Research On Vibration Characteristics And Support Losses Of Center-supported Micromechanical Disk Resonators

Micromechanical resonator is a kind of micromechanical structure.It realizes the conversion between electric energy,magnetic energy and mechanical energy.Because of its superior vibration function and perfect sensitivity at natural frequency,it has attracted attention in the fields of inertial sensors(gyroscope and accelerometer),biochemical sensors,radio frequency communication and etc.The micro-machined disk resonator working in bulk acoustic vibration mode has the advantages of high resonance frequency,high quality factor and high sensitivity.It is an important scheme to realize high-performance gyroscope and other devices,and is one of the key and frontier hotspots in the field of micromechanical resonator.During the process of resonator working,the quality factor is a key index to measure dynamic characteristics,while the energy loss is an important factor affecting the quality factor.In vacuum packaging,the air damping on the micro-mechanical disk resonator can be neglected,and the thermal elastic damping is greatly reduced.The support energy loss,originally thought to be negligible,has become one of the main factors limiting the quality factor.In order to reveal the mechanism of the supported energy loss in micromechanical disk resonator,it is necessary to accurately analyze the vibration characteristics,so as to obtain the analytical expression of the quality factor.Till now,only the working mode of the resonator is considered,the influence of elastic support is ignored,and there is a lack of comprehensive understanding of the vibration characteristics of the center-supported micromechanical disk resonator.Therefore,the vibration characteristics and support energy loss of the center-supported micromechanical disk resonator are studied in this paper.The main researches are as the followings:(1)To analyze the vibration characteristics of the center-supported micromechanical solid disk resonator,the influence of the support rod elasticity on the natural frequency is taken into account in the established theoretical model for the vibration of the "disk-rod" composite structure.The theoretical solutions of the low-order torsional mode,in-plane vibrational mode and out-plane vibrational mode are obtained.Among of them,the theoretical solution of outplane vibration mode of the disk supported by annular spring is derived firstly.(2)The theoretical model is validated by the finite element model by the comparisons of the results of the two models.Based on the theoretical solution predicted by the theoretical model,the influences of the sizes of the disk and the supporting rod on the vibration characteristics of the resonator structure are investigated.(3)For the actual non-solid disk resonator,the theoretical formulas of the vibrational models are derived based on the theoretical model of the solid disk resonator.The relationship between the hollow rate and the equivalent elastic modulus is systematically studied by using the equivalent stiffness method.(4)Based on COMSOL software,using perfect match layer method,the influences of the geometric sizes of the support rod,the shape of the cross section of the support rod and the concentricity of the support rod in the disk on the quality factor of resonator are investigated.The present investigation can provide a certain reference for the optimization design of the support loss of resonator.