中文摘要：

基于Timoshenko—Midlin假设及Hamilton变分原理，建立了层舍中厚非圆柱壳的非线性运动控制方程，采用伽辽金技术，得到仅含时间参数的Mathieu型方程，然后应用增量谐波平衡法进行求解．数值计算中，以两端简支L曲线截面层合中厚柱壳为例，讨论了截面形状参数、几何非线性和横向剪切效应等因素对层合中厚非圆截面柱壳非线性动力稳定性的影响．结果表明：这些因素对层合L曲线截面中厚柱壳的非线性主要动力不稳定区域有较大影响．

英文摘要：

Based on the Timoshenko-Mindlin hypothesis and the Hamilton Principle, a set of governing equations of motion for the laminated non-circular cylindrical thick shells were founded. Using the Galerkin procedure, the Mathieu equation only with time variable was obtained, and this equation was solved by the method of increase harmonic balance. In numerical calculation, the laminated L-curve section cylindrical thick shells with both ends simply supported were investigated, and the effects of sectional shape, geometrically nonlinear factors and transverse shear on the nonlinear dynamic stability of laminated non-circular cylindrical shells were discussed. The results indicate these factors have a tremendous influence on the nonlinear dynamic stability of laminated non-circular cylindrical shells.