摘要
旋转薄壳作轴对称自由振动的本征圆频率,在薄壳理论的精率范围内,最高只能求到量级ω～0(h-1/2),称为超高频,对应的本征模态在空间尺度上是快变的,变化指数为1/2。在时间尺度上是多重尺度的,在两端边界处存在着非完整的边界层,其频谱分为两个子系列,一个频率子系列所对应的本征模态是拟切向的,它们主要受面内边条件的影响,另一个频率子系列对应着拟法向本征模态,它们主要受面外边条件的影响。本文用奇异摄动方法得到以上结论,给出了在全部可能的齐次条件下的求解步骤,最后举了圆柱壳的数值算例。
Within the accuracy of the theory of thin shells, the calculated natural frequency of thin shells of revolution will at most be equal to the order of magnitude O(h-1/2). It is referred to as super—high frequency. In this case the principal modes are the quick function of the space variables with index of variability 1/2, and have multi—scale with respect to the time variable. Besides, the degeneracy boundary layer exists at both edge of truncated shells. Its spectrum of frequency can be broken into two sub—spectrum with corresponding modes of quasi—tangential and quasi—transverse, respectively.The solving processes for all possible homogeneous boundary conditions are presented. Finally, a numerical result of cylindrical shell is given.
出处
《应用力学学报》
CAS
CSCD
北大核心
1991年第1期40-46,129,共7页
Chinese Journal of Applied Mechanics
关键词
薄壳
自由振动
奇异摄动解
shell, vibration, perturbation, asymptotic.
