具有平移和旋转组合系统的摆的变量迭代法

IF 1 Q4 ENGINEERING, MECHANICAL Acta Mechanica et Automatica Pub Date : 2024-01-05 DOI:10.2478/ama-2024-0006
Muhammad Amir, Asifa Ashraf, J. A. Haider
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引用次数: 0

摘要

摘要 复杂机械系统的动态分析往往需要应用先进的数学技术。在本研究中,我们提出了一种基于变异迭代的摆式系统解法,该系统与滚动轮耦合,形成一个平移和旋转组合系统。此外,拉格朗日乘数是通过埃尔扎基变换计算得出的。所研究的系统包括一个连接到轮子上的摆锤,轮子在水平表面上滚动而不打滑。摆锤和滚动轮的耦合运动产生了一个具有平移和旋转自由度的复杂系统。为了求解支配运动方程,我们采用了变分迭代法,这是一种强大的数值技术,结合了变分原理和迭代方案的优点。拉格朗日乘法器在将系统的约束条件纳入运动方程中起着至关重要的作用。在本研究中,我们使用 Elzaki 变换来确定拉格朗日乘数,这为计算受约束机械系统的拉格朗日乘数提供了有效的方法。所提出的求解技术被应用于分析带滚动轮系统的摆锤的动力学。研究了摆长、轮子半径和初始条件等各种系统参数的影响,以了解它们对系统动力学的影响。结果表明,变异迭代法与 Elzaki 变换相结合,能有效捕捉平移和旋转组合系统的复杂行为。所提出的方法是分析和理解各种工程应用中遇到的类似机械系统动态的重要工具。
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The Variational Iteration Method for a Pendulum with a Combined Translational and Rotational System
Abstract The dynamic analysis of complex mechanical systems often requires the application of advanced mathematical techniques. In this study, we present a variation iteration-based solution for a pendulum system coupled with a rolling wheel, forming a combined translational and rotational system. Furthermore, the Lagrange multiplier is calculated using the Elzaki transform. The system under investigation consists of a pendulum attached to a wheel that rolls without slipping on a horizontal surface. The coupled motion of the pendulum and the rolling wheel creates a complex system with both translational and rotational degrees of freedom. To solve the governing equations of motion, we employ the variation iteration method, a powerful numerical technique that combines the advantages of both variational principles and iteration schemes. The Lagrange multiplier plays a crucial role in incorporating the constraints of the system into the equations of motion. In this study, we determine the Lagrange multiplier using the Elzaki transform, which provides an effective means to calculate Lagrange multipliers for constrained mechanical systems. The proposed solution technique is applied to analyse the dynamics of a pendulum with a rolling wheel system. The effects of various system parameters, such as the pendulum length, wheel radius and initial conditions, are investigated to understand their influence on the system dynamics. The results demonstrate the effectiveness of the variation iteration method combined with the Elzaki transform in capturing the complex behaviour of a combined translational and rotational system. The proposed approach serves as a valuable tool for analysing and understanding the dynamics of similar mechanical systems encountered in various engineering applications.
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来源期刊
Acta Mechanica et Automatica
Acta Mechanica et Automatica ENGINEERING, MECHANICAL-
CiteScore
1.40
自引率
0.00%
发文量
45
审稿时长
30 weeks
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