基于四元数的三维几何精确梁结构非线性模态和频率响应有限元计算

IF 2.6 2区 工程技术 Q2 MECHANICS
Marielle Debeurre, Aurélien Grolet, Olivier Thomas
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引用次数: 0

摘要

本文提出了一种计算三维(3D)高柔性细长结构非线性动力学的新方法。这是将之前仅限于平面(二维)变形的工作扩展到三维。它以几何精确梁模型为基础,采用有限元方法对其进行离散化处理,并通过谐波平衡法(HBM)和渐近数值法(ANM)在频域内对周期解进行求解。一个重要的考虑因素是横梁截面旋转的参数化,这比二维情况下的要求高得多。在这里,旋转是用四元数参数化的,其优点是自然导致模型中的多项式非线性,非常适合应用 ANM。由于采用了 HBM-ANM 框架,这种数值计算策略既能计算周期振荡下结构的频率响应,也能计算其非线性模式(即自由保守振荡下的骨干曲线和变形形状)。为了说明和验证这一策略,我们用它来解决文献中的两个三维变形测试案例:在近似正方形横截面的情况下,两个伴弯模态之间发生一对一(1:1)内部共振的悬臂梁和夹紧-夹紧梁。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Quaternion-based finite-element computation of nonlinear modes and frequency responses of geometrically exact beam structures in three dimensions

Quaternion-based finite-element computation of nonlinear modes and frequency responses of geometrically exact beam structures in three dimensions

In this paper, a novel method for computing the nonlinear dynamics of highly flexible slender structures in three dimensions (3D) is proposed. It is the extension to 3D of a previous work restricted to inplane (2D) deformations. It is based on the geometrically exact beam model, which is discretized with a finite-element method and solved entirely in the frequency domain with a harmonic balance method (HBM) coupled to an asymptotic numerical method (ANM) for continuation of periodic solutions. An important consideration is the parametrization of the rotations of the beam’s cross sections, much more demanding than in the 2D case. Here, the rotations are parametrized with quaternions, with the advantage of leading naturally to polynomial nonlinearities in the model, well suited for applying the ANM. Because of the HBM–ANM framework, this numerical strategy is capable of computing both the frequency response of the structure under periodic oscillations and its nonlinear modes (namely its backbone curves and deformed shapes in free conservative oscillations). To illustrate and validate this strategy, it is used to solve two 3D deformations test cases of the literature: a cantilever beam and a clamped–clamped beam subjected to one-to-one (1:1) internal resonance between two companion bending modes in the case of a nearly square cross section.

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来源期刊
CiteScore
6.00
自引率
17.60%
发文量
46
审稿时长
12 months
期刊介绍: The journal Multibody System Dynamics treats theoretical and computational methods in rigid and flexible multibody systems, their application, and the experimental procedures used to validate the theoretical foundations. The research reported addresses computational and experimental aspects and their application to classical and emerging fields in science and technology. Both development and application aspects of multibody dynamics are relevant, in particular in the fields of control, optimization, real-time simulation, parallel computation, workspace and path planning, reliability, and durability. The journal also publishes articles covering application fields such as vehicle dynamics, aerospace technology, robotics and mechatronics, machine dynamics, crashworthiness, biomechanics, artificial intelligence, and system identification if they involve or contribute to the field of Multibody System Dynamics.
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