Transverse Vibration And Stability Of An Eccentric Rotating Circular Plate

In the practical engineering circular plates appear as components. By Differential Quadrature Method (DQM), the transverse vibration and stability of the rotating circular plate and the eccentric rotating circular plate are studied in this paper. The main research works are as follows:DQM is one of numerical methods of solving boundary problem of differential equation. It combines the advantages of simple and convenient calculation, high accuracy and easy implementation.The transverse vibration and stability of the circular plate is analyzed by DQM. The natural frequencies respectively with clamped edge, simple support edge and free edge are obtained, and are compared with the existing results. On the basis of above studies, the transverse vibration and stability of the spinning circular plate is studied. Based on the classical Kirchhoff plate theory, the governing differential equation of the homogeneous rotating circular plate with uniform thickness is established. The equations are discretized by the differential quadrature method, and the variation of natural frequency with clamped edge, free edge and simple support edge versus the angular speed for spinning circular plate are obtained respectively. This paper gives the critical angular speed and dynamic characteristics of the plate under different angular speed.A variety of reasons lead to errors, which make the plate rotation eccentrically. Using DQM, the transverse vibration and stability of the homogeneous eccentric rotating circular plate is studied. Based on the classical Kirchhoff plate theory, the governing differential equation of the eccentric rotating circular is established. The equations are discretized by the differential quadrature method (DQM), and the natural frequencies with clamped edge versus the angular speed for spinning circular plate are got when the eccentricity is different. This paper gives the critical angular speed and dynamic characteristics of the plate. The influence of eccentricity on the natural frequency is determined. All the results are valuable in designing and running theengineering systems.