中文摘要：

新型非均匀复合材料,功能梯度材料具有防止脱层和减缓热应力等优良性能,将其应用于功能梯度梁的结构有着非常重要的工程应用价值.基于Euler-Bernoulli梁理论和Hamilton原理,建立轴向运动功能梯度梁横向自由振动的运动微分方程,其中假设功能梯度梁的材料特性沿梁厚度方向按各组分材料体积分数的幂函数连续变化;再对运动微分方程和边界条件进行量纲一处理,采用微分求积法对其进行离散化,导出系统的广义复特征方程,然后计算分析轴向运动功能梯度简支梁横向振动复频率的实部和虚部随量纲一轴向运动速度、梯度指标等参数的变化情况,并讨论量纲一轴向运动速度和梯度指标对功能梯度梁的横向振动特性以及失稳形式的影响.

英文摘要：

As a new type of heterogeneous composite materials, the functionally gradient materials with preventing the delaminating and slowing down the heat stress are applied to the engineering structure of the beams, which has an important engineering value. Based on Euler-Bernoulli beam theory and the Hamilton＇s principle, the differential equations of motion of the transverse free vibration of the axially moving beam made of functionally gradient materials is derived, where the materials properties of the functionally gradient beam are assumed to vary continuously follows a power law distribution of the volume fraction of the constituents along the thickness of the beam. Dimensionless parametrization is carried out for the differential equations and boundary conditions, and the nondimensional differential equations are discretized by differential quadrature method, and then the system complex characteristic equation is derived. With the change of the dimensionless axial movement speed and gradient index, the complex frequencies of transverse vibration of the axially moving beam made of functionally gradient materials with simply supported are analyzed, and the influences of the dimensionless axial movement speed and gradient index on the transverse vibration characteristics and instability forms of the axially moving beam made of functionally gradient materials are discussed.