重物落水后运动过程的数学模型

Mathematical model of weight's movement process after fell into water

为更好描述重物落水后的运动过程,设计了模拟封堵溃口小型试验,首先对重物落水后运动过程的影响因素进行分析,对采集的试验数据进行了分类处理,并对典型的试验数据进行比较分析,突出主要影响因素.其次对水中的重物进行了受力分析,以大实心方体为例,初步建立重物在水中运动过程的二阶微分方程模型(模型1),结合步长搜索法和最小二乘法确定压差阻力系数的初始范围,然后在Matlab平台下做非线性最小二乘拟合求解运动模型中压差阻力系数kx、ky;在模型1的基础上引入速度后损率kv,完善了重物在水中运动过程的二阶微分方程模型(模型2),并对模型中2的参数进行求解.模型结果验证显示,引入速度后损率后的模型2能比较好地反映重物落水后的运动过程,并对以后的研究提供了参考.

The issue of weight movement process after fell into water in the bench-scale test of simulation blocking dyke breach was studied;the main influential factors were analyzed in the weight movement process after fell into water,the second-order differential equation model（model one） of weight movement process in the water was available.And then,this article introduces after the loss rate（kv） of velocity based on the model one,so as to establish an improvement of a second order differential equation model（model two）.Finally,the pressure drag coefficient（kx,ky） and after the loss rate（kv） of the model in the platform of Matlab.The computation results show that the model two could well reflect the motion process of the mass after fell into water.