Vibration analysis of nonsmooth structural systems

本研究的目的是提供更好的理解，建模和预测复杂的可能结构系统的振动响应。这将通过开发创新的数值方法来实现，这些方法能够解决由于优化设计和恶劣的操作环境而导致的动态现象日益复杂的问题。在飞机和直升机发动机中发现的叶盘系统将作为这种分析和计算程序的优选工业应用。本文将着重讨论涉及非光滑界面量（即单边接触和摩擦条件）的系统振动的数值处理。其他建模复杂性将包括大模型尺寸和时间延迟现象。为此，拟议的发现补助金申请将集中在两个主要方面： 1.第一个推力将是发展有效的数值技术，致力于一般简单结构和几何形状的非光滑模态分析。嵌入不连续量的现代数值公式将首选复杂界面的可靠处理，并将开辟途径，系统地探索更广泛的非光滑现象。 2.第二个重点将涉及全旋转结构的高保真建模和分析，这些结构应作为一个整体来处理。将构造具有各自的非光滑支撑装置和周围柔性壳体的完整多级叶盘组件的降阶模型。这也意味着在现有结构设计的模态意义上的优化，使它们变得更加顺应和宽容的单边接触和摩擦条件，以及在随机分析中放宽制造公差的可能性。

The objective of this research is to provide improved understanding, modeling, and prediction of the vibration response of complex possibly structural systems. This will be accomplished by developing innovative numerical methods capable of tackling the growing complexity of dynamical phenomena resulting from optimized designs and severe operational environments. Bladed disk systems found in aircraft and helicopter engines will serve as the preferred industrial applications of this analytical and computational program. Meticulous attention will paid to the numerical treatment of the vibrations of systems involving nonsmooth interface quantities, i.e. unilateral contact and friction conditions. Other modeling complexities will include large model size and time-delayed phenomena. To this end, the proposed Discovery Grant application will focus on two major thrusts: 1. The first thrust will be the development of efficient numerical techniques dedicated to the Nonsmooth Modal Analysis of generic simple structures and geometries. Modern numerical formulations embedding discontinuous quantities will be preferred for the reliable treatment of complex interfaces and will open avenues for a systematic exploration of a broader range of nonsmooth phenomena. 2. The second thrust will concern the high-fidelity modeling and analysis of full rotating structures that should be dealt with as a whole. Reduced-order models of full multistage bladed-disk assemblies with respective nonsmooth supporting devices and surrounding flexible casings will be constructed. This also implies the optimization in a modal sense of existing structural designs so that they become more compliant and tolerant to unilateral contact and friction conditions as well as the possibility of relaxed manufacturing tolerances within stochastic analyses.