Nonlinear Dynamics of Elastic Systems With Liquid Sloshing Pressure Impacts

运动容器中的液体自由面晃动可以以三种可能的形式之一发生：线性平面运动、弱非线性非平面运动或以水动力冲击为特征的强非线性运动。第二或第三区域与支承弹性结构动力学的相互作用直接影响到液罐车和汽车油箱的横摇稳定性和安全性。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，开发了能够描述移动的部分装满的油轮中液体压力影响的分析模型。在用粘弹性大功率非线性阻尼器表示冲击力的基础上，建立了液体压力冲击模型。所得到的运动方程是使用非线性非光滑生成解而不是通常用于弱非线性系统的三角函数来分析的。对于弱非线性区域，采用规范形法和李群理论相结合的统一方法来研究存在内共振时的液-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。数值模拟估计了两种液体晃动状态下的系统响应。通过数值估计Lyapunov指数和嵌入维度来考察响应的稳定性和特征。实验测试提供了关于插入液体容器的挡板的有利位置的额外安全研究，从而提高了液货船的横摇稳定性。这项研究的另一个贡献是开发了描述液体晃动碰撞的真实模型，这些模型可以用于车辆动力学仿真，也可以引入多体动力学程序。

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.