Axial dynamic analysis of a Bishop nanorod with arbitrary boundary conditions,ZAMM - Journal of Applied Mathematics and Mechanics

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Axial dynamic analysis of a Bishop nanorod with arbitrary boundary conditions
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2020-07-24 , DOI: 10.1002/zamm.202000039
Büşra Uzun ₁ , Uğur Kafkas ₁ , Mustafa Özgür Yaylı ₁

Affiliation

In the present work, axial vibrational behavior of nanorods with different boundary conditions is researched. Bishop's rod theory is implemented to simulate the axial deflection. Size‐dependency is captured by using Eringen's nonlocal elasticity theory. Based on nonlocal deformable boundary conditions and Stokes’ transformation, a system of linear equations is derived and then constructed an Eigen value problem. Several numerical examples are presented to investigate the significance of various parameters such as geometric parameters, vibrational modes, various values of nonlocal parameter and axial spring parameters on the axial frequencies of nanorods. The numerical examples indicate that the deformable boundary conditions and small scale parameter have considerable effects on the axial vibration response.

中文翻译：

具有任意边界条件的Bishop纳米棒的轴向动力学分析

在目前的工作中，研究了具有不同边界条件的纳米棒的轴向振动行为。Bishop的杆理论用于模拟轴向挠度。大小依赖性是通过使用艾林根的非局部弹性理论来捕获的。基于非局部可变形边界条件和斯托克斯变换，推导了线性方程组，然后构造了特征值问题。给出了几个数值示例，以研究各种参数（例如几何参数，振动模式，非局部参数的各种值和轴向弹簧参数）对纳米棒轴向频率的重要性。数值算例表明，可变形边界条件和小尺度参数对轴向振动响应具有相当大的影响。

更新日期：2020-07-24

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