精确的动态刚度公式，用于预测中等厚度的旋转壳的固有频率,Mathematical Problems in Engineering

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精确的动态刚度公式，用于预测中等厚度的旋转壳的固有频率
Mathematical Problems in Engineering Pub Date : 2018-06-04 , DOI: 10.1155/2018/4156360
Xudong Chen ₁ , Kangsheng Ye ₂

Affiliation

根据一阶Reissner-Mindlin理论，提出了一种精确的动力刚度公式来计算旋转壳的固有频率。如果指定了圆周波数，则将运动方程简化为一维，然后以汉密尔顿形式重写。因此，将具有中等厚度的旋转壳体作为特殊的骨骼结构进行分析，该结构在单元端具有五个自由度。动态刚度是使用经典骨架理论直接从一维控制振动方程构建的。通过应用Wittrick-Williams（WW）算法计算低于特定值的固有频率数，可以使用二等分法简单地获得准确的特征值。钳位频率J的数量的解还提出了WW算法中的₀，并被证明是可靠的。研究了具有不同边界条件的各种壳的数值示例，并对结果进行了很好的比较和验证。详细讨论了各种壳参数对圆柱壳和球形壳固有频率的影响，表明所提出的动态刚度公式适用于高精度分析中等厚度旋转壳的固有频率。

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An Exact Dynamic Stiffness Formulation for Predicting Natural Frequencies of Moderately Thick Shells of Revolution

An exact dynamic stiffness formulation is proposed for calculating the natural frequencies of shells of revolution based on the first-order Reissner-Mindlin theory. Equations of motion are reduced to be one-dimensional, should the circumferential wave number is specified, and then are rewritten in Hamilton form. Therefore, a shell of revolution with a moderate thickness is analysed as a special skeletal structure with five degrees of freedom at element ends. Dynamic stiffnesses are constructed directly from the one-dimensional governing vibration equations using classic skeletal theory. Number of natural frequencies below a specific value is counted by applying the Wittrick-Williams (W-W) algorithm, and exact eigenvalues can be simply obtained using bisection method. A solution to the number of clamped-end frequencies J₀ in the W-W algorithm is also proposed and proven to be reliable. Numerical examples on a variety of shells with different boundary conditions are investigated, and results are well compared and validated. Influences of a variety of shell parameters on natural frequencies of both cylindrical and spherical shells are discussed in detail, demonstrating that the proposed dynamic stiffness formulation is applicable to analyse natural frequencies of moderately thick shells of revolution with high accuracy.

更新日期：2018-06-04

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