摘要
本文采用打靶法数值分析了质量密度沿径向连续变化的圆形和环形薄膜的轴对称横向自由振动。针对密度以半径的二次函数变化的情形 ,计算了系统的一阶固有频率 ,并与文献 [7]中分别用DifferentialQuadratureMethod和Rayleigh’sQuotientMethod所得结果进行了比较 ,显示出本文结果的精确性和方法的优越性。然后 ,数值求解了密度沿半径以指数函数变化的非均匀圆形和环形膜的自由振动 ,给出了一阶固有频率的数值结果。
In the paper,a computational analysis of axisymmetric transversal free vibrations of circular and annular membranes with continuously varying density is presented.For the membtanes with the mass density varying quadratically with radial co_ordinate,the first order natural frequencies are obtained by shooting method and are compared with the results obtained by differential quadrature method and Rayleigh's quotient method in reference[7].It has been shown that the results of this paper are more accurate and the shooting method is better than others.The free vibrations of circular and annular membranes with continuously exponentially varying mass density along the radial direction are further solved numerically and the first order natural frequecies are also presented.
出处
《振动与冲击》
EI
CSCD
2000年第2期52-53,共2页
Journal of Vibration and Shock
关键词
连续变密度
圆形薄膜
环形薄膜
轴对称振动
continuously varying density,circular and annular membranes,natural frequency,transversal vibrations,shooting method
