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首页> 外文期刊>Proceedings of the institution of mechanical engineers >Non-local vibration of simply supported nano-beams: Higher-order modes
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Non-local vibration of simply supported nano-beams: Higher-order modes

机译：简单支撑的纳米光束的非局部振动：高阶模

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摘要

In this article, the effects of some parameters, including rotary inertia, non-local parameter, and length-to-thickness ratio, on natural frequencies are studied for both classical and non-local theories. For Timoshenko beam, the equations of motion and the boundary conditions are derived from Hamilton's principle and then non-local constitutive equations of Eringen are employed to altogether formulate the problem. Afterward, obtained governing equations are used to study the free vibrations of a Timoshenko's simply supported nano-beam. And finally, the effects of above-mentioned parameters on estimated frequencies in classical and non-local elasticity theories are investigated. Results show that the discrepancy between the frequencies of higher-order vibration modes obtained from two theories increases and also significant reductions in natural frequencies occur when the rotary inertia is considered in the computations.
机译：在本文中，针对经典和非局部理论，研究了包括惯性，非局部参数和长厚比在内的某些参数对固有频率的影响。对于Timoshenko梁，根据汉密尔顿原理导出运动方程和边界条件，然后使用Eringen的非局部本构方程来完全解决该问题。然后，将获得的控制方程用于研究蒂莫申科简单支撑的纳米束的自由振动。最后，研究了经典和非局部弹性理论中上述参数对估计频率的影响。结果表明，从两种理论获得的高阶振动模式的频率之间的差异增大，并且在计算中考虑旋转惯性时，固有频率也会显着降低。

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