Multi-parametric optimization for controlling bifurcation structures

IF 2.9 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES
A. Mélot, E. Denimal, L. Renson
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引用次数: 0

Abstract

Bifurcations organize the dynamics of many natural and engineered systems. They induce qualitative and quantitative changes to a system’s dynamics, which can have catastrophic consequences if ignored during design. In this paper, we propose a general computational method to control the local bifurcations of dynamical systems by optimizing design parameters. We define an objective functional that enforces the appearance of local bifurcation points at targeted locations or even encourages their disappearance. The methodology is an efficient alternative to bifurcation tracking techniques capable of handling many design parameters ( > 10 2 ). The method is demonstrated on a Duffing oscillator featuring a hardening cubic nonlinearity and an autonomous van der Pol-Duffing oscillator coupled to a nonlinear tuned vibration absorber. The finite-element model of a clamped-free Euler–Bernoulli beam, coupled with a reduced-order modelling technique, is also used to show the extension to the shape optimization of more complicated structures. Results demonstrate that several local bifurcations of various types can be handled simultaneously by the bifurcation control framework, with both parameter and state target values.
控制分叉结构的多参数优化
分岔组织了许多自然和工程系统的动力学。它们会引起系统动力学的质和量的变化,如果在设计过程中忽视这些变化,就会造成灾难性后果。在本文中,我们提出了一种通用计算方法,通过优化设计参数来控制动力系统的局部分岔。我们定义了一个目标函数,该函数可强制在目标位置出现局部分岔点,甚至鼓励其消失。该方法是分岔跟踪技术的有效替代方法,能够处理许多设计参数 ( > 10 2 )。该方法在具有硬化立方非线性的达芬振荡器和与非线性调谐振动吸收器耦合的自主范德波尔-达芬振荡器上进行了演示。无夹钳欧拉-伯努利梁的有限元模型与降阶建模技术相结合,也被用于展示更复杂结构的形状优化扩展。结果表明,分岔控制框架可以同时处理多个不同类型的局部分岔,并同时具有参数和状态目标值。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
6.40
自引率
5.70%
发文量
227
审稿时长
3.0 months
期刊介绍: Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.
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