Study On Internal Resonance Characteristics In Coupled Cantilevers For Mass Sensing

The microcantilever reflects the measurand by changes in its own static or dynamic properties.As a commonly used sensor,the microcantilever has the advantages of small size,easy integration,and easy batch manufacturing.In this paper,a new type of sensor based coupled cantilevers is designed for high-sensitivity detection of tiny molecules and particles in environmental monitoring,food safety,industrial production,etc.The mechanism of nonlinear internal resonance is studied to amplify the sensitivity.The main work and results of this paper are as follows:The structure of coupled cantilevers under magnetic force is proposed,and the spring-mass-damping model of the vibration system is established.The magnetic force of the cantilever is calculated by the magnetic dipole method,and the influence of the initial spacing of the magnets on the amplitude-frequency response is studied.The 1:3 internal resonance characteristics of the coupled cantilevers are analyzed,and the amplitude of each harmonic in the response is further calculated.The influence of the cantilever dimension on the modal frequency and the vibration response is described.The initial spacing of magnets is optimized so that the modal frequency ratio is close to the integer,which maximizes the third harmonic amplitude and yield the cantilever with greater noise immunity.The mass sensing mechanism of the coupled cantilever sensor is studied,and the sensing criteria based on the first and third harmonic frequency offsets are proposed.It is found that the information of the third harmonic can be used to amplify the detection sensitivity.To be specific,the sensitivity is more than three times the single beam without internal resonance.Moreover,the limitations of coupled cantilever sensor in sensing are analyzed,and the upper limit of mass sensing is discussed.The vibration characteristics of the coupled cantilevers are simulated and analyzed.The influence of the dimension on the modal frequency and frequency ratio is studied in detail.As a result,the dimension that satisfies the integer frequency ratio is determined.Further,the adjustment of the frequency ratio is realized by changing the clamping position.The simulation shows that the smaller the remaining clamping length,the larger the second-order to first-order modal frequency ratio.The magnetic force between two small magnets is investigated by COMSOL,which verifies the theoretical calculations.The influence of the position error of the magnet on the vibration of the coupled cantilevers is also studied.It is found that the smaller the gap between the two magnets along the vibration direction of the cantilever,the larger the amplitude of the third harmonic in response.A coupled cantilever resonator was fabricated,and the vibration characteristic test platform was built.The open-loop test of the resonator was carried out to analyze the amplitude-frequency characteristics of the coupled cantilevers under different initial spacing of magnets.The proper spacing is determined so that the energy transfer between the modes is the strongest and the third harmonic amplitude is the largest.A milligram-level mass is applied at the end of the cantilever 1,the experimental results show that the frequency offset of the third harmonic is three times that of the first harmonic frequency offset,thus improving the mass sensing sensitivity by the high frequency response under internal resonance.Through theoretical calculation,simulation analysis and experimental verification,the vibration characteristics and mass sensing performance of the coupled cantilevers under magnetic force are studied,and the high-sensitivity detection of small mass is realized,which expands the application of internal resonance in sensing.