Analytical solution of couple-mass-spring systems by novel homotopy perturbation method

IF 2.8 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics Pub Date : 2024-10-09 DOI:10.1016/j.ijnonlinmec.2024.104923

Nazmul Sharif, Helal Uddin Molla, M.S. Alam

引用次数: 0

Abstract

In this paper, a novel homotopy perturbation method is employed to estimate the approximate angular frequencies of highly nonlinear oscillators. This innovative methodology is extended to generate periodic solutions for the nonlinear free vibration observed in a conservative couple-mass-spring system. The system is characterized by both linear and nonlinear stiffness, specifically incorporating cubic nonlinearity. The application of this technique involves a detailed analysis of two practical instances of such systems. The validation process, comparing the results against published findings and exact solutions, reveals a notable alignment in the approximated angular frequencies and the corresponding periodic solutions. Noteworthy for its precision and easy to use application, this approach proves suitable for addressing a diverse range of nonlinear oscillatory problems encountered in both scientific and engineering domains.

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用新型同调扰动法分析求解耦合-质量-弹簧系统

本文采用了一种新颖的同调扰动方法来估算高度非线性振荡器的近似角频率。这一创新方法被扩展用于生成在保守耦合-质量弹簧系统中观察到的非线性自由振动的周期解。该系统具有线性和非线性刚度，特别是包含立方非线性。该技术的应用包括对此类系统的两个实际实例进行详细分析。在验证过程中，将结果与已发表的研究结果和精确解进行比较，发现近似角频率与相应的周期解明显一致。值得注意的是，这种方法不仅精确，而且应用简便，适用于解决科学和工程领域遇到的各种非线性振荡问题。

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

International Journal of Non-Linear Mechanics 物理-力学

CiteScore

5.50

自引率

9.40%

发文量

192

审稿时长

67 days

期刊介绍： The International Journal of Non-Linear Mechanics provides a specific medium for dissemination of high-quality research results in the various areas of theoretical, applied, and experimental mechanics of solids, fluids, structures, and systems where the phenomena are inherently non-linear. The journal brings together original results in non-linear problems in elasticity, plasticity, dynamics, vibrations, wave-propagation, rheology, fluid-structure interaction systems, stability, biomechanics, micro- and nano-structures, materials, metamaterials, and in other diverse areas. Papers may be analytical, computational or experimental in nature. Treatments of non-linear differential equations wherein solutions and properties of solutions are emphasized but physical aspects are not adequately relevant, will not be considered for possible publication. Both deterministic and stochastic approaches are fostered. Contributions pertaining to both established and emerging fields are encouraged.