Investigation On Integration Of Nonlinear Vibration Suppression And Piezoelectric Energy Harvesting

Vibration control of engineering structures is one of hot topics that attract many researchers.The approaches of vibration control include passive vibration control,active vibration control and integrated passive and active vibration control.The nonlinear energy sink(NES)can be applied to realize vibration suppression of structures,which is a method of passive nonlinear vibration control.Its essence is targeted energy transfer,that is,the primary structure of vibration energy can be irreversibly transferred into the nonlinear attachment.Part of transferred vibration energy can be transformed into electric energy,which means that vibration energy of the main structure can be recycled in nonlinear vibration reduction problems.The device composed of NES and piezoelectric material is explored.The primary structure is coupled with this device.The complexification-averaging technique(CX-A)and the 4th-order Runge-Kutta algorithm are applied to examine vibration control of the excited primary structure and to analyze the harvested energy which is transferred into NES.The integration of vibration reduction by NES and energy harvesting by the piezoelectric device is explored.The main issues of the investigation are as follows:A harmonically excited structure is coupled with a nonlinear energy sink and a piezoelectric device.The equations of motion is derived.Based on the Runge-Kutta algorithm,global bifurcation diagrams are presented for varying NES mass,nonlinear stiffness and damping.The complexification-averaging technique is employed to obtain periodic responses.The approximate analytical solutions are used to examine the effects of the excitation amplitude,NES damping,NES nonlinear stiffness and piezoelectric device's parameters on the bifurcation of the system response and output voltage response.The displacement amplitude frequency response curves of the structure and the output voltage amplitude frequency response curves of the piezoelectric device are all predicted.Besides,their stabilities are analyzed and the saddle-node bifurcation and the Hopf bifurcation are determined.The numerical simulations support the approximate analytical results.The assessment indexes of the integration of vibration reduction and energy harvesting are proposed.The averaged energy of primary structure,the modified transmissibility and the root-mean-square output voltage are all computed.Based on these results,the effects of NES nonlinear stiffness coefficients on the integration are discussed.It's concluded that quasi-periodic response of the system may contribute to realizing the integration.The NES-piezoelectric system is attached to a 2-degree-of-freedom primary system subjected to a shock load.This NES-piezoelectric system consists of a piezoelectric device and a nonlinear energy sink.The equations of motion are derived and solved by the 4th-order Runge-Kutta algorithm.This mechanical-piezoelectric system is investigated based on the percentage of energy transition and energy transition measure.The strong target energy transfer occurs for some certain transient excitation amplitude and NES nonlinear stiffness.The plots of wavelet transforms are applied to indicate that nonlinear beats initiate energy transitions between the NES-piezoelectric system and the primary system in the transient vibration,and a 1:1 transient resonance capture occurs between two subsystems.The investigation demonstrates the integrated NES-piezoelectric mechanism can reduce vibration and harvest some of vibration energy.A harmonically excited 2-degree-of-freedom primary system is coupled with the NES-piezoelectric system.Based on the complexification-averaging method,the displacement response of the primary system and the output voltage response of the piezoelectric device can be determined.Stabilities of amplitude-frequency response curves are analyzed.The Runge-Kutta algorithm is applied to examine the accuracy of the approximate analytical method.Based on the assessment indexes of the integration of vibration reduction and energy harvesting,both the approximate analytical method and the numerical method demonstrate that the integration can be realized in broadband frequency.When the response of the primary structure is quasi-periodic,the investigation explores the effects of NES nonlinear stiffness coefficients on the realization of the integration in broadband frequency.