Research On Induction Mechanism Of Mass Sensors Via Nonlinear Coupled Cantilever System

Micro-cantilever mass sensor based on resonance principle has become a hotspot in recent years due to its advantages of high resolution,high stability and easy integration.However,due to the limitation of technology and detection environment,it is difficult to measure small molecule accurately under the condition of a certain structure size.Therefore,the sensitivity and resolution of the resonant cantilever based mass sensor are improved by a new method of nonlinear coupling sensing in this study.Considering the different sensing characteristic in a series of structure scale via nonlinear coupling structure,and further accomplish the different market demand of the array of manufacture and the low cost of small batch manufacture.This study suggest mass sensing verification in weak coupling cantilevers via synchronization and mass sensing verification in strong coupling cantilevers via internal resonance.In the aspect of synchronization,a physical model of coupled oscillators is established.And we derive the formula of synchronized region via nonlinear averaging method,analyse the effect factors of synchronized region and the range of application.In the aspect of internal resonance,we analyse the nonlinear characteristic of super-harmonic resonance of single cantilever and internal resonance of coupling cantilevers.We proved the internal resonance with lower driving frequency can realize a higher amplitude compare with 1/3 primary resonance of super-harmonic via Fourier transform,hence,it was beneficial to the improvement of the sensor sensitivity and resolution.Based on the nonlinear phase locking principle,we design the coupling beamstructure with integer resonant frequency ratio.Moreover,the coupling part is improved into a three-segment symmetrical structure design,which reduces the deflection of the high-order resonant coupling beam.And we further optimizes the structure design of the coupling part according to the simulation results.We established the relationship with the structural characteristics of the coupling part and the coupling strength.Finding the proportion of the structure dimension and coupling strength via the fitting curve of the simulation results.Furthermore,we design a series of cantilevers according to the characteristics of the resonant cantilever detect molecule through the surface sensitive film.The relationship between the detected concentration and frequency shift is obtained by simulation.It provides a reference for the structural design of coupling beam with high sensitivity.Based on two sensing methods of synchronization and internal resonance,two experimental schemes of micro and macro are established.Micro experiment:single-crystal silicon-based coupling beam structure was fabricated by micro processing technology.By applying pg order mass perturbation at the tip of the low-frequency beam,the effects of mass perturbation on the amplitude-frequency characteristic curve,synchronized region,and super-harmonic region under the condition of weak coupling are studied experimentally.The experimental results show that after applying small mass perturbation(8.609 pg polystyrene microspheres),low-frequency cantilever under the primary resonance frequency excitation of synchronized coupling beam have a obvious frequency shift.(low-frequency cantilever shift 6.13 kHz,high-frequency cantilever shift 12.26 kHz),but the frequency shift of super harmonic excitation frequency beam almost invisible(0.1 kHz)and the area and shift of the synchronized area are larger than super-harmonic area.The experiment results proved that the synchronization can realize frequency enhancement,improve the sensitivity of the sensor and have a wider detecting range.Therefore,in the case of sensing,synchronization is more suitable than super harmonic.According to the frequency shift of synchronized coupling beam,the calculated mass disturbance is 8.792 pg,which is very close to microspheres,the error is only 2%.Therefore,it can be considered that the micro-coupled cantileverbeam can realize pg order mass sensing.Macro aspect: the structure of brass based coupling beam is fabricated by using precision machining technology.The nonlinear soft spring characteristic of single brass based beam is proved by experiment,but its third super harmonic peak(1/3main resonance frequency excitation)is very weak,which cannot be used in mass sensing.However,The third harmonic peak of the high frequency beam is obvious when the low frequency beam is excited by the main resonance frequency in internal resonance.The trend is the same as the numerical simulation results in chapter 2.Fourier transform is used to obtain the range of excitation frequency,that is,the range of internal resonance region,where the third harmonic frequency peak is higher than first one.The results show that internal resonance coupling beam has larger frequency shift and higher sensitivity than the single beam under low frequency excitation.In addition,the experimental results show that the linearity of mass sensing is better when the coupling strength increased(the length of the coupling part increased)and the internal resonance region increased.The coefficient of coupling strength was defined as C.It was proved by analysis and calculation that there was a stronger consistency between coupling strength coefficient and linearity in macroscopic coupling beam.When the coupling coefficient is increased,the linearity increased and the sensing performance improved.The coupling coefficient and its calculation method have certain guiding significance for the design of the coupling part of the macroscopic coupled beam.