摘要
推导了运动矩形薄膜以挠度函数和内力函数表示的Von Kárman方程,对四边固支矩形运动薄膜的非线性振动特性进行了分析。首先对边界条件齐次化后的Von Kárman方程采用Bubnov-Galerkin法将时间与空间变量分离,其次对关于空间变量的偏微分方程边值问题采用DQ法求解,得到了关于时间变量的常微分方程,求得了运动薄膜非线性振动基频的表达式,最后讨论了运动薄膜的运动速度、张力比、长宽比、振动初值等对薄膜非线性振动基频和振动状态的影响。
The Von Kárman equations expressed by the deflection function and the internal force function of moving rectangular membrane are derived,and the nonlinear vibration behaviors of a moving rectangular membrane with four fixed edges is analyzed.First,for the Von Kárman equations whose boundary condations have been homogenized,the time and spatial variables are sparated by Bubnov-Galerkin method.Then,the new boundary value problems of partial differential equations are solved by DQ method,and the nonlinear ordinary differential equation about time variable is obtained.After that,the nonlinear vibrational fundamental frequency expression of the membrane is given.Finally,The effects of the moving speed,tension ratio,aspect ratio and vibrational initial value of moving rectangular membrane on the nonlinear vibration fundamental frequency and vibrational state are discussed.
出处
《机械科学与技术》
CSCD
北大核心
2010年第6期768-771,共4页
Mechanical Science and Technology for Aerospace Engineering
基金
西安理工大学度校科学研究计划项目
西安理工大学博士启动金项目资助
