轴向运动层合薄壁圆柱壳内共振的数值分析

张宇飞1,3，王延庆2，闻邦椿3

(1. 沈阳航空航天大学航空航天工程学部, 沈阳110136； 2.东北大学应用力学研究所，沈阳110819； 3.东北大学机械工程与自动化学院，沈阳110819)

摘要：以轴向运动复合材料薄壁圆柱壳为研究模型，考虑其弹性模量随振动频率变化(动态弹性模量)，据Donnell非线性扁壳理论及经典层合壳理论获得模型非线性振动微分方程。采用含四个广义模态坐标的位移展开式，利用Galerkin方法对振动微分方程离散化；用变步长四阶Runge-Kutta法对非线性模态方程组进行数值积分，研究复合材料圆柱壳1:1:1:1的内共振现象；讨论圆柱壳轴向运动速度、阻尼系数及外激励幅值对系统1:1:1:1内共振响应作用。

关键词：复合材料圆柱壳；动态弹性模量；内共振；轴向运动；响应

中图分类号:O322文献标志码：A

基金项目：国家自然科学基金(11072072,11502120)；河南省基础与前沿技术研究(152300410016)

收稿日期：2015-04-01修改稿收到日期：2015-05-26

Internal resonance of axially moving laminated thin cylindrical shells

ZHANGYu-fei1,3,WANGYan-qing2,WENBang-chun3(1. Faculty of Aerospace Engineering, Shenyang Aerospace University, Shenyang 110136, China；2. Institute of Applied Mechanics, Northeastern University, Shenyang 110819, China；3. School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China)

Abstract:A thin composite circular cylindrical shell moving in axial direction was investigated. Based on the Donnell’s nonlinear shallow-shell theory, together with the classical laminated shell theory, a nonlinear vibration equation of the system was derived, in which the effects of dynamic Young’s modulus, damping and geometric large deformation were considered. The modal expansion with four generalized modal coordinates was adopted, and the vibration equation was discretized by using the Galerkin method. Applying variable step-size four-order Runge-Kutta method, the nonlinear modal equations of the system was solved, and the nonlinear frequency response curves, which show 1:1:1:1 internal resonance phenomenon in the system were obtained. The effects of moving speed, damping coefficients and amplitudes of external force on the nonlinear vibration response of the shell were also analysed.

Key words:composite circular cylindrical shell; dynamic Young’s modulus; internal resonance; axially moving; response

圆柱壳结构广泛用于土木、航空航天、海洋及机械、核工业、化学、汽车等工程领域。因此已有诸多针对其结构振动特性的研究[1-4]。

较传统的金属材料，复合材料具有比强度高、比模量大、化学及环境适应性好等优点。因此，复合材料圆柱壳的振动分析颇受关注。Hua等[5]利用广义微分求积法分析不同边界条件下各向同性旋转复合材料薄壁圆柱壳的固有频率。李健等[6]通过对复合材料圆柱壳的固有特性实验研究表明，复合材料圆柱壳的弹性模量随壳体振动频率变化。……