Study On Mode Localization Based Mass Detection With A Detuned Cantilever Array

In recent years,with the rapid development of MEMS technology and the urgent need for tiny mass detection,micro-cantilever beam sensors have attracted extensive research interest in the field of sensing and detection because of their high sensitivity,small size and easy integration.The traditional frequency-shift-based beam mass-sensitive sensors are difficult to achieve high sensitivity detection of small molecules such as viruses,so there is an urgent need to explore a new mass-sensitive mechanism to achieve more efficient and high-sensitivity detection with high accuracy.Among them,the mode localization phenomenon uses the amount of change in the overall modal vibration of the resonator as the output,which can achieve a sensitivity increase of 2～3 orders of magnitude relative to the amount of frequency shift.However,manufacturing errors in the actual processing make it difficult to guarantee the strictly required initial tuning state of the mode localization,which is one of the main reasons why the application of this phenomenon is limited.Therefore,this paper takes a three-degree-of-freedom coupled cantilever beam array as an example to study the influence law of the initial detuning of the structure on the energy distribution,and proposes a high-precision mass detection method for detuned structures based on mode localization.The research contents of this paper include as follows:An equivalent physical model of the three-degree-of-freedom weakly coupled detuned beam array is developed,and the manufacturing errors on the resonant oscillators are equated to the superposition of stiffness and mass perturbations,and the manufacturing errors in each dimension are derived as a function of the physical parameters of the structure.The system matrix of the detuned structure is reconstructed using the Lanczos algorithm assisted by the inverse eigenvalue method,and then the calibration of the manufacturing error on all resonators is achieved by transforming the equivalent stiffness and equivalent mass in the matrix into variables related to the manufacturing error only at the same time.The change form of eigenvalues and eigenvectors for adding the mass disturbance to be measured to the geometric manufacturing error structure is analyzed using the first-order regression method,and the calibrated manufacturing error is equated to the determined disturbance to give a high-precision correction scheme for manufacturing error during quality inspection,and the corrected sensing parameters include not only the mode vector changes of modal localization concern,but also the first three orders of eigenvalue changes.At the same time,the small detuning range required by the mode localization phenomenon is defined in the field of manufacturing error based on the finite element simulation software.The influence of geometric manufacturing errors on the sensing output signal in each dimension is studied.By comparing the linear range and sensitivity of mass detection in each case,it is found that the influence of width error on sensing is much smaller than that of other dimensions,the influence of detuning on the middle beam is likewise much smaller than that on the side beam,and the influence of detuning on the coupling structure is much smaller than that of detuning on the resonant oscillator,and the length error of the resonant oscillator is taken into account in the comprehensive comparison of the processing process.The main object of study.At the same time,the "v" sensing phenomenon of the sensing process is found,which can broaden the linear interval of sensing while ensuring high sensitivity,and this provides ideas for further optimization of the structure and utilization of the detuning caused by manufacturing errors.Finally,an experimental test system was built to verify the three localized eigenmodes of the error-free structure in theory and simulation,and to verify the effectiveness of the error calibration scheme and error correction scheme,as well as to verify the occurrence of the "v" sensing phenomenon,and to summarize the reasons for the difference between the experimental and simulation values.The research work of this paper provides some guidance for high accuracy,high sensitivity and wide linearity range of micro mass detection in resonant structures with manufacturing errors.