权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Vibrational energy distributions in large built-up structures - a wave chaos approach

大型建筑结构中的振动能量分布 - 波混沌方法

基本信息

批准号：
EP/F069189/1
负责人：
Gregor Tanner
金额：
$ 27.74万
依托单位：
University of Nottingham
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2009
资助国家：
英国
起止时间：
2009 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FF069189%2F1
关键词：
Vibrational energy distributions large built

项目摘要

Predicting the response of a large, complex mechanical system such as a car or an aeroplane to high frequency vibrations is a remarkably difficult task. Still, obtaining good estimates for the distribution of vibrational energy in such structures, including coupling between sub-components, damping and energy loss in form of acoustic radiation, is of great importance to engineers. An increasing demand for low vibration, low noise products to meet performance specifications and to reduce noise pollution makes any improvement in predicting vibrations response characteristics of immediate interest for industrial applications. Demand for improved virtual prototyping, as opposed to the use of expensive and time-consuming physical prototypes, is another area of application in reducing development costs and time scales. Numerical tools are often based on 'Finite Element Analysis' (FEM). While these methods work well in the low frequency regime, that is, tackling wavelengths of the order of the size of the system, they become too expensive computationally in the mid-to-high frequency regime. In particular, FEM fails to describe accurately so-called mid-frequency problems where sub-components are characterized by a wide variation of wave-lengths. While FEM is suitable for handling 'stiff' elements such as the body frame in a car, it cannot routinely capture energy transport through 'soft' components such as thin, flexible plates coupled to stiff components. A common numerical tool for predicting the vibrational contribution of short wave length components is Statistical Energy Analysis (SEA); it is, however, based on a set of restrictive assumptions which, so far, are often hard to control and generally only fulfilled in the high frequency limit and for low damping. Thus, SEA can not deliver the degree of reliability necessary to make it attractive for a wider end user community in industrial R & D departments. It is suggested here that mathematical tools from wave or quantum chaos can considerably improve the situation sketched above. Recent results by the PI Tanner show that by combining methods ranging from operator theory, dynamical systems theory and small wavelength asymptotics, SEA can be embedded into a more general theory. The new approach is based on semiclassical expansions of the full Green function in terms of rays and describing the nonlinear ray-dynamics in terms of linear operators. The resulting method captures the full correlations in the ray dynamics and has such a much improved range of validity compared to SEA. The method could revolutionise the treatment of vibrations in complex mechanical systems. Not only does it allow (i) to give quantitative bounds for the applicability of SEA (of interest to SEA users); it will also (ii) improve predictive capability in situation where SEA does not apply at a moderate computational overhead; in addition, (iii) it can be easily combined with FEM methods thus making it an ideal candidate for tackling mid-frequency problems. The approximations made are well controlled by starting from a semiclassical approach which makes it possible (iv) to systematically incorporate wave interference effects (absent in standard SEA treatments) into the method.By tackling the issues addressed above we will be able to provide improved and conceptually completely new solution methods to the engineering community based on advanced mathematical methods. The proposed research evolved out of pump-prime EPSRC funding in terms of a Springboard Fellowship. The project is thus by default of interdisciplinary nature and will be tackled jointly by the PI Tanner (Nottingham, Mathematics) and PI Mace (Southampton, ISVR, Engineering) with industrial partners from the FEM/software side (inuTech) and an engineering consulting firm (DS2L) providing input about end-user demands.

预测大型复杂机械系统（如汽车或飞机）对高频振动的响应是一项非常困难的任务。尽管如此，获得良好的估计，在这样的结构中的振动能量的分布，包括子组件之间的耦合，阻尼和声辐射形式的能量损失，是非常重要的工程师。对低振动、低噪声产品以满足性能规格和减少噪声污染的需求不断增加，使得在预测振动响应特性方面的任何改进对于工业应用具有直接的意义。对改进的虚拟原型的需求，而不是使用昂贵和耗时的物理原型，是降低开发成本和时间尺度的另一个应用领域。数值工具通常基于“有限元分析”（FEM）。虽然这些方法在低频范围内工作良好，也就是说，处理系统大小的量级的波长，但是它们在中高频范围内在计算上变得太昂贵。特别是，有限元法无法准确地描述所谓的中频问题，其中子组件的特点是波长的变化很大。虽然FEM适用于处理“刚性”元件，例如汽车中的车身框架，但它不能常规地捕获通过“软”部件（例如耦合到刚性部件的薄柔性板）的能量传输。预测短波长分量的振动贡献的常用数值工具是统计能量分析（SEA）;然而，它是基于一组限制性假设，到目前为止，这些假设通常难以控制，并且通常仅在高频率极限和低阻尼下实现。因此，SEA不能提供必要的可靠性程度，使其具有吸引力，为更广泛的最终用户社区在工业研发部门。这里建议，来自波或量子混沌的数学工具可以大大改善上述情况。PI坦纳最近的研究结果表明，通过结合算子理论，动力系统理论和小波长渐近的方法，SEA可以嵌入到一个更一般的理论。新方法基于全绿色函数的射线半经典展开式和描述的线性算子的非线性射线动力学。由此产生的方法捕获的射线动力学的全部相关性，并具有这样一个大大改善的范围内的有效性相比，SEA。该方法可能会彻底改变复杂机械系统中振动的处理方法。它不仅允许（i）给出SEA的适用性的定量界限（SEA用户感兴趣）;它还将（ii）在SEA不适用于中等计算开销的情况下提高预测能力;此外，（iii）它可以容易地与FEM方法结合，从而使其成为解决中频问题的理想候选者。从半经典的方法，这使得有可能（iv）系统地将波的干扰效应（缺乏在标准的SEA治疗）的方法。通过解决上述问题，我们将能够提供改进的和概念上全新的解决方法，以先进的数学方法的基础上，工程界的近似控制。拟议的研究演变出泵总理EPSRC资金方面的跳板奖学金。因此，该项目默认为跨学科性质，将由PI坦纳（诺丁汉，数学）和PI梅斯（南安普顿，ISVR，工程）与FEM/软件方面的工业合作伙伴（inuTech）和工程咨询公司（DS 2L）共同解决，提供有关最终用户需求的输入。