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移动粘弹性轴向功能梯度纳米梁的振动与稳定性

On the Vibrations and Stability of Moving Viscoelastic Axially Functionally Graded Nanobeams.

作者信息

Shariati Ali, Jung Dong Won, Mohammad-Sedighi Hamid, Żur Krzysztof Kamil, Habibi Mostafa, Safa Maryam

机构信息

Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam.

Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam.

出版信息

Materials (Basel). 2020 Apr 6;13(7):1707. doi: 10.3390/ma13071707.

DOI:10.3390/ma13071707
PMID:32268480
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7178716/
Abstract

In this article, size-dependent vibrations and the stability of moving viscoelastic axially functionally graded (AFG) nanobeams were investigated numerically and analytically, aiming at the stability enhancement of translating nanosystems. Additionally, a parametric investigation is presented to elucidate the influence of various key factors such as axial gradation of the material, viscosity coefficient, and nonlocal parameter on the stability boundaries of the system. Material characteristics of the system vary smoothly along the axial direction based on a power-law distribution function. Laplace transformation in conjunction with the Galerkin discretization scheme was implemented to obtain the natural frequencies, dynamical configuration, divergence, and flutter instability thresholds of the system. Furthermore, the critical velocity of the system was evaluated analytically. Stability maps of the system were examined, and it can be concluded that the nonlocal effect in the system can be significantly dampened by fine-tuning of axial material distribution. It was demonstrated that AFG materials can profoundly enhance the stability and dynamical response of axially moving nanosystems in comparison to homogeneous materials. The results indicate that for low and high values of the nonlocal parameter, the power index plays an opposite role in the dynamical behavior of the system. Meanwhile, it was shown that the qualitative stability of axially moving nanobeams depends on the effect of viscoelastic properties in the system, while axial grading of material has a significant role in determining the critical velocity and natural frequencies of the system.

摘要

在本文中，对尺寸相关振动以及移动的粘弹性轴向功能梯度（AFG）纳米梁的稳定性进行了数值和解析研究，旨在提高平移纳米系统的稳定性。此外，还进行了参数研究，以阐明材料的轴向梯度、粘性系数和非局部参数等各种关键因素对系统稳定性边界的影响。系统的材料特性根据幂律分布函数沿轴向平滑变化。结合伽辽金离散化方案实施拉普拉斯变换，以获得系统的固有频率、动态构型、发散和颤振失稳阈值。此外，还对系统的临界速度进行了解析评估。研究了系统的稳定性图，可以得出结论，通过微调轴向材料分布，可以显著抑制系统中的非局部效应。结果表明，与均质材料相比，AFG材料可以极大地提高轴向移动纳米系统的稳定性和动态响应。结果表明，对于非局部参数的低值和高值，幂指数在系统的动态行为中起着相反的作用。同时，结果表明，轴向移动纳米梁的定性稳定性取决于系统中粘弹性特性的影响，而材料的轴向梯度在确定系统的临界速度和固有频率方面起着重要作用。

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