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首页> 外文期刊>European Physical Journal Plus >Dynamic analysis of nano-beams embedded in a varying nonlinear elastic environment using Eringen's two-phase local/nonlocal model
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Dynamic analysis of nano-beams embedded in a varying nonlinear elastic environment using Eringen's two-phase local/nonlocal model

机译：eringen的两阶段局部/非局部模型在不同非线性弹性环境中嵌入纳米梁的动态分析

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Recently it was shown that the differential form of Eringen's nonlocal elastic theory is unable to model, predict and track the mechanical behaviors of many nano-structures due to their boundary conditions. Therefore, having an accurate model for formulating such structures became an important issue. With respect to this concern, in this study, the influence of having an axially varying elastic environment on vibrational behavior of nanobeams is investigated for the first time. Size-dependent effects are modeled using Eringen's two-phase local/nonlocal integral model which is well-posed with higher accuracy. The elastic environment is modeled using the Pasternak-Winkler method which could vary through the length of the nanobeam. Moreover, the environment's stiffness variation is presented by using power-law function covering wide ranges of variations. The generalized differential quadrature method is used to solve the problem and verification is done by comparing the results with previous studies on simplified problems. First four natural frequency terms for different boundary conditions are computed considering the presence of the elastic medium. A comprehensive parametric study is done to show the influence of a varying elastic environment and nonlocal terms on first four natural frequencies of beams with different boundary conditions. It is concluded that increasing the nonlocal terms will reduce the natural frequency terms of nanobeam on the elastic environment especially for cantilever nanobeams in which previous studies were unable to track such behavior. This study could be a step forward in analyzing nanostructures resting on a medium as sensors, actuators, switches, resonators, etc.
机译：最近，结果表明，由于边界条件，eringen的非局部弹性理论的差异形式不能模拟，预测和跟踪许多纳米结构的机械行为。因此，具有用于制定这种结构的准确模型成为一个重要问题。关于该问题，在该研究中，首次研究了在纳米芯片的振动行为上具有轴向变化的弹性环境的影响。使用eringen的两相局部/非局部积分模型建模大小依赖性效果，其具有更高的精度良好。弹性环境采用Pasternak-Winkler方法进行建模，其可以通过纳米云的长度而变化。此外，通过使用覆盖宽范围的变化范围来呈现环境的刚度变化。广义差分正交方法用于解决问题，通过将结果与先前的简化问题进行比较来解决问题和验证。考虑到弹性介质的存在，计算不同边界条件的前四个自然频率术语。完成了综合的参数研究，以展示不同的弹性环境和非局部术语对具有不同边界条件的梁的前四个自然频率的影响。得出结论，增加非局​​部术语将减少纳米束对弹性环境的自然频率术语，特别是对于先前研究无法跟踪这种行为的悬臂纳米束。该研究可以是在分析纳米结构上搁置在媒体上的纳米结构，执行器，开关，谐振器等方面的一步。

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