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Vibration of nonlocal Timoshenko beams

机译：非局部Timoshenko梁的振动

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摘要

This paper is concerned with the free vibration problem for microanobeams modelled after Eringen's nonlocal elasticity theory and Timoshenko beam theory. The small scale effect is taken into consideration in the former theory while the effects of transverse shear deformation and rotary inertia are accounted for in the latter theory. The governing equations and the boundary conditions are derived using Hamilton's principle. These equations are solved analytically for the vibration frequencies of beams with various end conditions. The vibration solutions obtained provide a better representation of the vibration behaviour of short, stubby, microanobeams where the effects of small scale, transverse shear deformation and rotary inertia are significant. The exact vibration solutions should serve as benchmark results for verifying numerically obtained solutions based on other beam models and solution techniques.
机译：本文关注的是基于Eringen的非局部弹性理论和Timoshenko梁理论建模的微/纳米梁的自由振动问题。在前一种理论中考虑了小尺度效应，而在后一种理论中考虑了横向剪切变形和旋转惯性的影响。利用汉密尔顿原理导出控制方程和边界条件。这些方程式针对各种最终条件下的梁的振动频率进行了解析求解。所获得的振动解决方案可以更好地表示短，短而微/纳米的振动行为，其中小比例，横向剪切变形和旋转惯性的影响非常明显。精确的振动解应作为基准结果，用于验证基于其他梁模型和解技术的数值解。

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