Electromechanical Coupling Model Of Cantilever Piezoelectric Energy Harvester And Influence Of Parameters On Performance

In the past few decades,some researchers some researchers have focused on harvesting energy from environmental vibrations by using piezoelectric effect in order to provide power for the requirements of small electronic components such as wireless sensor networks.The mathematical models of piezoelectric energy harvesters with various geometric conFig.urations were established and verified by experiments.The most common conFig.uration of energy harvester is cantilever structures.The following contents are explored in this research:According to the internal energy of the piezoelectric linear continuum and using the Legendre transform,the four different constitutive equations and their corresponding thermodynamic potentials of electric-mechanical coupling are deduced.The Hamilton variational principle of the electro-mechanical coupling problem is demonstrated to be equivalent to the differential equations of motion of electro-mechanical coupling,the divergence equation of the electric displacement,the boundary conditions of the forces and electric charge.According to the assumption of Bernoulli beam,the general expressions of the Hamilton variational principle of piezoelectric laminated beams are given.For the cantilevered energy harvester with finite-sized tip mass,taking into account the influence of eccentricity and inertia of the tip mass,and using the Hamilton variational principle,the distributed parameter type electromechanical coupled differential equations of motion has been established for piezoelectric bimorph energy harvester.Using the separation variable method and the vibration mode function of the beam,the electro-mechanical coupling differential equations of motion is transformed into a set of ordinary differential equations.Under harmonic base excitation,the analytical solutions have been presented for the electro-mechanical coupling equation of the cantilever piezoelectric energy harvester carrying a finite-size tip mass.The analytical expressions have been obtained for the displacement,current,voltage and power of the piezoelectric energy harvester.Using the presented analytical solution,the influence of the load resistance and the eccentricity of the tip mass on the tip displacement and harvesting energy of the energy harvester have been analyzed.For the cantilevered energy harvester carrying a dynamic amplifier,the influences of the eccentricity and the moment of inertia of the finite-size tip mass have been considered.Using the Hamilton variational principle,the modified distributed parameter type electromechanical coupled differential equations of motion and boundary conditions have been established for piezoelectric bimorph energy harvester carrying a dynamic amplifier.Using the proposed differential equations and boundary conditions,the analytical expressions of the mode shape function and the natural frequency of the cantilever beam with a dynamic amplifier and the two orthogonality conditions of the mode shape function are presented.Using the separation variable method and the proposed mode function,the electro-mechanical coupling differential equations of motion are transformed into ordinary differential equations.Under harmonic base excitation,the analytical solutions to the electro-mechanical coupling equations have been presented for the cantilevered piezoelectric energy harvester with a dynamic amplifier.The analytical expressions have been obtained for the displacement,current,voltage and power of the piezoelectric energy harvester carrying a dynamic amplifier.The effects of load resistance,eccentricity of the tip mass,and stiffness of the dynamic amplifier on the tip displacement and harvesting energy of the energy harvester have been analyzed.The numerical results show that the eccentricity and the moment of inertia of the tip mass significantly affect the accuracy of the analysis.By properly selecting the power amplifier and the tip mass design parameters,the energy harvesting efficiency of the energy harvester can be significantly improved.The modified model can more accurately predict the energy harvesting efficiency of the cantilever piezoelectric energy harvester with a dynamic amplifier.A new-type dynamic amplifier,which is composed of translational and rotational restraint spring-mass system,is proposed.The influences of eccentricity and inertia of the masses,and stiffness coefficient of translation and rotation constraints are considered.Using the Hamilton variational principle,a distributed parameter type electromechanical coupled differential equations of motion and boundary conditions have been established for piezoelectric bimorph energy harvester with a new-type dynamic amplifier.The analytical expressions of the mode shape function and the natural frequency of the cantilever beam with the new-type dynamic amplifier and two orthogonality conditions of the mode shape function are proposed.Under harmonic base excitation,the analytical expressions have been obtained for the displacement,current,voltage and power of the piezoelectric energy harvester with a new-type dynamic amplifier.The effects of the load resistance,the eccentricity of the tip mass,and the ratio of the translational and rotational restraint stiffness of the new-type power amplifier on the tip displacement and the harvesting energy efficiency of the energy harvester carrying a new-type dynamic amplifier are analyzed.The numerical results show that reasonable choice of dynamic stiffness of the power amplifier can improve the energy harvesting efficiency of the energy harvester and reduce the resonant frequency of the energy harvester.