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目前国内外采用的储液罐简化模型多为基于线性理论的弹簧-质量系模型,该模型在外激励远离对流固有频率时是有效的,但当外激励接近对流固有频率时不适用。该文提出一种适用于圆柱形储液罐简化计算的非线性单摆系模型,该文首先应用拉格朗日法建立了相应的非线性运动方程,然后采用多尺度法对方程的主共振进行了分析,求得其一次近似解和幅频响应方程,并讨论了定常解的稳定性。以某特大型LNG储罐为例运用此方法进行了数值模拟分析。分析结果表明:模型主共振呈软式非线性特性;储液高度的降低会加剧系统的非线性反应,当储液高度为储罐总高度的一半时,主共振会出现峰值现象;与以往试验研究结果对比可以看出该文模型适用于计算储罐系统在外激励频率接近对流频率时的共振响应。
At present, the simplification model of liquid storage tanks adopted both at home and abroad is mostly a spring-mass model based on linear theory. This model is effective when the external excitation is far away from the natural convection frequency. However, it is not applicable when the external excitation approaches the natural convection frequency. In this paper, a simple non-linear pendulum model which is suitable for the simplified calculation of cylindrical liquid storage tanks is proposed. In this paper, the corresponding nonlinear equations of motion are first established by using Lagrange method. Then the main resonance The first approximation solution and amplitude-frequency response equation are obtained, and the stability of the stationary solution is discussed. Taking a very large LNG storage tank as an example, this method was used for numerical simulation analysis. The results show that the main resonance of the model shows a soft nonlinear characteristic. The decrease of reservoir height aggravates the nonlinear reaction of the system. When the reservoir height is half of the total tank height, the main resonance will appear the peak phenomenon. The comparison of the research results shows that the proposed model is suitable for calculating the resonance response of tank system when the external excitation frequency is close to the convection frequency.