Analysis of natural vibration of truncated conical shells partially filled with fluid

IF 3.4 Q1 ENGINEERING, MECHANICAL 国际机械系统动力学学报(英文) Pub Date : 2024-05-15 DOI:10.1002/msd2.12105
Sergey A. Bochkarev, Sergey V. Lekomtsev
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Abstract

In this paper, we study the vibrational behavior of shells in the form of truncated cones containing an ideal compressible fluid. The sloshing effect on the free surface of the fluid is neglected. The dynamic behavior of the elastic structure is investigated based on the classical shell theory, the constitutive relations of which represent a system of ordinary differential equations written for new unknowns. Small fluid vibrations are described in terms of acoustic approximation using the wave equation for hydrodynamic pressure written in spherical coordinates. Its transformation into the system of ordinary differential equations is carried out by applying the generalized differential quadrature method. The formulated boundary value problem is solved by Godunov's orthogonal sweep method. Natural frequencies of shell vibrations are calculated using the stepwise procedure and the Muller method. The accuracy and reliability of the obtained results are estimated by making a comparison with the known numerical and analytical solutions. The dependencies of the lowest frequency on the fluid level and cone angle of shells under different combinations of boundary conditions (simply supported, rigidly clamped, and cantilevered shells) have been studied comprehensively. For conical straight and inverted shells, a numerical analysis has been performed to estimate the possibility of finding configurations at which the lowest natural frequencies exceed the corresponding values of the equivalent cylindrical shell.

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部分填充流体的截顶锥形壳体的自然振动分析
本文研究了含有理想可压缩流体的截顶锥形壳体的振动行为。流体自由表面上的荡动效应被忽略。弹性结构的动态行为以经典壳理论为基础进行研究,其构成关系代表了一个为新未知数编写的常微分方程系统。小的流体振动用声学近似来描述,使用的是在球面坐标中写入的流体动力压力波方程。应用广义微分正交法将其转换为常微分方程组。利用戈杜诺夫正交扫频法解决了边界值问题。壳体振动的自然频率采用逐步法和穆勒法进行计算。通过与已知的数值解法和分析解法进行比较,估算了所得结果的准确性和可靠性。对不同边界条件组合(简单支撑、刚性夹紧和悬臂壳体)下壳体的最低频率与液面和锥角的关系进行了全面研究。对锥形直壳和倒壳进行了数值分析,以估计找到最低固有频率超过等效圆柱壳相应值的配置的可能性。
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