Alibakhshi Amin, Dastjerdi Shahriar, Malikan Mohammad, Eremeyev Victor A
Department of Mechanical Engineering, Science and Research Branch, Islamic Azad University, Tehran 1477893855, Iran.
Civil Engineering Department, Division of Mechanics, Akdeniz University, Antalya 07058, Turkey.
Nanomaterials (Basel). 2021 Nov 14;11(11):3066. doi: 10.3390/nano11113066.
In recent years, the static and dynamic response of micro/nanobeams made of hyperelasticity materials received great attention. In the majority of studies in this area, the strain-stiffing effect that plays a major role in many hyperelastic materials has not been investigated deeply. Moreover, the influence of the size effect and large rotation for such a beam that is important for the large deformation was not addressed. This paper attempts to explore the free and forced vibrations of a micro/nanobeam made of a hyperelastic material incorporating strain-stiffening, size effect, and moderate rotation. The beam is modelled based on the Euler-Bernoulli beam theory, and strains are obtained via an extended von Kármán theory. Boundary conditions and governing equations are derived by way of Hamilton's principle. The multiple scales method is applied to obtain the frequency response equation, and Hamilton's technique is utilized to obtain the free undamped nonlinear frequency. The influence of important system parameters such as the stiffening parameter, damping coefficient, length of the beam, length-scale parameter, and forcing amplitude on the frequency response, force response, and nonlinear frequency is analyzed. Results show that the hyperelastic microbeam shows a nonlinear hardening behavior, which this type of nonlinearity gets stronger by increasing the strain-stiffening effect. Conversely, as the strain-stiffening effect is decreased, the nonlinear frequency is decreased accordingly. The evidence from this study suggests that incorporating strain-stiffening in hyperelastic beams could improve their vibrational performance. The model proposed in this paper is mathematically simple and can be utilized for other kinds of micro/nanobeams with different boundary conditions.
近年来，由超弹性材料制成的微纳梁的静态和动态响应受到了广泛关注。在该领域的大多数研究中，许多超弹性材料中起主要作用的应变强化效应尚未得到深入研究。此外，对于这种对大变形很重要的梁，尺寸效应和大旋转的影响也未得到探讨。本文试图研究一种考虑应变强化、尺寸效应和适度旋转的超弹性材料微纳梁的自由振动和受迫振动。基于欧拉-伯努利梁理论对梁进行建模，并通过扩展的冯·卡门理论获得应变。通过哈密顿原理推导边界条件和控制方程。应用多尺度方法获得频率响应方程，并利用哈密顿技术获得自由无阻尼非线性频率。分析了诸如强化参数、阻尼系数、梁的长度、长度尺度参数和强迫振幅等重要系统参数对频率响应、力响应和非线性频率的影响。结果表明，超弹性微梁呈现非线性硬化行为，这种非线性通过增加应变强化效应而增强。相反，随着应变强化效应的降低，非线性频率相应降低。本研究的证据表明，在超弹性梁中考虑应变强化可以改善其振动性能。本文提出的模型在数学上很简单，可用于具有不同边界条件的其他类型的微纳梁。
