Abstract

The paper presents the results of studies of natural vibrations of circular vertical layered cylindrical shells completely or partially filled with a quiescent compressible fluid and subjected to hydrostatic load. The behavior of the elastic structure and the fluid medium is described using the classical shell theory and the Euler equations. The effects of sloshing on the free surface of the fluid are not considered. The linearized equations of motion for shells, together with the corresponding geometric and physical relations, are reduced to a system of ordinary differential equations with respect to new unknowns. The acoustic wave equation is transformed to a system of differential equations using the generalized differential quadrature method. The formulated boundary-value problem is solved by Godunov’s method of orthogonal sweep. The natural frequencies of the vibrations are calculated based on the combination of a stepwise procedure and subsequent refinement by the method of dividing in half. The reliability of the obtained results is verified by comparison with the known numerical solutions. The dependence of the lowest vibration frequencies on the ply angle and the fluid level for simply supported, rigidly clamped, and cantilevered two-layer and three-layer cylindrical shells with a fluid are analyzed in detail. It is demonstrated that the possibility of changing the frequencies and vibration modes through a suitable choice of lay-up scheme and the ply angle of the composite material is notably determined by a prescribed combination of boundary conditions for an elastic body.

中文翻译：

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部分填充流体的复合圆柱壳的自然振动

摘要

本文介绍了完全或部分填充静态可压缩流体并承受静水载荷的圆形垂直分层圆柱壳的自然振动研究结果。使用经典壳理论和欧拉方程描述弹性结构和流体介质的行为。不考虑晃动对流体自由表面的影响。壳的线性运动方程以及相应的几何和物理关系被简化为关于新未知数的常微分方程组。使用广义微分求积法将声波方程变换为微分方程组。公式化的边值问题通过戈杜诺夫正交扫描方法求解。振动的固有频率是基于逐步过程和随后通过二分之一法细化的组合来计算的。通过与已知数值解的比较验证了所得结果的可靠性。详细分析了简支、刚性夹紧、悬臂两层和三层流体圆柱壳的最低振动频率对层角和液位的依赖性。结果表明，通过适当选择复合材料的铺层方案和铺层角度来改变频率和振动模式的可能性主要是由弹性体边界条件的规定组合决定的。