变厚度圆板轴对称非线性振动的有限元分析

用3节点变厚度环形有限元研究厚度为半径的任意函数的圆板轴对称非线性振动,给出了一个避免发散并加速收敛的加权平均迭代算法.算例的计算结果与文献的已有结果完全吻合。文章还分析了振幅、半径比、质量比和厚度系数对频率的影响.

FINITE ELEMENT ANALYSIS FOR NON-LINEAR AXISYMMETRICAL VIBRATION OF CIRCULAR PLATES HAVING VARIABLE THICKNESS

In this paper,by the use of three-nodes annular element,a finite element analysis is carried out for non-linear axisymmetrical vibration of elastic circular plates with a variable thickness which is an arbitrary function of the radius. A weighting-average iteration method is given to avoid divergence and to accelerate convergence. In some particular cases, the obtained results for linear and non-linear vibration are compared with the available appoximate or exact solutions and it is found that they are in excellent agreement with each other. The behavior of an annular plate and a circular plate with parabolic thickness has been investigated and it is found that the frequency response is affected by the amplitude,the radius,the coefficient of thickness and the ratio of the mass.