, and determining the mean square voltage function; Squaring the second equivalent algebraic analysis formula and taking mathematical expectations to obtain a second moment analysis formula of the mean square current, substituting the displacement speed joint distribution function, the displacement accumulated distribution function and the speed accumulated distribution function into the second moment analysis formula of the mean square current, and determining the mean square current function; And based on the superposition relation of the average output power of the piezoelectric branch and the electromagnetic branch, carrying out weighted combination on the mean square voltage function and the mean square current function to obtain an average output power function.
8. A computer readable storage medium, characterized in that the computer readable storage medium comprises a stored executable program, wherein the executable program when run controls a device in which the storage medium is located to perform the method of any one of claims 1 to 7.
9. A computer program product comprising a computer program which, when executed by a processor, implements the method according to any one of claims 1 to 7.

Description

Random response analysis method of piezoelectric-electromagnetic hybrid energy collector under pulsating wind excitation Technical Field The invention relates to the technical field of response analysis of hybrid energy collectors, in particular to a random response analysis method of a piezoelectric-electromagnetic hybrid energy collector under pulsating wind excitation. Background The piezoelectric and electromagnetic vibration energy collection technology can convert vibration energy in the environment into electric energy, has the characteristics of simple structure, no need of external power supply, easy miniaturization and the like, and is widely applied to the scenes of structural health monitoring, low-power consumption sensors, wireless node energy supply and the like. In wind-induced vibration energy harvesting, energy harvesters based on blunt body relaxation (Galloping) are attracting attention because of the low start-up wind speed and the ability to generate large vibrations over a wide wind speed range. In order to improve output capability and applicability, a hybrid energy collector integrating piezoelectric and electromagnetic transduction mechanisms is presented in the prior art, so as to obtain voltage and current output simultaneously under the vibration source with the same structure. However, actual wind farms typically contain significant pulsating wind components, with wind speeds fluctuating randomly over time around an average value, resulting in the relaxation aerodynamic forces exhibiting significant randomness and non-linear characteristics, such that the displacement, velocity, and electrical output (voltage, current) of the collector appear as random processes. In the existing analysis method, one type of method simplifies the wind speed into a constant average wind speed, steady-state response and power evaluation are carried out under a deterministic model, response distribution, mean square quantity change and power statistical characteristics caused by pulsating wind are difficult to reflect, and the other type of method relies on numerical integration or Monte Carlo simulation to carry out statistics on random response, and has the advantages of wider application range, high calculation cost, unfriendly parameter scanning and control parameter design, and easiness in occurrence of convergence and efficiency problems when strong nonlinearity, electromechanical coupling and random excitation coexist. On the basis, in the hybrid collector, bidirectional coupling exists between the mechanical end and the piezoelectric/electromagnetic branch, and the control item and random aerodynamic force jointly act on system dynamics, so that response solving is more complex. It should be noted that the information disclosed in the above background section is only for enhancing understanding of the background of the invention and thus may include information that does not form the prior art that is already known to those of ordinary skill in the art. Disclosure of Invention The invention provides a random response analysis method of a piezoelectric-electromagnetic hybrid energy collector under pulsating wind excitation, a computer readable storage medium and a computer program product, which can effectively overcome the defects in the prior art. Other features and advantages of the invention will be apparent from the following detailed description, or may be learned by the practice of the invention. According to a first aspect of the present invention, there is provided a method of random response analysis of a piezoelectric-electromagnetic hybrid energy harvester under pulsating wind excitation, the method comprising: Constructing a mechanical vibration equation based on a mechanical end dynamic balance relation of the relaxation type hybrid energy collector; Combining a mechanical vibration equation, a voltage state equation of a piezoelectric branch of a relaxation type hybrid energy collector and a current state equation of an electromagnetic branch to construct an initial electromechanical coupling equation set; carrying out pulsating wind equivalent modeling on the initial electromechanical coupling equation set by utilizing dimensionless pulsating wind speed analytic type and multiplicative noise to obtain a random electromechanical coupling equation set under the excitation of pulsating wind; Decoupling the random electromechanical coupling equation set based on harmonic transformation to obtain an equivalent electromechanical decoupling equation; and solving an equivalent machine decoupling equation based on an energy envelope random average method to obtain a random response analysis result of the relaxation type hybrid energy collector. In some exemplary embodiments, the constructing a mechanical vibration equation based on the mechanical end dynamic balance relationship of the relaxation type hybrid energy harvester includes: Constructing a structural dynamics item of a mecha