Application Of Galerkin Meshless Method In Vibrations Of Moving Membrane

Galerkin meshless method, similar to Finite element method, is a new numerical method developed recently. Because Galerkin meshless method doesn't need any finite element grid or boundary element grid and it has high accuracy and easy postprocess, more and more attentions are paid to it. On the basis of the existing literatures, the transverse free vibration of rectangular membrane and the transverse vibration and stability of moving rectangular membrane subjected to the pull forces are investigated by Galerkin meshless method in this paper.This paper mainly includes the following contents:Firstly, the basic principle of approximate technique of Galerkin meshless method-moving least-squares is introduced. Based on the Hamilton's principle for the elastic dynamics system, the penalty parameters are introduced to satisfy the essential boundary conditions, then the differential equations of motion of the elastic system were established.Secondly, the transverse free vibrations of static rectangular membrane subjected to bidirectional pull force were investigated. By Galerkin meshless method, the equations of motion of static rectangular membrane is established. The first ten natural frequencies of the different aspect ratios and the different pull ratios of rectangular membrane with four clamped edges, three clamped edges and one free edge, two opposite free edges and other two clamped edges were calculated. It is feasible and valid to solve the transverse vibration problem of membrane by Galerkin meshless method.Thirdly, based on the study of the transverse free vibration of static rectangular membrane, the transverse vibration and stability of the moving rectangular membrane subjected to bidirectional pull force were investigated. The equations of motion of the moving rectangular membrane were established by Galerkin meshless method. Because of the effect of the moving speed, the Coriolis's matrix occur in the equations of motion, It is the important the difference in the equations of static and axially rectangular membrane. Dimensionless complex frequencies of an axialiy moving rectangular membrane with four clamped edges, three clamped edges and one free edge, two opposite free edges and other two clamped edges were calculated. The effects of the aspect ratio, the pull ratio on the transverse vibration and stability of the axially moving rectangular membrane were analyzed.