【作者】 刘占芳； 张凯； 颜世军；

【Author】 Liu Zhanfang,Zhang Kai,Yan Shijun (School of resource and environmental science,Chongqing Universtity,Chongqing,400030)

【机构】 重庆大学资环学院；

【摘要】 应用拉格朗日方程于离心场中振动系统得到二阶常微分动力学有限元方程组,其中科氏矩阵为反对称矩阵表示运动耦合,离心软化和几何刚化矩阵分别对应了系统的刚度减小和增大。对于离心场中有q个自由度的振动系统,系统存在q对共轭的复特征值和复特征矢量。对复模态矢量进行复分解,得到系统自由振动的实空间通解形式,避免了取通解中复共轭常系数的传统方法。证明了单一复模态矢量对应着振动系统的q维空间的椭圆型运动形式。当振动系统退化为两自由度的质量弹簧阻尼系统时,给出了系统特征频率的解析形式和系统单一复模态的质点圆螺旋耦合运动轨迹。更多还原

【Abstract】 A second order ordinary differential dynamic finite element equations for vibration system with two degrees of freedom in a centrifugal field is given out based on Lagrange equations.Coriolis matix is a skew-symmetric matrix and it denotes system motion coupling.Centifugal softening matrix makes system stiffness decrease and geometric stiffening matrix is on the contrary.There are q pair conjugated eigenvalues and complex eigenvectors as the vibration system in a centrifugal field.System free vibration general solution in the real space is obtained by complex decomposition of complex modal vectors, avoiding applying the ordinary method which makes the constant coefficients conjugate.And it is proved that individual complex modal vector of vibration system in a centrifugal field is associated with structure ellipse type motion in q-dimensional space.As a mass-spring-damping system with two degrees of freedom in a centrifugal field,analytical form of system eigenfrequencies and individual complex modal vector associated with helix circular coupling motion of mass are get.更多还原