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）是工程学最重要的领域之一。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、更环保、更安全的下一代结构的关键推动因素。动力学面临的一个“巨大挑战”是非线性特性。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很强的抵抗力，因为数学是建立在线性基础上的。尽管工程师通过使用近似和计算机能力取得了进步，但他们却无法从运动结构方程的精确解中获得洞察力，因为这些方程无法使用传统方法求解。同样的问题意味着通常不可能证明精确的解决方案存在或唯一。该研究计划的首要目标是通过非传统方法找到准确的结果；基于 PI 在非线性动力学和现代机器学习方面 30 多年的经验，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，工程师转向更直接的方法紧迫的问题——首先找到运动方程。从第一原理来看，这通常是不可能的，因为连接过程（例如焊接）的未知物理原理使除了最简单的组合结构之外的所有结构的分析变得模糊。该问题通过开发“系统识别”（SI）方法得到解决，其中所需的方程是根据测量数据推断出来的。同样，线性系统首先被“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，它现已在工作理论和实践中得到确立，可供工程师利用。可以说，线性系统最强大的技术是“模态分析”。这种方法具有看似神奇的特性，涉及许多耦合动力系统的问题可以简化为一组非耦合问题，每个问题都涉及一个在其自身弹簧上振荡的质量。不幸的是，正如在精确解的情况下一样，模态分析不能推广到非线性系统。由于缺乏支撑通用技术，工程师被迫开发一种“工具箱”理念，其中不同类型的非线性系统需要不同的非线性 SI (NLSI) 方法。尽管已经有一些通用方法的暗示，但还没有一种技术能够成为“统治所有技术的一环”。非线性模态分析的一些版本已经被开发出来，但没有一个版本表现出线性理论的所有理想特性。该计划的第二个目标是为 NLSI 创建一个完全通用的框架，该框架可以推导出运动方程及其预测的统计置信度。该计划还将考虑解耦非线性系统的新方法 - 看待非线性模态分析的新方法。这里的研究将为非线性动力学提供非常新的方法。将开发寻找运动方程的新的通用方法。给定这些方程，该程序将提供解决这些方程的新方法；精确解决以前从未解决过的问题，并且没有使用分析方法解决的前景。问题将包括：非线性微分方程的精确解；非线性系统到线性系统的精确和近似变换，以及多元系统的精确和近似解耦（非线性模态分析）。创建一种期望找到精确解决方案的研究文化是一种真正思考非线性动力学的新方式。在某些方面，新的精确解决方案将与动物学中新物种的发现一样重要。通过剖析它们，人们可以增进对整个学科的了解。