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

走向中频状态 - 结合波混沌方法和“统计能量分析”

基本信息

批准号：
EP/D064422/1
负责人：
Gregor Tanner
金额：
$ 10.41万
依托单位：
University of Nottingham
依托单位国家：
英国
项目类别：
Fellowship
财政年份：
2006
资助国家：
英国
起止时间：
2006 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FD064422%2F1
关键词：
Towards mid frequency regime combining

项目摘要

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

拟议的奖学金旨在建立机械工程界和应用数学之间的联系，在大型结构和线性波动方程的短波长渐近振动的接口。研究人员广泛研究了波问题的本征谱的性质，无论是从短波长的角度还是从统计的角度来看-这是一个通常被称为量子或波混沌的研究领域。该领域在历史上与量子力学的问题密切相关，但可以通过修改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，该方法广泛应用于机械工程界，用于分析复杂结构（如建筑物、飞机等）中高频振动的能量流。可以改进SEA中的误差估计，并且可以结合系统特定的特征，这将使得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，调查人员在研究金有效期内力求获得这方面的知识