Nonlinear Dynamics of Elastic Systems With Liquid Sloshing Pressure Impacts

移动容器中的液体自由表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流体动力冲击为特征的强非线性运动。第二态或第三态与支撑弹性结构动力学的相互作用，直接影响到液罐车和汽油罐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、数值和实验工具来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，开发了能够描述液体压力影响的分析模型。在用粘弹性高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用非线性“非光滑”生成解来分析的，而不是通常用于弱非线性系统的三角函数。对于弱非线性区域，采用范式方法和李群理论相结合的统一方法研究了存在内共振时的液固相互作用。通过数值模拟和实验验证了分析结果的有效性。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指数和嵌入维数来检验响应的稳定性和表征。通过试验，对液体容器中挡板的位置进行了进一步的安全性研究，从而提高了液体罐车的横摇稳定性。本研究的另一个贡献是建立了描述液体晃动冲击的真实模型，该模型可用于车辆动力学仿真，也可用于多体动力学代码。

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.