位于非局部弹性地基上的功能分级曲面非局部纳米梁自由振动的有限元计算公式

IF 2.3 3区 工程技术 Q2 ACOUSTICS
Yuan Tang, PeiLiang Bian, Hai Qing
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引用次数: 0

摘要

本研究基于局部/非局部两相模型,研究了弹性地基对随尺寸变化的功能分级(FG)曲面欧拉-伯努利纳米梁自由振动的影响。通过汉密尔顿原理导出了控制方程和标准边界条件。积分构成方程等效地转化为微分形式,并具有相应的构成边界条件。地基产生的轴力、弯矩和反作用力通过位移变量明确表达。借助构成边界条件,可以灵活地满足高阶变量的要求。利用基于两相非局部弹性差分形式的有限元公式对纳米梁进行离散化,并得到了关于振动频率的一般特征值方程。通过与文献结果的比较,验证了所提出的有限元模型的效率和准确性。研究了不同边界条件下非局部参数、温克勒弹性参数、弯曲纳米梁的中心角和长高比对振动频率的影响。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Finite element formulation for free vibration of the functionally graded curved nonlocal nanobeam resting on nonlocal elastic foundation
In this work, the influence of elastic foundation on a size-dependent free vibration of functionally graded (FG) curved Euler-Bernoulli nanobeam is investigated on the basis of two-phase local/nonlocal models. The governing equation and standard boundary conditions are derived through Hamilton’s principle. The integral constitutive equation is equivalently transformed into differential forms with the corresponding constitutive boundary conditions. The axial force, bending moment, and react force due to foundation are explicitly expressed with respect to displacement variables. With the aid of the constitutive boundary conditions, the possibility of flexibly meeting higher-order variables is achieved. A finite element formulation based on the differential form of the two-phase nonlocal elasticity is utilized to discretize the nanobeam, and a general eigenvalue equation is obtained about the vibration frequency. The efficiency and accuracy of the proposed finite element model are validated by comparison with the results in the literature. The influences of nonlocal parameters, Winkler elastic parameter, central angle of the curved nanobeam, and length–height ratio on the vibration frequencies are studied for different boundary conditions.
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来源期刊
Journal of Vibration and Control
Journal of Vibration and Control 工程技术-工程:机械
CiteScore
5.20
自引率
17.90%
发文量
336
审稿时长
6 months
期刊介绍: The Journal of Vibration and Control is a peer-reviewed journal of analytical, computational and experimental studies of vibration phenomena and their control. The scope encompasses all linear and nonlinear vibration phenomena and covers topics such as: vibration and control of structures and machinery, signal analysis, aeroelasticity, neural networks, structural control and acoustics, noise and noise control, waves in solids and fluids and shock waves.
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