Study On Internal Resonance Based Energy Transfer Mechanism In Coupled Cantilevers

Cantilever sensor has attracted much attention due to its good performance and strong adaptability.Based on the application requirements of increasing the adsorption area,this paper takes the π-type coupled cantilever as the research object to explore the energy transfer characteristics between harmonics of the cantilever in the internal resonance,and analyzed the effect of different system parameters on energy transfer.The results show that rationally varying the coupling stiffness has the potential to optimize energy transfer and improve detection resolution.In this paper,the main contents and results are as follows:The frequency shift characteristics of the π-type coupled cantilever and the rectangular coupled cantilever are compared,and the structural rationality of the π-type coupled cantilever is verified.The physical and mathematical models of the π-type coupled cantilever are established,and the nonlinear motion equations are theoretically deduced by the multi-scale method.The nonlinear vibration steady-state equations of the theoretical group and the control group are obtained.Through numerical simulation,the amplitude-frequency characteristic curves of the main harmonics in the theoretical group and the control group are compared.The energy transfer mechanism between harmonics in the internal resonance is clarified.According to the operability of the experiment,the excitation,linear coupling stiffness and nonlinear coupling stiffness are as the research objects to explore their effects on energy transfer.Base on the characteristics of energy transfer between harmonics,the energy transfer region is defined,and its nonlinear characteristics are studied.Through numerical simulation,the variation of the amplitude of the main harmonics and the amplitude ratio of the third harmonic to the first harmonic in the high-frequency cantilever with excitation,linear coupling stiffness and nonlinear coupling stiffness are obtained,and it is found that increasing the excitation will increase the harmonic output,which is caused by the increased energy input into the system,but the change of amplitude ratio in high-frequency cantilever is small.And the increase of the linear coupling stiffness will reduce amplitude of the third harmonic and amplitude ratio in the high-frequency cantilever.The influence of nonlinear coupling stiffness on harmonic amplitude is not linear,and there is an extreme value.At this extreme value,the energy transfer is the most,and the third harmonic amplitude and amplitude ratio in the high-frequency cantilever reach the maximum,which indicates that the nonlinear coupling stiffness can effectively adjust the energy transfer.Based on these results,the regulation mechanism of energy transfer is proposed.The geometric dimension of the π-type coupled cantilever is determined by simulation,and the experimental platform for energy transfer is built.The output responses of the low-frequency cantilever and the high-frequency cantilever are analyzed,and it is verified that there is energy transfer in the internal resonance.The harmonic amplitude-frequency characteristic curves with and without coupling are analyzed,and the energy transfer mechanism between harmonics is verified.By changing the excitation voltage and the geometric dimension of the coupling part,the regulation of the excitation and coupling stiffness on the energy transfer is verified.It is proved that the appropriate system parameters are conducive to promote the energy transfer,enhance the output response of the third harmonic and improve the amplitude ratio in the high-frequency cantilever.