基于多元L-P法的复合材料圆柱壳内共振分析

以不同材料构成的复合材料圆柱壳作为研究模型,考虑几何非线性,动态弹性模量等因素,根据Donnell’s简化壳理论及经典层合壳理论建立其非线性振动方程。采用Galerkin方法对振动方程进行离散化,应用多元L-P法求解了系统包含两个相邻轴向模态的非线性振动响应,得到了反映复杂内共振的幅频特性曲线,表明能量在两个模态之间相互传递,彼此影响牵制,系统存在1∶1内共振现象。最后利用多尺度法与多元L-P法所得结果进行比较,得到了相同的结论。

ANALYSIS OF INTERNAL RESONANCE OF COMPOSITE CIRCULAR CYLINDRICAL SHELLS BASED ON THE MULTIDIMENSIONAL L-P METHOD

A composite circular cylindrical shell made from different materials is investigated.Based on Donnell's shallow shell theory and classical laminated shell theory,nonlinear vibrating equation is derived,in which the effects of dynamic Young's modulus and geometric large-amplitude are considered.Galerkin method is used to disperse the vibrating equation.The nonlinear vibrating responses of the system with the participation of two neighboring axial modes are solved by applying the multidimensional L-P method.And complex frequency-response curves indicating internal resonance are obtained,showing that the energy is transferred between the two modes which affect each other,and there is 1:1 internal resonance phenomenon in the system.Result of multiple scales method is compared with that of multidimensional L-P method,and the same conclusion is drawn.