An innovative methodology in analyzing two-degrees-of-freedom of coupled dynamical system

IF 5.9 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Ain Shams Engineering Journal Pub Date : 2025-09-25 DOI:10.1016/j.asej.2025.103770

Asma Alanazy , Galal M. Moatimid , T.S. Amer , Mona A.A. Mohamed

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引用次数: 0

Abstract

Analyzing two-degrees-of-freedom (2DOF) coupled dynamical systems is crucial in understanding complex interactions in mechanical, structural, and aerospace engineering. Advanced analytical and numerical methods elucidate complicated behavior relevant to bio-inspired systems, smart materials, and vibration control. Consequently, the present topic centers on a recognized benchmark challenge in the field of a cart-pendulum system. The non-perturbative approach (NPA) underlies the unique analysis. The principal aim of the NPA is to convert weakly nonlinear oscillators of ordinary differential equations (ODEs) into linear forms. The swift evaluation of the frequency-amplitude correlation is essential in acquiring successive approximations of responses to parametric nonlinear fluctuations. The influence of several parameters on the stability of steady states is examined. The results demonstrated that the suggested technique is exceptionally intuitive, extremely effective, and firmly established. The alteration of bifurcation parameters influences the configuration of the bifurcation curve. The Lyapunov exponent (LE) curves are additionally illustrated.

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一种分析二自由度耦合动力系统的创新方法

分析两自由度（2DOF）耦合动力系统对于理解机械、结构和航空航天工程中的复杂相互作用至关重要。先进的分析和数值方法阐明了与仿生系统、智能材料和振动控制相关的复杂行为。因此，当前的主题集中在小车摆系统领域公认的基准挑战上。非摄动方法（NPA）是独特分析的基础。NPA的主要目的是将常微分方程（ode）的弱非线性振子转换成线性形式。在获得参数非线性波动响应的连续逼近时，快速评估频率-幅度相关性是必不可少的。考察了几个参数对稳态稳定性的影响。结果表明，建议的技术是非常直观的，非常有效，并牢固建立。分岔参数的改变会影响分岔曲线的构型。李雅普诺夫指数（LE）曲线也作了说明。

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来源期刊

Ain Shams Engineering Journal Engineering-General Engineering

CiteScore

10.80

自引率

13.30%

发文量

441

审稿时长

49 weeks

期刊介绍： in Shams Engineering Journal is an international journal devoted to publication of peer reviewed original high-quality research papers and review papers in both traditional topics and those of emerging science and technology. Areas of both theoretical and fundamental interest as well as those concerning industrial applications, emerging instrumental techniques and those which have some practical application to an aspect of human endeavor, such as the preservation of the environment, health, waste disposal are welcome. The overall focus is on original and rigorous scientific research results which have generic significance. Ain Shams Engineering Journal focuses upon aspects of mechanical engineering, electrical engineering, civil engineering, chemical engineering, petroleum engineering, environmental engineering, architectural and urban planning engineering. Papers in which knowledge from other disciplines is integrated with engineering are especially welcome like nanotechnology, material sciences, and computational methods as well as applied basic sciences: engineering mathematics, physics and chemistry.