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储有液体的圆筒罐受地震作用。假设液体是理想不可压缩的,其运动是无旋的,重力波是线性小振幅的。首先将罐体当作刚体,求得罐内液体自由表面波的各阶自振频率与振型,以及罐壁、罐底的动压力分布。随后分析液体与结构的相互作用,问题归结为顶端带有集中质量的伸臂梁在地震扰动和液动压力作用下的剪切型振动。分别求得了罐体质量与地震干扰因子的增长系数以及罐体自振频率与阻尼比的折减系数;还求得地震作用下罐壁上液动压力的分布。上述分析结果均分别用简明的公式表达,并对常用的储油罐系列绘成动力特性曲线,以便于工程应用。
Cylinders with liquids are affected by earthquakes. Assuming that the liquid is ideally incompressible, its motion is non-rotating and the gravity waves are linearly small amplitude. Firstly, the tank body is regarded as a rigid body, and the free vibration frequency and vibration mode of the free surface wave of the liquid in the tank, and the dynamic pressure distribution of the tank wall and the tank bottom are obtained. Subsequently, the interaction between the liquid and the structure was analyzed. The problem was attributed to the shear-type vibration of the boom beam with concentrated mass at the top under the action of seismic disturbance and hydraulic pressure. The growth coefficients of the tank mass and the seismic disturbance factor, the reduction factor of the natural frequency and the damping ratio of the tank were obtained, and the distribution of the hydraulic pressure on the tank wall under the action of the earthquake was also obtained. The above analysis results are expressed in simple and concise formulas respectively, and the commonly used oil storage tank series is drawn into a dynamic characteristic curve to facilitate engineering application.