层合薄壁圆柱壳1:1内共振研究  

Study on 1:1 internal resonance of thin laminated circular cylindrical shells

作　　者：王延庆[1,2] 梁力[2] 郭星辉[1] 楼玲娜[1] 

机构地区：[1]东北大学应用力学研究所,沈阳110004 [2]东北大学资源与土木工程学院,沈阳110004

出　　处：《振动与冲击》2011年第9期10-14,共5页Journal of Vibration and Shock

基　　金：国家自然科学基金;上海宝钢集团公司联合资助(50574019)

摘　　要：针对一端固定,一端自由的层合薄壁圆柱壳模型,根据Donnell’s非线性简化壳理论建立其非线性振动方程。采用Galerkin方法对非线性振动方程进行离散化,应用平均法对系统包含两个相邻轴向模态的非线性振动响应进行了解析分析,与数值模拟进行了比较,并得到了不同参数对层合薄壁圆柱壳复杂的振动响应的影响。结果表明,1)由于所选的两个相邻轴向模态频率相距较近,能量在两个模态之间相互传递,系统存在1∶1内共振现象;2)系统复杂的振动响应受激振力大小的影响比较大,而对于阻尼不敏感。A cantilever thin laminated circular cylindrical shell was investigated.Based on Donnell＇s nonlinear shallow shell theory,nonlinear wave equation of the system was derived,in which the effects of dynamic Young＇s modulus,damping and geometric large-amplitude were considered.Galerkin method was used to disperse the wave equation.Applying averaging method,the nonlinear response of the system was solved with two neighboring axial modes participation,and the results obtained were compared with those gained by numerical method.The effects of different parameters on the complex dynamic response were also investigated.The results show that： due to the frequencies of the two modes selected are very close,there exists 1∶ 1 internal resonance in the system;the complex vibration response of the system is affected by exciting force evidently,but it is not very sensitive to damping.

关 键 词：层合圆柱壳 内共振 平均法 非线性 Donnell’s理论 

分 类 号：O322[理学—一般力学与力学基础]