径向任意变厚度圆板轴对称横向振动频率的计算

The Natural Frequencies of Axisymmetric Vibration of Circular Plates with Arbitrarily Varying Thickness

用有限元法计算了径向任意变厚度圆板和环形板横向振动的频率，构造了三结点变厚度环形单元，使计算模型和实际结构的几何形状达到了完全一致。该方法可以方便地计算双线性变厚度、二次变厚度及其它各种复杂变厚度环形板与圆板的振动频率及振型。计算出的前几阶固有频率的精度很好。

The natural frequencies of axisymmetric tansverse vibration of circular plates with arbitrarily varying thickness has been studied by the finite element method. Provided the function of the plate thickness is known, the thickness of the elements will vary according to the function, so the modelled structure is exactly the same as the actual one. The element matrixes are calculated by combining the analytical and the numerical methods.This method can calculate the natural frequencies and mode shapes of circular plate with linear,parabolic and other complicated variable thickness.Comparison with available exact results proved that the first five frequencies obtained by this method are very accurate.