用Timoshenko梁修正理论研究功能梯度材料梁的动力响应

摘要

The dynamic response of a beam with functionally graded materials was studied with Timoshenko beam correction theory. The neutral plane site of the beam with functionally graded materials was determined with the static equilibrium equations, and the vibration equations of the beam with functionally graded materials were established with Timoshenko beam correction theory, the expression for the natural frequencies of the beam with functionally graded materials and the analytical solution to forced vibration of the beam under the action of harmonic load were obtained. The effect of neutral plane site and gradient index on the dynamic responses of the beam were discussed, and Timoshenko beam correction theory was verified with finite element method. Analysis of examples indicated that the neutral plane site has larger influence on the dynamic responses of the beam with functionally graded materials.%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.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.