New Ways Forward for Nonlinear Structural Dynamics

非线性结构动力学的新方法

• 批准号: EP/X040852/1
• 负责人: Keith Worden
• 金额: $ 311.48万
• 依托单位: University of Sheffield
• 依托单位国家: 英国
• 项目类别: Fellowship
• 财政年份: 2024
• 资助国家: 英国
• 起止时间: 2024 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FX040852%2F1
• 关键词: New; Ways; Forward; Nonlinear; Structural

Structural Dynamics (or the Theory of Vibrations), is one of the most important fields of Engineering. Understanding vibrations is vital for new design standards and technologies; it is a key enabler in the design of lighter, greener and safer future-generation structures. A 'Grand Challenge' faced by dynamics is the property of nonlinearity. Unfortunately, almost all real structures are nonlinear to some extent, and highly resistant to mathematical analysis, because mathematics has been built on linear foundations. Although engineers have made progress by using approximations and computer power, they have been denied the insight that comes from exact solutions of structural equations of motion, because those equations have been impossible to solve using traditional methods. The same issue means that it is often impossible to prove that exact solutions even exist, or are unique. The first aim of the programme of research here is to find exact results by non-traditional methods; using state-of-the-art machine learning/evolutionary search methods, based on the PI's 30+ years of experience in nonlinear dynamics and modern machine learning.Because approximation and computation partly removed the need for exact solutions, engineers turned to a more immediately pressing problem - that of finding equations of motion in the first place. This is often impossible from first principles because the unknown physics of joining processes (e.g. welding), obscures the analysis of all but the simplest built-up structures. The problem was solved by developing 'system identification' (SI) methods, where the required equations were inferred from measured data. Again, linear systems were 'solved' first. Although linear SI proved to have technical difficulties, after fifty years of development, it is now established in working theory and practice which engineers can exploit. Arguably the most powerful technology for linear systems is that of 'modal analysis'; this method has the seemingly miraculous property that problems involving many coupled dynamical systems can be reduced to a set of uncoupled problems, each involving a single mass oscillating on its own spring. Unfortunately - as in the case of exact solutions - modal analysis does not generalise to nonlinear systems. Lacking an underpinning general technology, engineers have been forced to develop a 'toolbox' philosophy, whereby different types of nonlinear systems require different nonlinear SI (NLSI) methods. Although there have been hints at general approaches, no one technology has emerged as 'the one ring to rule them all'. Some versions of nonlinear modal analysis have been developed, but none exhibit all the desirable properties of the linear theory. The second aim of this programme will be to create a completely general framework for NLSI, which can derive equations of motion together with statistical confidences in their predictions. The programme will also consider new approaches to decoupling nonlinear systems - new ways of looking at nonlinear modal analysis.The research here will provide very new ways forward in nonlinear dynamics. New and general ways of finding equations of motion will be developed. Given the equations, the programme will provide new ways to solve them; exact solutions to problems which have never been solved before and do not have the prospect of solution using analytical methods. Problems will include: exact solution of nonlinear differential equations; exact and approximate transformation of nonlinear systems into linear ones, and the exact and approximate decoupling of multivariate systems (nonlinear modal analysis). Creating a research culture with an expectation of finding exact solutions is a truly new way of thinking about nonlinear dynamics. In some ways, new exact solutions will be as important as the discovery of new species in zoology; by dissecting them, one can advance knowledge in the whole subject.

结构动力学（或振动理论）是工程的最重要领域之一。了解振动对于新的设计标准和技术至关重要。它是设计更轻，更绿，更安全的未来生成结构的关键推动力。动态面临的“巨大挑战”是非线性的财产。不幸的是，几乎所有真实的结构在某种程度上都是非线性的，并且对数学分析具有高度抵抗力，因为数学已经建立在线性基础上。尽管工程师通过使用近似值和计算机功率取得了进步，但它们被剥夺了来自运动结构方程的精确解决方案的见解，因为这些方程式是无法使用传统方法求解的。同样的问题意味着通常不可能证明存在或独特的确切解决方案。这里的研究计划的第一个目的是通过非传统方法找到确切的结果。根据PI在非线性动力学和现代机器学习方面的30多年经验，使用最先进的机器学习/进化搜索方法。由于近似和计算部分消除了对精确解决方案的需求，工程师将更加立即紧迫的问题 - 首先找到运动方程。从第一原则中通常是不可能的，因为连接过程的未知物理（例如焊接）掩盖了除最简单的建筑结构以外的所有分析。通过开发“系统识别”（SI）方法来解决该问题，其中从测量数据中推断出所需的方程式。同样，线性系统首先“解决”。尽管线性SI被证明存在技术困难，但经过五十年的发展，现在在工作理论和实践中建立了工程师可以利用的工作理论和实践。可以说，线性系统最强大的技术是“模态分析”。该方法具有看似奇迹的属性，即涉及许多耦合动力学系统的问题可以简化为一组未耦合的问题，每个问题都涉及在其自身春季振荡的单个质量。不幸的是 - 与精确解决方案一样，模态分析不会推广到非线性系统。由于缺乏基础的一般技术，工程师被迫开发“工具箱”理念，不同类型的非线性系统需要不同的非线性SI（NLSI）方法。尽管对一般方法有暗示，但没有一个技术出现为“统治所有这些戒指”。已经开发了一些非线性模态分析的版本，但没有一个线性理论的所有理想特性。该程序的第二个目的是为NLSI创建一个完全一般的框架，该框架可以得出运动方程以及其预测中的统计信心。该计划还将考虑解耦非线性系统的新方法 - 研究非线性模态分析的新方法。此处的研究将为非线性动态提供非常新的方式。将开发新的和一般的寻找运动方程的方法。鉴于方程式，该程序将提供新的方法来解决它们；精确解决以前从未解决过的问题，并且没有使用分析方法的解决方案的前景。问题将包括：非线性微分方程的精确解决方案；非线性系统到线性系统的精确转换，以及多元系统的确切和近似解耦（非线性模态分析）。建立一个希望找到精确解决方案的研究文化是对非线性动态思考的真正新方法。在某些方面，新的精确解决方案将与在动物学中发现新物种一样重要。通过解剖它们，可以促进整个主题的知识。