复合材料薄壁圆柱壳内共振的受迫响应

Forced response of composite thin circular cylindrical shells with internal resonance

采用多尺度法分析复合材料悬臂圆柱壳考虑内共振的受迫振动。建立考虑动态弹性模量、阻尼、几何非线性时系统的振动方程;利用Galerkin方法将时间和空间变量进行分离,然后应用多尺度法推导出内共振条件下系统的频率-振幅方程;通过算例获得了系统参数变化导致复杂非线性振动响应变化的规律。理论分析发现:由于所采用的两个轴向模态相距较近,引起了能量在两个模态之间相互传递,系统存在1:1内共振现象;相比较而言,激振力大小对系统内共振下的复杂振动响应影响比较大,而阻尼的变化对其影响则很小。

A cantilever composite thin circular cylindrical shell is investigated by using multiple scales method in this paper.Nonlinear equation of motion of the system is derived,in which the effect of dynamic Young’s modulus,damping and geometric large-amplitude are considered.The Galerkin method is used to separate the time and space variables in the equation.Applying multiple scales method,we solve the nonlinear response of the system with two neighboring axial modes being in internal resonant.The effects of different parameters on the complex dynamic response are also investigated in this study.Results show that,due to the frequencies of the two modes selected are very near a 1:1 internal resonance exists in the system;in addition,the complex vibration response of the system is affected by exciting force evidently,but it is not very sensitive to damping.