| Resonant sensors have been widely used in environmental monitoring,biological and medical fields for the detection of small substances due to their small size,simple structure and easy integration.At present,the resonant sensors based on the frequency deviation mainly improve the detection sensitivity of the sensor in a certain range by optimizing the shape and size of the vibrating element and using high-order resonance,but these methods are still difficult to meet the detection requirements of high sensitivity for small mass.In order to improve the quality detection sensitivity of the nonlinear resonance sensor,a new method for detecting the quality of the resonance sensor is proposed based on the principle of super-harmonic resonance frequency multiplication and amplification in nonlinear vibration.In this paper,by using the principle of super-harmonic resonance in nonlinear vibration,the detection model of automobile exhaust particulate matter is established,and a method for improving the detection sensitivity of small masses is studied.The main research work was as follows:Firstly,a particle detection method based on the coupling structure of fixed beams was studied.The particle adsorption method for uniform adsorption,the establishment of the clamped beam coupling structure of the particle detection model and dynamic equations of the model,according to the boundary conditions of the clamped beam and the vibration mode function,the dynamic equation of modal orthogonalization processing,then the method multiple scales are applied to processing is applied to solve the dynamic equation of the model of vibration amplitude frequency response equation obtained.The nonlinear vibration characteristics of the test model were analyzed by a numerical example,and the vibration simulation analysis of the model was carried out by COMSOL software.Secondly,a particle detection method-considering surface stress cantilever coupling structure is studied.To further analyze the influence of the adsorption layer on the beam frequency and make the research results closer to the actual engineering application,the particles are absorbed by the uniform distribution,and the surface stress generated by the particles after uniform adsorption is considered.To establish the structure of the cantilever beam-coupled vehicle exhaust particulate detection model and the dynamic equation of the model,according to the boundary conditions of the beam and the vibration mode function,the dynamic equation of modal orthogonalization processing,then the method of multiple scales applied processing applied to solve the dynamic equation of the vibration amplitude frequency response of the model equation is obtained.The nonlinear vibration characteristics of the test model were analyzed by a numerical example.To verify the frequency-doubling mechanism of the super-harmonic resonance in the nonlinear vibration,the vibration equivalent test of the cantilever coupling structure with a glial adsorption layer was set up.Finally,a cantilever coupling structure of vehicle exhaust particulate matter detection method is studied.The theoretical calculations and experimental verification above are combined with the vehicle exhaust particle catcher,and the COMSOL multi-physical field simulation analysis of the two-dimensional single-channel particle catcher is carried out.automobile exhaust particulate attachment methods for the free end focus,set up the structure of the cantilever beam-coupled vehicle exhaust particulate detection model and the dynamic equation of the model,according to the boundary conditions of the beam and the vibration mode function,the dynamic equation of modal orthogonalization processing,then the method of multiple scales applied to processing are applied to solve the dynamic equation of The amplitude-frequency response equations of the low-frequency beam and high-frequency beam with natural frequency ratio close to 1:3 are obtained.The nonlinear vibration characteristics of the test model are analyzed by numerical examples.To verify the frequency-doubling mechanism of super-harmonic resonance in nonlinear vibration,a vibration test of the cantilever coupling structure is constructed.The results show that the nonlinear vibration characteristics of the automobile exhaust particulate matter detection model will change by changing the relevant parameters of the system,that is,with the increase of the system damping,the vibration amplitude of the low-frequency beam and the high-frequency beam will gradually decrease.With the increase of the external excitation in the low-frequency beam,the vibration amplitude of the low-frequency beam and the high-frequency beams will also increase.With the increase in the mass of particles attached to the low-frequency beam,the vibration frequencies of the low-frequency beam and the high-frequency beam decrease,and the vibration amplitude and frequency changes of the high-frequency beam are greater than those of the low-frequency beam.Through the experiment of automobile exhaust detection model,it can be found that when the super-harmonic resonance occurs in the high-frequency beam,the main resonance frequency of the low-frequency beam decreases with the increase of the mass of the detected particulate matter,but the frequency offset is small and the sensitivity is low,and the third super-harmonic resonance frequency of the high-frequency beam decreases with the increase of the mass of the detected particulate matter,but the frequency offset is large and the sensitivity is high;The third super-harmonic resonance frequency of the high frequency beam is three times of the main resonance frequency of the low frequency beam,and the offset of the frequency also meets the triple relationship.The principle of super-harmonic resonance in nonlinear dynamics is used to realize the multiplication of mass detection sensitivity,which provides theoretical support for improving the detection sensitivity of automobile exhaust particles. |
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