Free Vibration Characteristics Of Rotating Thin-Wall Cylindrical Shell With Pre-installation Angle

Rotating structures are widely used in various modern machinery and daily electrical appliances,such as gas turbines,steam turbines,hydraulic turbines,various booster pumps,and electric fans,etc,so it has important practical significance for the study of the vibration characteristics of rotating systems.In engineering practice,due to the different requirements for rotating machinery,a certain installation angle is often preset when installing a rotating cylindrical shell.In this paper,the free vibration characteristics of a rotating thin-wall cylindrical shell with a pre-installed angle are studied,and the effects of various parameters on the system vibration characteristics are discussed.Specific research work includes:(1)Based on the Euler-Bernoulli beam theory and the Hamilton principle,the free vibration of a rotating hollow circular cross-section beam with a pre-installed angle was studied,and the effects of the diameter-length ratio,installation angle,and dimensionless hub speed on the first three natural frequencies of the system were analyzed.(2)Based on the deformation of the rotating thin-walled cylindrical shell and the constitutive equation of the Donnell thin-shell theory,a mechanical model of the rotating thin-walled cylindrical shell with a pre-installed angle is established,and the Hamilton principle is used to derive the The differential equations of motion and boundary conditions of thin-walled cylindrical shells are then dimersionlessly processed,and then the differential quadrature method is used to discretize the differential equations of motion and boundary conditions after dimensionlessization.The characteristic equation of the system is obtained.(3)When the installation angle and diameter-to-length ratio are not considered,the system can be regarded as a general thin-walled cylindrical shell rotating around the axis,and then the differential equation of motion of the rotating thin-walled cylindrical shell is obtained,so that the The problem of free vibration was analyzed.First,it is compared with the existing literature to verify the feasibility of the method in this paper;then the effects of circumferential wave number,rotation speed,slenderness ratio and thickness-length ratio on the imaginary part of system dimensionless complex frequency of the system are studied.(4)When considering the installation angle and radius-length ratio,the free vibration characteristics of the rotating thin-walled cylindrical shell with pre-installation angle were studied The effects of circumferential wave number,radius-length ratio,slenderness ratio,thickness-length ratio,installation angle and hub speed on the system dimensionless complex frequency are analyzed.The main conclusions:With the increase of the installation angle,the imaginary part and the real part of the dimensionless complex frequency are increasing,but when the hub speed is small,the effect of the installation angle on the imaginary part of the system's dimensionless complex frequency is tiny,and at larger non-dimensional wheel speeds,the effect of the mounting angle becomes more pronounced.