Thermoelastic vibration of bidirectional functionally graded nanobeams with the influence of micromechanical models

IF 2.2 3区工程技术 Q2 MECHANICS

Archive of Applied Mechanics Pub Date : 2025-03-27 DOI:10.1007/s00419-025-02790-y

Ngoc Anh Thi Le, An Ninh Thi Vu, Dinh Kien Nguyen

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引用次数: 0

Abstract

The thermoelastic vibration of power-law bidirectional functionally graded material (BFGM) nanobeams considering the influence of different micromechanical models is studied for the first time. The material properties of the nanobeams are temperature-dependent, and they are predicted by four micromechanical models, namely the Voigt, Mori–Tanaka, Hashin–Shtrikman, and Reuss models. Based on the third-order shear deformation theory and Eringen’s nonlocal elastic theory, the governing equations are derived using the transverse shear rotation rather than cross-sectional rotation as an independent variable. Natural frequencies are predicted for BFGM nanobeams with various boundary conditions by the Galerkin finite element method. The result reveals that the micromechanical model is of great importance in predicting the frequencies, and the frequencies obtained by the Mori–Tanaka and Hashin–Shtrikman models are close to each other, while those predicted by the Voigt and Reuss models are the most and the least conservative, respectively. It is also shown that the influence of the temperature rise on the frequencies is more significant for the higher nonlocal parameter. The effects of the material distribution, nonlocal parameter, temperature rise, and aspect ratio on the vibration of the BFGM nanobeams are studied in detail and highlighted.

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受微力学模型影响的双向功能梯度纳米梁热弹性振动

首次研究了考虑不同微观力学模型影响的幂律双向功能梯度材料纳米梁的热弹性振动。纳米梁的材料特性与温度有关，并通过四种微观力学模型进行预测，即Voigt模型、Mori-Tanaka模型、Hashin-Shtrikman模型和Reuss模型。基于三阶剪切变形理论和Eringen非局部弹性理论，以横向剪切旋转为自变量，而不是以截面旋转为自变量，推导了控制方程。采用伽辽金有限元法对具有不同边界条件的BFGM纳米梁的固有频率进行了预测。结果表明，微力学模型在预测频率方面具有重要意义，Mori-Tanaka模型和Hashin-Shtrikman模型预测的频率较为接近，而Voigt模型和Reuss模型预测的频率最保守，Reuss模型预测的频率最不保守。非局部参数越高，温升对频率的影响越显著。重点研究了材料分布、非局部参数、温升和长径比等因素对BFGM纳米梁振动的影响。

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来源期刊

Archive of Applied Mechanics 物理-力学

CiteScore

4.40

自引率

10.70%

发文量

234

审稿时长

4-8 weeks

期刊介绍： Archive of Applied Mechanics serves as a platform to communicate original research of scholarly value in all branches of theoretical and applied mechanics, i.e., in solid and fluid mechanics, dynamics and vibrations. It focuses on continuum mechanics in general, structural mechanics, biomechanics, micro- and nano-mechanics as well as hydrodynamics. In particular, the following topics are emphasised: thermodynamics of materials, material modeling, multi-physics, mechanical properties of materials, homogenisation, phase transitions, fracture and damage mechanics, vibration, wave propagation experimental mechanics as well as machine learning techniques in the context of applied mechanics.