碳纳米管增强复合材料圆锥薄壳非线性自由振动

考虑碳纳米管复合材料作为功能梯度材料的不均匀性，基于连续介质理论以及哈密尔顿变分原理，建立了功能梯度碳纳米管增强复合材料开口圆锥薄壳结构的非线性运动偏微分控制方程，然后利用Galerkin法，将非线性偏微分控制方程转化为常微分控制方程，进而采用谐波平衡法求解了开口圆锥壳的非线性自由振动问题，并探讨了圆锥薄壳几何参数、碳纳米管参数对结构非线性自由振动的影响．数值研究表明结构的无量纲非线性自由振动频率与线性自由振动频率的比值随圆锥薄壳长厚比的增大而变小、并随圆锥角的增大而变大．

Nonlinear Free Vibration of Nanotube Reinforced Composite Conical Shells

Considering the inhomogeneity of nanotube-reinforced composites as functionally graded materials, the nonlinear dynamic partial differential control equations of nanotube-reinforced composite opening conical shells are established based on the continuum theory and Hamilton variational principle. Applying Galerkin method, the nonlinear dynamic partial differential equations are transformed into a series of nonlinear dynamic ordinary differential equations. Furthermore, the harmonic balance method is used to solve the free vibration of nanotube-reinforced composite opening conical shells. Finally, the effects of geometric parameters of conical shells and the nanotube materials parameters on the nonlinear free vibration are discussed. Numerical results show that the ratios of non-dimensional nonlinear frequency to linear frequency would decrease with the increase of the length-to-thickness ratio, and increase with the the increase of taper angle of the structure.