Analysis Of Dynamic Characteristics Of Nonlinear Multi-stable Piezoelectric Energy Harvester

In recent years,many scholars have focused on using piezoelectric energy capture technology to collect energy from environmental vibration and supply power for some low-power microelectronic components.Traditional piezoelectric energy harvesters are mostly linear systems,because of its narrow frequency bandwidth,it is very inefficient to capture energy in non-resonance case.In order to solve this problem,a multi-stable piezoelectric energy capture system is established to collect broadband energy.The main research contents and innovations of this paper are as follows:1.Based on the euler-bernoulli beam hypothesis and the generalized Hamilton variational principle,the distributed parametric electro-mechanical coupling equation of the nonlinear bi-stable cantilever piezoelectric energy harvester is established.The analytical expressions of system displacement,output voltage and output power are obtained by multi-scale method.Using the presented analytical solution,the influence of magnet spacing,damping ratio,acceleration amplitude of foundation excitation,electromechanical coupling coefficient,thickness ratio of piezoelectric layer and substrate,the mass of tip magnet and load resistance on the performance of bi-stable piezoelectric energy harvester under harmonic foundation excitation are studied.The results show that the excitation acceleration threshold which makes the system generate inter-well motion is related to the distance between magnets and the frequency of external excitation.There is an optimal electromechanical coupling coefficient to maximize the peak power of the system.By optimizing and adjusting the system parameters,the output power of the piezoelectric energy harvester can be increased and the range of working frequency band can be widened.2.The distributed parametric electro-mechanical coupling equation of the nonlinear tri-stable cantilever piezoelectric energy capture system is established by using the generalized Hamilton variational principle,and the analytical solution of the equation is obtained by using the multi-scale method.This investigation is focused on the effects of potential wells depth,initial starting position and material parameters on the performance of the system.The results show that choosing the appropriate initial starting position can make it easier for the system to enter the high-energy orbit and generate large inter-well motion.The potential well depth can be changed by reasonably adjusting the magnet spacing,so as to improve the energy capture efficiency of the system.The optimal load impedance of the inter-well motion increase along with the increase of thickness ratio of piezoelectric layer and substrate,and decrease along with the increase of thickness of piezoelectric beam.3.Taking into account the size effect and the rotary inertia of tip magnet,a more accurate distributed parametric electro-mechanical coupling equation of tri-stable cantilever piezoelectric energy harvester is established by using the generalized Hamilton variational principle.Analytical expressions of the dynamic response of the system are obtained by using the multi-scale method.This investigation is focused on the effects of relative position of magnets,load resistance,mass and eccentricity of the tip magnet on the performance of the harvester.The maximum output power and operating frequency range of the inter-well motion increase along with the eccentricity of the tip magnet.Increasing the mass of tip magnet can greatly broaden the working frequency range of the inter-well motion and enhance the output power of the inter-well motion.4.A tri-stable structure with asymmetric potential energy function is formed by the asymmetric arrangement of fixed magnets.A distributed parametric differential equation of motion for an asymmetric tri-stable piezoelectric cantilever beam energy capture system is established.The effects of the starting position and excitation conditions on the tri-stable piezoelectric energy harvester with asymmetric potential function are studied by Runge-Kutta method and multi-scale method.The results show that under low-frequency excitation,the tri-stable piezoelectric energy harvester with asymmetric well is more likely to generate large amplitude inter-well motion,thus improving the energy capture efficiency of the system.Considering the influence of the eccentricity and the rotary inertia of the end magnet,the frequency band width and peak output power of the energy capture system increase obviously.