The Transverse Vibration And Stability Of An Axially Moving Membrane

In this paper, the transverse vibration and stability of an axially moving rectangular membrane, subjected to two direction pull forces, are analyzed. The main research work is as follows:(1) By the analysis of force-balance of an axially moving rectangular membrane elements with four edges fixed, the differential equation of motionfor axially moving rectangular membrane are derived by D' Alembert's principle. The vibration differential equations of moving membrane are converted into dimensionless vibration mode equations with introduction of dimensionless quantities and assumption of main vibration form, which is a production between exponent function of time and vibration mode function. On the basis of studies above, the dynamic behaviors and stabilities of axially moving membrane are calculated by analytical method. In the case of constant axially moving speed, the effect of pull ratio λ and aspect ratio r on dimensionless complex frequency ω is analyzed.(2) The transverse vibration and stability of an axially moving rectangular membrane with four edges fixed, three edges fixed and one edge free, two edges fixed and two edges free are studied by the differential quadrature method. Thebasic equation treated the differential quadrature method is a NxN order linear algebra equations taking deflection of node as unknown quantity. The eigen-equations. included pull ratio, aspect ratio and moving speed, are obtained. In the case of constant axially moving membrane, the effect of pull ratio A and aspect ratior on dimensionless complex frequency ω is discussed. Compared to other methods, differential quadrature method has much less computing efforts due to avoiding a large series of numerical integration, and the much lower the order of the equation to be solved.(3) For the large deflection of axially moving membrane, based on the studies of (1) and (2) above, Von Karman's large deflection equations of axially moving membrane are derived using elastic theory, and have analyzed an axially moving rectangular membrane with four edges fixed using Bubnov-Galerkin method.