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Study on Nonlinear Random Vibrations of Structures Carrying Liquid Tanks

液罐运载结构非线性随机振动研究

基本信息

批准号：
12650230
负责人：
IKEDA Takashi
金额：
$ 2.3万
依托单位：
Shimane University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2001
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12650230/
关键词：
Vibration Coupled with Liquid Motion Sloshing Cylindrical Tank Nonlinear Vibration Vertically Random Excitation Mean Square Response Probability Density Function Swirl Motion of Liquid Surface 流体関連振動 2乗平均値液体容器不規則励振鉛直励振液体ダンパー

项目摘要

The nonlinear random interaction of an elastic structure with liquid sloshing in a cylindrical tank is investigated in the neighborhood of a 1 : 2 internal resonance. The structure, modeled by a mass-spring-dashpot system carrying an upright cylindrical liquid tank, is vertically subjected to a narrow-band random excitation. The excitation is generated from the response of a linear shaping filter subjected to a Gaussian white noise. By using the Galerkin method, the analytical model is constructed taking into account three sloshing modes ; (1,1), (0,1) and (2,1). In addition, the modes whose nodal diameters are perpendicular to those of the original modes (1,1) and (2,1) are also taken into account. The validity of the analytical model was certified by experiments when the excitation was sinusoidal. In the case of random excitation, the system response statistics are numerically estimated using Monte Carlo simulation. The influence of the center frequency and the bandwidth of the random excitation and the liquid level on the system responses are presented. It is found that there is an irregular energy exchange between the structure and the liquid free surface motion when the center frequency is close to the structure natural frequency. Close to this condition, the liquid rotational (swirl) motion takes place due to the nonlinear coupling of orthogonal modes of the same frequency. Depending on the excitation power spectral density, the liquid free surface experiences zero motion, uncertain motion (intermittency), partially developed motion, and fully developed random motion. The structure response probability density function is almost Gaussian, while the liquid elevation deviates from normality. The unstable region, where the liquid motion occurs, becomes wider as the excitation intensity increases or as the bandwidth decreases. In addition, it is found that the statistics of the structure displacement can be obtained if only one sloshing mode is considered.

在 1:2 内部共振附近研究弹性结构与圆柱形罐中液体晃动的非线性随机相互作用。该结构以带有直立圆柱形液体罐的质量弹簧缓冲器系统为模型，垂直受到窄带随机激励。激励是由受到高斯白噪声影响的线性整形滤波器的响应生成的。利用伽辽金法，建立了考虑三种晃动模式的分析模型； (1,1)、(0,1) 和 (2,1)。此外，还考虑了节点直径与原始模式(1,1)和(2,1)垂直的模式。当激励为正弦波时，通过实验验证了分析模型的有效性。在随机激励的情况下，使用蒙特卡罗模拟对系统响应统计数据进行数值估计。给出了随机激励的中心频率和带宽以及液位对系统响应的影响。研究发现，当中心频率接近结构固有频率时，结构与液体自由表面运动之间存在不规则的能量交换。接近该条件时，由于相同频率的正交模态的非线性耦合而发生液体旋转（旋流）运动。根据激励功率谱密度，液体自由表面经历零运动、不确定运动（间歇性）、部分发展的运动和完全发展的随机运动。结构响应概率密度函数几乎呈高斯分布，而液体高程偏离正态分布。随着激发强度的增加或带宽的减小，发生液体运动的不稳定区域变得更宽。此外还发现，仅考虑一种晃荡模态即可得到结构位移的统计数据。