功能梯度梁在轴向移动载荷作用下的动态响应

Dynamic Response of Functionally Graded Beams Subjected to the Axial Moving Load

研究了功能梯度材料梁在沿轴向移动的集中力作用下的动态响应特性,其中考虑功能梯度材料的物理性能参数沿厚度方向以幂指数形式连续变化。首先基于经典Euler梁理论建立动态响应控制方程,并求解获得功能梯度两端简支梁的固有频率及主振型,同时推导证明了其主振型的正交性。然后采用模态叠加法研究梁在轴向移动载荷作用下的动态响应及共振特性,求解获得了中点最大挠度随时间的变化及共振速度的解析解,并采用数值结果分析了共振速度及其影响因素。

Dynamic response of an functionally graded material （FGM） beam subjected to an axially moving load is analyzed, in which material properties of FGM are assumed to vary continuously in the thickness direction of the beam according to a power function. Firstly, based on Euler-Bernoulli beam theory, equations of motion are de- rived and solved to obtain nature frequencies and principal modes of FGM beam with simply-supported two edges. The orthogonality of principal modes is also confirmed. And then, the dynamic response and resonance characteris- tics of FGM beam subjected to an axially moving load are studied by the method of principal mode superposition. The responses of the maximum deflections of mid-point and resonant velocities are obtained. At the same time, the comparison of present results with the published ones in the literature is given to certify the correctness of theoretical analysis and numerical calculation when the functionally graded beam is reduced to uniform one.