本研究探討一具有隨機性幾何缺陷的複合層圓柱殼之非線性振動行為 ,圓
柱殼的控制方程式採用von Karman-Donnell非線性理論的方程式,其隨機
性幾何缺陷以高斯隨機場(Gaussian random field)來描述,並利用其平均
值函數(mean function)及自方差函數(autocovariance function)來做數
值模擬.設定圓柱殼非線性振動之近似解為多模(multimode)型式且滿足協
調方程式(compatibility equation)及所有邊界條件,利用Galerkin 方法
可得到一組為時間函數的非線性常微分方程式,並以諧合平衡法
(Harmonic Balance Method)來解這組方程式.數值分析以蒙地卡羅法
(Monte Carlo Method)為之,數值結果包括了複合層圓柱殼在不同的平均
幾何缺陷幅度,長度對半徑比,半徑對厚度比及曲率參數下之自然振動頻率
及自然振動頻率的可靠度,同時也探討伸張彎曲偶合效應對自然振動頻率
的影響.

Nonlinear vibration of generally laminated circular cylindrical
shells with random initial geometric imperfections are examined
using the von Karman-Donnell theory. The random initial
geometric imperfections of these cylindrical shells are
described by Gaussian random fields and simulated numerically
from their mean and autocovariance functions. A solution for
nonlinear free vibration of these cylindrical shells is
formulated by a multimode procedure and satisfies the
associated compatibility equation and all boundary conditions.
The Galerkin procedure furnishes an infinite system of
equations for time functions which are solved by the method of
harmonic balance. Monte Carlo analyses are performed for
detailed numerical calculations. Numerical results include
nonlinear free vibration frequencies and frequency reliability
of composite circular cylindrical shells for various mean
imperfection amplitudes, length-to-radius ratios,radius-to-
thickness ratios and curvature parameters. Investigations are
also made for the effects of bending-stretching coupling on
vibration frequencies.