变曲率FGM拱的面内自由振动分析

摘要

基于Euler-Bemoulli曲梁理论,考虑材料沿拱厚度方向呈梯度分布时中性层的改变,将变曲率功能梯度材料(Functionally Graded Materials,FGM)拱在弧线方向离散成多个曲拱单元.视每个曲拱单元为半径一定的圆弧拱单元,根据Hamilton变分原理推导出FGM圆弧拱单元的面内自由振动方程,进而求得了单元传递矩阵.利用传递矩阵法(Transfer Matrix Method,TMM)推导出变曲率FGM拱的面内自由振动特征方程,求解两端固定边界条件下变曲率FGM拱面内自由振动的固有频率,并将得到结果与现有文献作了比较,证明TMM对求解该问题的有效性.分析了曲率变化系数和材料体积分数变化系数对变曲率FGM拱的面内自由振动频率的影响.%Based on the theory of Euler-Bernoulli curved beam,the shifting of neutral layer was considered when materials were gradually distributed trapezoidally along the arch thickness,and functionally graded material (FGM) arches with variable curvature were discretized into a number of curved arch elements along the arc direction.Every curved arch element was considered as a circular arch element with a constant radius,according to Hamilton variational principle,the in-plane free vibration equation of a FGM circular arch element was derived,then the element transfer matrix was deduced.Furthmore,using TMM,the in-plane free vibration characteristic equation of the FGM arch with variable curvature was derived,the in-plane free vibration natural frequencies of theFGM arch with variable curvature under two-clamped end boundary condition were solved,the results were compared with those previously reported.It was shown that TMM is effective to solve this problem.The influences of curvature varying coefficient and material volumn fraction varying coefficient on the in-plane free vibration frequencies of the FGM arch with variable curvature were analyzed.