A novel weighted averaging operator for frequency analysis of nonlinear free vibrations

IF 2.8 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics Pub Date : 2025-02-19 DOI:10.1016/j.ijnonlinmec.2025.105057

Anh Tay Nguyen , Nguyen Ngoc Linh , Nguyen Cao Thang , Nguyen Anh Ngoc , Le Quang Vinh , N.D. Anh

引用次数: 0

Abstract

The paper develops a weighted equivalent linearization (WEL) using a novel weighted averaging operator (WAO) for deterministic nonlinear oscillation problems. WAO is based on a linear combination of global and local integrations involving an embedding parameter. The main properties of WAO are systematically presented and proven. Further selecting the embedding parameter as a function of the local variable is implemented. WEL with the proposed weighted averaging operator is then applied to analyze frequency of nonlinear conservative oscillations, and some case studies are subsequently carried out in order to verify the accuracy of WEL. It is shown that WEL provides the lowest maximal errors among the approximate solutions obtained from several analytical methods for various nonlinearities considered, including strong nonlinear levels.

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非线性自由振动频率分析的加权平均算子

本文利用一种新的加权平均算子（WAO），提出了一种求解确定性非线性振荡问题的加权等效线性化方法。WAO是基于涉及嵌入参数的全局和局部集成的线性组合。系统地介绍和证明了WAO的主要性质。进一步实现了将嵌入参数作为局部变量的函数进行选择。然后将加权平均算子的自适应加权算子应用于非线性保守振荡的频率分析，并通过实例分析验证了自适应加权算子的准确性。结果表明，对于所考虑的各种非线性，包括强非线性水平，WEL在几种解析方法得到的近似解中提供了最小的最大误差。

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.