【摘要】 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 .分别考虑密度为半径的线性、二次、三次函数变化的情况 ,计算出了系统的一阶固有频率 ,并将结果与用微分求积法 ( differential quadrature method)和瑞利商方法 ( Rayleigh’s quotient method)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 .最后 ,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更多还原

【Abstract】 A numerical analysis of axisymmetric transverse free vibrations of circular and annular membranes with non uniformly varying density is presented. For the membranes with the mass density varying linearly, quadratically, and cubically with the radius, the first order natural frequencies are calculated by shooting method and are compared with the results obtained by differential quadrature method and Rayleigh’s quotient method. It is shown that the results of this paper are more accurate and the shooting method adopted is better. Finally, the free vibrations of circular and annular membranes with continuously and exponentially varying mass density along the radial directions are solved numerically and the first order natural frequencies are given.更多还原