Towards the mid-frequency regime - combining wave chaos methods and 'Statistical Energy Analysis'

拟议的研究金旨在建立机械工程界和应用数学之间的联系，在大型结构的振动和线性波动方程的短波长渐近性的界面上。这位研究人员从短波长的角度以及从统计学的角度对波动问题的本征谱的性质进行了广泛的研究-这一研究领域通常被称为量子-或波-混沌。该领域在历史上与量子力学中的问题密切相关，但经过修改后，可以应用于其他线性波动方程，如弹性动力学的波动方程。本文提出了将量子混沌方法引入统计能量分析(SEA)方法的可能性，该方法在机械工程界被广泛用于分析建筑物、飞机等复杂结构中的高频振动的能量流。这里将论证，通过重新评估和修改该技术的一些基本假设，可以改进SEA中的误差估计，并且可以结合系统特有的特征，从而使该方法也适用于中频范围。对方法本身及其应用范围的详细了解对这项任务至关重要，调查员希望在研究金有效期内获得这项任务。

The proposed fellowship aims at forging links between the Mechanical Engineering community and Applied Mathematics at the interface of vibrations in large-scale structures and short wavelength asymptotics of linear wave equations. The investigator has worked extensively on the properties of eigenspectra of wave problems both from a short wavelength perspective as well as from a statistical point of view - an area of research often referred to as quantum - or wave - chaos. The field is historically closely linked to problems in quantum mechanics, but can with modifications be applied to other linear wave equations such as the wave equations of elastodynamics. It is proposed here to evaluate the possibility of incorporating quantum chaos methods in a Statistical Energy Analysis (SEA) approach, widely used in the mechanical engineering community for analysing energy flow of high-frequency vibrations in complex structures such as buildings, aeroplanes and so on. It will be argued here that by re-evaluating and modifying some of the basic assumptions of the technique, error estimates in SEA may be improved and system specific features may be incorporated which would make the method applicable also in the medium frequency range. Detailed knowledge of the method itself and its range of applications is essential for this task, which the investigator seeks to obtain during the lifetime of the fellowship