Vibration And Stability Of Axially Moving Flexible Membrane Considered Of Aerodynamic Effects

Membrane materials are widely used in aerospace,biomedicine,mechanical instrumentation and other fields.Due to the high speed transmission,the membrane products are easy to relax,fold,drift and other unstable phenomena in the preparation process,so it is important to study the vibration characteristics and stability of a moving membrane.In this paper,the dynamic characteristics of linear free vibration and nonlinear forced vibration of flexible membrane under different working conditions considered of aerodynamic effects are studied.The main contents are:(1)The vibration characteristics of an axially moving flexible membrane considered of aerodynamic effects is analyzed.Based on Hamilton's principle,the motion differential equation is established,and normalized in dimension.An analytical method is used to solve the equation in the case of simply supported on four sides.The effects of tension ratio,dimensionless air resistance and length-width ratio on the dimensionless frequency of the moving membrane are analyzed.The critical rate of instability,the stable operating interval of the moving membrane is obtained.(2)The vibration characteristics of variable density membrane considered of aerodynamic effects under nonuniform tension is analyzed.Based on Hamilton's principle,the vibration differential equation of the moving membrane is established,which is normalized in dimension and solved by differential quadrature method.The effects of dimensionless air resistance,tension ratio,length-width ratio and other parameters on the dimensionless frequency of the membrane with variable density are analyzed,and the stable operating range of the membrane is obtained.(3)The dynamic characteristics of nonlinear forced vibration of an axially moving flexible membrane considered of aerodynamic effects is analyzed.Based on Von Karman's large deflection theory and Hamilton's principle,the motion differential equations of the moving membrane are established.After proceed dimensionless,The Bubnov-Galerkin's method is used to discrete the motion differential equations,and the fourth-order Runge-Kutta method is used to solve the equations.The bifurcation diagram,phase diagram and Poincare maps of the moving membrane system are obtained.The effects of dimensionless velocity,amplitude of external excitation force and other parameters of the membrane system are analyzed,and the periodic motion interval of the moving membrane is obtained.