Nonlinear Dynamics of Elastic Systems With Liquid Sloshing Pressure Impacts

液体在运动容器中的自由表面晃动可以以三种可能的方式之一发生：线性平面运动、弱非线性非平面运动或以流体动力学冲击为特征的强非线性运动。第二或第三状态与支撑弹性结构的动力学的相互作用直接影响液体罐车和携带汽油罐的汽车的侧倾稳定性和安全性。本研究项目的主要目标是开发分析，数值和实验工具，以检查这些系统的稳定性和动态特性，以提高其侧翻稳定性。为了实现这一目标，分析模型的开发是能够描述液体压力的影响，在移动部分填充油轮。采用粘弹性高次非线性阻尼器描述冲击力，建立了液压冲击模型。由此产生的运动方程进行了分析，使用非线性“非光滑”生成的解决方案，而不是三角函数通常用于弱非线性系统。对于弱非线性区域，采用规范形方法和李群理论相结合的统一方法研究了内共振下的液体-结构相互作用。数值模拟和实验测试验证了分析结果的正确性。数值模拟估计两种液体晃动制度的系统响应。的稳定性和表征的响应进行了研究，通过数值估计的Lyapunov指数和嵌入维数。实验测试提供了额外的安全研究有关的挡板的有利位置，插入液体容器，这提高了液体油轮的侧倾稳定性。本研究的另一个贡献是开发现实的模型描述液体晃动的影响，可用于车辆动力学仿真，也可以引入多体动力学代码。

Liquid free surface sloshing in moving containers can occur in the form of one of three possible regimes: linear planar motion, weakly nonlinear non-planar motion, or strongly nonlinear motion characterized by hydrodynamic impacts. The interaction of the second or third regime with the dynamics of the supporting elastic structure has direct impact on the roll stability and safety of liquid tankers and automotive vehicles carrying gasoline tanks. The main objective of this research project is to develop analytical, numerical, and experimental tools to examine the stability and dynamic characteristic of these systems in order to improve their rollover stability. To accomplish this objective, analytical models are developed which are capable of describing liquid pressure impacts in moving partially filled tankers. The liquid pressure impact model is formulated based on representing the impact forces by a visco-elastic high power nonlinear damper. The resulting equations of motion are analyzed using nonlinear `non-smooth` generating solutions rather than trigonometric functions commonly used for weakly nonlinear systems. For weakly nonlinear regime, a unified approach combining the method of normal form and the theory of Lie groups is used to study the liquid-structure interaction in the presence of internal resonance. The validity of analytical results are verified by numerical simulation and experimental tests. The numerical simulations estimate the system response for both liquid sloshing regimes. The stability and characterization of the response are examined by numerically estimating the Lyapunov exponents and embedding dimensions. The experimental tests provide additional safety study regarding the favorable locations of baffles, to be inserted in liquid containers, which enhances the roll stability of liquid tankers. Another contribution of this research is to develop realistic models describing liquid sloshing impacts which can be used for vehicle dynamic simulation, and also that can be introduced in multibody dynamics codes.