用Timoshenko梁修正理论研究功能梯度材料梁的动力响应

采用Timoshenko梁修正理论研究了功能梯度材料梁的动力响应问题，利用静力方程确定了功能梯度材料梁的中性轴位置，在此基础上应用Timoshenko梁修正理论建立了功能梯度材料梁的振动方程，求得其自振频率表达式及其在简谐荷载作用下强迫振动的解析解。讨论分析了中性面位置、梯度指数等因素对功能梯度材料梁的动力响应的影响，并用有限元法验证了Timoshenko梁修正理论。通过实例计算，得到了中性轴位置对功能梯度材料梁动力响应有较大影响的结论。

Study on the dynamic responses of the beam with functionally graded materials by Timoshenko beam corrective theory

The dynamic response of the beam with functionally graded materials was studied by Timoshenko beam corrective theory. The neutral plane site of the beam with functionally graded materials was determined by the static equilibrium equations, and the vibration equations of the beam with functionally graded materials were also established by Timoshenko beam corrective theory, the expression for the natural frequency of the beam with functionally graded materials and the analytical solution for forced vibration of the beam with functionally graded materials under the action of harmonic load were obtained. The effect of neutral plane site, gradient index to dynamic responses of the beam with functionally graded materials were discussed, and Timoshenko beam corrective theory was verified by finite element method. Analysis of examples indicates that the neutral plane site had more greatly influence on dynamic responses of the beam with functionally graded materials.