Dynamic Characteristics Of Ring Shaped Periodic Structures Incorporating Base Movement

Ring shaped periodic structures have been increasingly used in practice,such as ring shaped gyroscope,stator and rotor of motor and gear rings.In running process,their dynamic characteristics are usually affected by base movement,so it's especially important to study their dynamic behaviors.This thesis makes microgyroscope as background and puts emphasis on the relationship between base movement and dynamic characteristics.The main contents and conclusions include:(1)A rigid-elastic coupled dynamic model incorporating base movement is built up by using energy method.This model mainly considers in-plane vibration and the rotation to coordinate axis of inertial frame is included.(2)Based on the dynamic model,analytical and numerical methods are applied respectively to get eigenvalues of smooth ring.The rules of unstable area versus supporting stiffness and rotation speed are predicted.The correctness of analytical method is verified by numerical calculation.(3)Perturbation method and superposition principle are applied to obtain the eigenvalues of ring shaped periodic structure.The real and imaginary parts of eigenvalues are classified and collected according to the sine and cosine mode of froward and backward traveling wave.According to the values of real and imaginary parts,the influences of rotation speed and supporting stiffness on nature frequency splitting and stability are analyzed.(4)Perturbation method is applied to obtain the contamination coefficients of combination instability under different classifications.The rules of the influence of base movement on mode contamination are revealed.It provides reference for practical optimization design.(5)On the basis of the dynamic model of the second chapter,for feature grouping structure,perturbation method is applied to study the eigenvalues of principal instability and contamination coefficients of combination instability.The influences of angle between two adjacent tilting springs in each group on nature frequency splitting and mode contamination are revealed by numerical calculation.Main study of this thesis is a part of the National Natural Science Foundation of China(Investigation on dynamic tuning and grouped configuration of cyclically symmetric machinery,Grant No.51675368).For ring shaped periodic structures incorporating base movement,this thesis provides theoretical reference for selections of basic parameters and suppression of nature frequency splitting as well as mode contamination.