功能梯度材料Timoshenko型剪切梁的自由振动分析

基于Timoshenko梁理论,研究各向异性功能梯度材料梁的自由振动。假设材料参数沿梁厚度方向按同一函数规律变化,建立了功能梯度材料梁的振动方程,求得简支条件下其自振频率表达式。通过算例,给出指数函数梯度变化Timoshenko梁的自振频率和模态图,结果表明不同梯度变化对材料结构动力响应有较大影响。该方法为发展功能梯度材料梁的设计与数值计算提供了理论依据。

Free Vibration Analysis of Functionally Graded Timoshenko Shear Beam

Based on Timoshenko beam theory,free vibration of anisotropic functionally graded material beam was analyzed.Assuming that material properties follow the same law along the beam-thickness direction,dynamic equation and frequency equation of the functionally graded beam with the simply supported boundary conditions were deduced.Through a numerical example,assuming that the elasticity modulus of the material has the exponential form distribution along the thickness,results demonstrate that different gradient changes have great influence on the dynamic response of the beam.The research serves as theoretical reference for the development of the design and numerical calculation of functionally graded material beam.