储液罐非线性简化模型及主共振研究

A NONLINEAR SIMPLIFIED MODEL OF LIQUID STORAGE TANK AND PRIMARY RESONANCE ANALYSIS

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。

Most simplified models for liquid storage tanks are the spring-mass models. These models are based on linear theory and are only applicable when frequencies of external excitations are sufficiently different from the convective natural frequencies of the storage tank systems. In this study, a nonlinear pendulum model is developed. The nonlinear equations of motion of model are derived using the Lagrange's method. The first-order approximation solution of the nonlinear vibration is formulated using multiple-scale analysis, from which the stability conditions of system primary resonance are obtained. Numerical analysis of an extra-large liquefied natural gas(LNG) storage tank is carried out using this method. Results show that the primary resonance mode of the tank presents weakly nonlinear behaviour, and the nonlinear response is elevated as the level of the liquid decreases. A peak value of the primary resonance was observed when the level of liquid equals half of the storage tank height. This study shows the model is capable of capturing resonance responses of liquid storage tanks when external excitation frequencies are in the immediate neighbourhood of the convective natural frequencies of the tanks.