Investigation On Mechanical Properties Of Grouped-Topological Ring-Shaped Periodic Structures

Ring-shaped periodic structure is widely used in engineering fields to fulfill the functions of driving,transmission and bearing etc.When subjected to operating load,the structure usually produces mechanical problems that affect performance,such as uneven stress and natural frequency splitting.In this thesis,the static and dynamic characteristics of grouped-topological ring-shaped periodic structure are studied by using theoretical and experimental methods.Main contents are as follows:Aiming at the solution of stress and deformation of the structure,a mathematical model subjected to a radial force is established by D’Alembert’s principle,and the analytical solutions of stress and deformation are formulated.For the case of complex radial forces,the distributions of stress and deformation are calculated by superposition method.The relationships between topology,parameters and static characteristics are obtained.The natural frequency splitting of the structure is studied,and the analytical conditions for eliminating the splitting are given.Based on Hamilton’s principle,the inplane vibration model incorporating geometric nonlinearity is established.The analytical results of the natural frequency are given,and the analytical conditions for eliminating the splitting are obtained.The relationships between the number of groups,the number of features in one group,the inclined angle in the group,radial stiffness,radial force and the natural frequency splitting are presented.In order to validate the analytical results,especially the influence of radial force on the natural properties,a modal test rig is built up,where the ring is supported by equal-stiffness springs in order to decouple the radial force from the stiffness.The effect of the radial forces on the natural properties is measured by using Laser Dopple Velometer,and the natural frequency splitting law is validated.