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

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.