| Micro/Nano-Electro-Mechanical System(M/NEMS)is an industrial technology that integrates microelectronics technology and mechanical engineering,and its operating range is in the micro/nano scale.As our country's process of becoming an independent and innovative country further deepens,M/NEMS,as a disruptive technology,has been widely used in many fields such as communications,consumer electronics,transportation,and medical health.Especially with the rapid development of mobile communication technology,M/NEMS is used as a highly sensitive sensor in the Internet of Things(IoT)system in the era of big data to realize the sound,light,heat,electricity,mechanics,and mechanics of the target object.It plays a key role in the real-time collection and monitoring of various required information such as chemistry,biology,and location.As one of the pivotal components of MEMS,the micromechanical resonator is a mechanical structure that can convert electrical energy,light energy,magnetic energy or external mechanical energy with its own vibration,and it has a small geometric size,good electrical performance,and material selection.The advantages of flexibility and structural design,as well as large-scale production and low-cost economy,contain huge application prospects.Since the 21st century,micro-nano processing technology has developed rapidly,and micro-mechanical resonators have been more miniaturized and integrated.In addition,mechanical resonators made of one-dimensional and two-dimensional materials in the past ten years have been able to detect and quantum information with ultra-high precision.With the vigorous development of the processing field,complex nonlinear behaviors and rich mode coupling phenomena inevitably appear when resonators work at the micro-scale.How to avoid their damage to the device performance or use them to achieve performance improvement is currently at problems in the field that need to be studied urgently.From the perspective of dynamics of micromechanical resonators,this thesis studies and explores micromechanical resonators around nonlinear behavior and mode coupling.Based on related disciplines such as materials science,microdynamics,microstructure,optics,micromechanics,and instrument science,guided by theoretical research,combined with finite element simulation and numerical simulation,the experimental realization and theoretical explaination of almost all nonlinear phenomena in the field of resonator research are depicted,including mode soft/hardening,parametric coupling,internal resonance,degenerate four-wave mixing,and strong coupling inducing mode splitting,acoustic frequency comb,mechanically induced transparency,bifurcation and chaos,etc.The thesis provides help and reference for enriching the theoretical research and application of the nonlinear behavior and mode coupling of micromechanical resonators.The main research contents of the thesis include:Chapter 1:Introduction of the background and research significance of the subject,briefly summarization the development history and application fields of micromechanical resonators,and then introduces the research status of the nonlinear behavior and mode coupling behavior of micromechanical resonators.The development direction of the resonator is briefly introduced,and finally the research purpose and main research content of this thesis are proposed.Chapter 2:The linear mode coupling of the micromechanical resonator is studied.The ?-shaped mechanical resonator was designed by finite element simulation.By comparing the simulation results with the actual experimental results,the feasibility of the ?-shaped mechanical resonator using a pair of adjacent orthogonal modes for mode coupling research was proved.By numerically solving the vibration equation of the system,the feasibility of realizing the degeneracy of the two modes by adding a coupled gyro term to the system is proved.The shape of the?-shaped mechanical resonator is adjusted by the laser that excites the vibration,so that the in-plane resonance mode without out-of-plane vibration component can be detected by the Doppler vibrometer at the same direction as the out-of-plane mode.By introducing the steady-state heating laser to adjust the asymmetric shape of the?-shaped mechanical resonator and the mode frequency,the linear coupling of the studied orthogonal modes is realized,and the degeneracy of the orthogonal modes is realized at the same time.It is found that the quality factor of the ?-shaped mechanical resonator is effectively improved after the orthogonal mode degeneration,which can be increased by up to 7.7 times compared with the initial state.The attraction,degeneracy and remote operation of the two orthogonal modes in the?-shaped mechanical resonator studied in this part are conducive to the development of high-precision gyroscopes.Chapter 3:The two-mode parametric coupling of SiNx membrane resonator periodically driven by optical fields is studied.After the membrane resonator is irradiated by the laser,it is dominated by the thermal stress generated by the thermal effect of the laser,and the overall trend of its mode resonance frequencies are continuously increasing.Due to the influence of the localization of the modes,the frequency change rate of each mode after being irradiated by the laser is different,making it possible for the laser irradiated membrane resonator to realize the mode crossing the anti-intersection point.By periodically driving the target mode of the membrane resonator to cross the anti-intersection point,the parametric coupling of the two modes is realized,the hybrid peak due to Landau-Zener-Stuckelberg-Majorana(LZSM)interference is observed in the frequency-amplitude response spectrum.The LZSM interferometry method has been successful in the quantum system.The LZSM interferometer based on the mechanical resonator couples the physical quantity to be measured with the external field such as light field,electric field or magnetic field,which has great applications for realizing high-precision detection and sensing.potential.Chapter 4:The nonlinear internal resonance mode coupling of micromechanical resonators is studied.Through the"Euler-Bernoulli beam”model,we found that the third-order and fourth-order out-of-plane resonance modes of the microcantilever naturally have a frequency proportional relationship close to 1:2.We further verified the relationship for any size and materials of microcantilevers are ubiquitous.The third-order and fourth-order out-of-plane resonance modes of the microcantilever resonator will produce internal resonance under large displacements,because the frequency relationship between them is close to 1:2.The typical phenomena of internal resonance such as amplitude saturation and frequency saturation were realized in the experiment.When internal resonance occurs in the third and fourth modes,an absorption band appears on the frequency-amplitude curve due to the nonlinear coupling of the modes.The absorption band is due to the Fano interference formed by the mode coupling near the fourth mode.We constructed the coupled vibration equations of the third-order and fourth-order out-of-plane resonance modes of the microcantilever,and solved them numerically by the method of rotating wave approximation,and the obtained results are in agreement with the actual experiments.Chapter 5:The nonlinear mode coupling under parametric excitation based on internal resonance is studied.Parametric excitation is applied in the 1:2 internal resonance system.Due to the strong nonlinear mode coupling induced by the internal resonance,significant degenerate four-wave mixing can be achieved in the microcantilever resonator with a lower quality factor.The critical pump intensity required for multi-mode nonlinear coupling obtained by applying parametric excitation in a 1:2 internal resonance system can be obtained by numerically solving the nonlinear Mathieu equation.The degenerate four-wave mixing in the microcantilever resonator can realize such as mechanically induced transparency,mode splitting,and acoustic frequency combing.The acoustic frequency comb obtained by internal resonance combined with parametric excitation in the microcantilever resonator has a quality factor of about 37000,which is much higher than the quality factor of the intrinsic mode of the microcantilever due to the efficient energy transfer between the internal resonance modes.Chapter 6:Summarize the work and research innovation of the full text,and prospect the content that can be further studied.The main innovations of this thesis include:(1)A ?-shaped mechanical resonator was designed and fabricated,which realized a pair of orthogonal modes linear coupling with asymmetric coupling term.Based on the finite element simulation,the mechanism that the orthogonal modes of the resonator can be excited and detected at the same direction is analyzed,and a motion equation with asymmetric coupling terms is constructed,which theoretically proves the feasibility of mode locking under linear coupling.Finally,the mode frequencies of the resonator are controlled by the photothermal effect of the laser.The locking of the linear coupling mode and the optimization of the Q factor of the resonator are realized,which provides a new idea for the research of Q factor control in the field of micromechanical resonators.(2)Through the parameter adjustment of the silicon nitride film mechanical resonator by the optical field,the non-adiabatic transformation of the mode under linear coupling is realized.Based on the Landau-Zener tunneling mechanism,the modulated laser drives the mode of the resonator to oscillate back and forth near the anti-crossing point,and the parametric coupling of the modes is obtained.The hybrid peak with a stable phase relationship on the frequency-amplitude curve can be expected to be used for multi-mode high-precision sensing detection with widened frequency.(3)For the first time,the 1:2 internal resonance of the third and fourth:flexural modes of the microcantilever beam resonator is realized.Aiming at the problem of strong mode coupling when internal resonance occurs,the"Euler-Bernoulli beam"model and finite element simulation are used to reveal the inherent law that the frequency ratio of the two low-order modes of the microcantilever resonator is close to 1:2,and the frequency response characteristics of the microcantilever when internal resonance occurs are observed experimentally.The amplitude response solution of the motion equation when the internal resonance occurs in 1:2 is given by the rotating coordinate approximation(RWA),and the experimental results are verified by numerical methods.It provides a reference basis for the wide application of internal resonance mode coupling in micromechanical resonators.(4)The dynamic characteristics of the internal resonance system under parametric excitation are studied for the first time.Starting from the self-parametric excitation characteristics when the 1:2 internal resonance occurs,for the first time,an external pump is introduced in the internal resonance system to achieve parametric resonance,which clarifies that the high efficiency limitation of the internal resonance system on the input energy is to achieve strong multi-mode coupling under parametric excitation.The reason for the coupling is that the parametric excitation threshold required for the system to enter the multi-mode strong coupling is predicted by the nonlinear Mathieu equation.The degenerate four-wave mixing of the microcantilever resonator is experimentally realized for the first time,and obtaining the mode splitting,frequency pulling and locking,amplitude suppression,acoustic frequency combing,mechanically induced transparency,bifurcation,chaos and other phenomena of great research value and their generation mechanism is analyzed.This research has made a complete demonstration of the nonlinear strong mode coupling of micromechanical resonators and the application of internal resonance systems,and provided a new idea for the high-efficiency parameter manipulation of micromechanical resonators. |
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