Elastic wave propagation in periodic stress-driven nonlocal Timoshenko beams

IF 3.4 3区 工程技术 Q1 MECHANICS
Gioacchino Alotta, Andrea Francesco Russillo, Giuseppe Failla
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引用次数: 0

Abstract

Nonlocal theories are well established to model statics and dynamics of small-size structures. Recent studies investigated elastic wave propagation in nonlocal beams and attention focused on periodic nonlocal beams, either endowed with resonators or resting on supports, for relevant applications at small scale. In this context, this work proposes a stress-driven nonlocal Timoshenko beam formulation and develops an original and comprehensive analytical/computational framework for wave propagation analysis in bare and periodic beams.
The framework addresses infinite and finite beams. First, exact analytical expressions are derived for the dispersion curves of the bare beam, which provide full insight into the effects of nonlocality. Second, an exact Plane Wave Expansion method is devised for periodic beams, either equipped with mass-spring resonators or resting on elastic supports; both ω(q) and q(ω) dispersion curves are derived in this work, where ω is the frequency and q is the wave number. Third, an approximate homogenization approach is formulated to estimate opening frequencies and sizes of band gaps induced by mass-spring resonators. Finally, a two-field finite element method is proposed to calculate the transmittance of finite periodic beams.
Numerical applications investigate the dispersion diagram of bare and periodic beams for different internal lengths of the stress-driven nonlocal model. Remarkably, results for finite periodic beams validate the predictions from wave propagation analysis of corresponding infinite ones. Moreover, parametric analyses show the capability of the stress-driven nonlocal model in capturing typical small-size effects.
周期应力驱动非局部季莫申科梁中的弹性波传播
非局部理论在模拟小尺寸结构的静力学和动力学方面已得到广泛应用。最近的研究调查了非局部梁中的弹性波传播,并将注意力集中在周期性非局部梁上,这些梁要么带有谐振器,要么位于支撑物上,可用于小尺度的相关应用。在此背景下,本研究提出了应力驱动的非局部季莫申科梁公式,并为裸梁和周期梁中的波传播分析开发了一个原创性的综合分析/计算框架。首先,推导出裸梁频散曲线的精确分析表达式,从而全面了解非局部性的影响。其次,针对配备质量弹簧谐振器或位于弹性支撑上的周期梁,设计了精确的平面波展开方法;在这项工作中,ω(q) 和 q(ω) 扩散曲线都被推导出来,其中 ω 是频率,q 是波数。第三,提出了一种近似均质化方法来估算质量弹簧谐振器诱导的开口频率和带隙大小。最后,提出了一种双场有限元方法来计算有限周期梁的透射率。数值应用研究了应力驱动非局部模型不同内部长度的裸梁和周期梁的色散图。值得注意的是,有限周期梁的结果验证了相应无限周期梁的波传播分析预测。此外,参数分析表明应力驱动非局部模型能够捕捉典型的小尺寸效应。
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
CiteScore
6.70
自引率
8.30%
发文量
405
审稿时长
70 days
期刊介绍: The International Journal of Solids and Structures has as its objective the publication and dissemination of original research in Mechanics of Solids and Structures as a field of Applied Science and Engineering. It fosters thus the exchange of ideas among workers in different parts of the world and also among workers who emphasize different aspects of the foundations and applications of the field. Standing as it does at the cross-roads of Materials Science, Life Sciences, Mathematics, Physics and Engineering Design, the Mechanics of Solids and Structures is experiencing considerable growth as a result of recent technological advances. The Journal, by providing an international medium of communication, is encouraging this growth and is encompassing all aspects of the field from the more classical problems of structural analysis to mechanics of solids continually interacting with other media and including fracture, flow, wave propagation, heat transfer, thermal effects in solids, optimum design methods, model analysis, structural topology and numerical techniques. Interest extends to both inorganic and organic solids and structures.
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