非均匀张力作用下运动薄膜的稳定性研究

摘要

The dynamic characteristics and stability of the moving membrane under non-uniform tension are studied in this paper.The axially moving membrane is taken as a model.The calcula-tion model of the moving membrane under non-uniform tension is established.The motion differ-ential equation of the membrance under inhomogeneous tension is derived,and the complex spe-cial value equation in motion system is established using differential quadrature method.The rela-tion curves of the aspect ratio,speed and tension variation coefficient of the real part and mem-brane of the complex frequencies in the system can be obtained through numerical calculation. The effects of the tension variation coefficient,the aspect ratio and the speed on the dynamic characteristics of the membrane are analyzed.%文章研究了非均匀张力作用下运动薄膜的动力特性及其稳定性问题.以轴向运动薄膜为模型,建立非均匀张力作用下运动薄膜的计算模型,推导运动薄膜在面内非均匀张力作用下的运动微分方程,采用微分求积法,建立运动系统的复特征值方程.通过数值求解,得到了系统复频率的实部与薄膜长宽比、速度及张力变化系数的关系曲线,并分析了张力变化系数、长宽比和运动速度等参数对薄膜动力特性及稳定性的影响.