Escape dynamics in engineering systems

该项目旨在对工程系统中的逃逸现象进行理论和实验评估。势阱和势阱逃逸的概念在物理学、化学和工程学中至关重要。与逃逸过程相关的物理学研究主题非常不完整的列表包括分子和吸收粒子的动力学，天体力学和引力坍缩，能量收集和约瑟夫森结的物理学。在机械工程中，逃逸动力学通常表现在振动系统的瞬态共振响应，离散和连续结构的屈曲，甚至船舶的倾覆。 逃逸动力学提出了双重的分析挑战-它既是瞬态的，强非线性。以前的工作和额外的初步结果表明，至少对于简单的基准势威尔斯和谐波强迫一个可以定量预测的逃逸阈值的依赖关系的激励频率在孤立共振近似的框架。此外，一些有希望的初步结果涉及的安全区的空间的初始条件，铺平了道路，有效的控制和监测的逃逸相关的现象。 该项目旨在将该方法扩展到维度、次谐波/超谐波和组合外力方面的更通用设置，并预测初始条件空间中安全盆地的详细结构。提出了在孤立共振近似不相关的系统中探索逃逸动力学的新方法，特别是对于具有一般/部分强阻尼的单自由度和多自由度（DOF）模型。为了验证近似解析方法的有效性和局限性，我们建议设计并进行简单单自由度和两自由度系统的强迫屈曲基准实验。 该项目的成功完成将使人们能够更好地理解、设计和控制大量工程系统中的逃逸现象。

The project aims at theoretical and experimental assessment of escape phenomena in engineering systems. The concepts of potential well, and escape from it, are crucial in physics, chemistry and engineering. Very incomplete list of research topics in physics, that are related to the escape processes includes dynamics of molecules and absorbed particles, celestial mechanics and gravitational collapse, energy harvesting and physics of Josephson junctions. In mechanical engineering, the escape dynamics commonly exhibits itself in transient resonance responses of oscillatory systems, buckling in discrete and continuous structures, and even in capsize of ships. The escape dynamics poses double analytic challenge – it is both transient and strongly nonlinear. Previous work and additional preliminary results demonstrate that at least for simple benchmark potential wells and harmonic forcing one can quantitatively predict the dependence of the escape threshold on the excitation frequency in the framework of isolated resonance approximation. Moreover, some promising preliminary results concern the safe zones in the space of initial conditions, paving way to an efficient control and monitoring of the escape-related phenomena. The project aims to extend the method for more generic settings in terms of the dimensionality, subharmonic/superharmonic and combined external forcing, and prediction of detailed structure of the safe basins in the space of initial conditions. It is proposed to develop new methods for exploration of the escape dynamics in the systems where the isolated resonance approximation is irrelevant, in particular for one- and multi-degree-of freedom (DOF) models with general/partial strong damping. In order to verify the validity and limitations of the approximate analytic methods, we suggest to design and perform benchmark experiments on forced buckling in simple single – and two - DOF systems. Successful accomplishment of the project will allow better understanding, design and control of the escape phenomena in a plethora of engineering systems.