📝 Abstract

In the present paper, small-scale effects on the free transverse vibration of nanobeams are investigated employing nonlocal elasticity theory. Equations of motion of the nonlocal plate model for the aforementioned study are derived and presented. The small scale effect is considered in this theory while the transverse shear deformation effects and rotary inertia are taken into account in presented Timoshenko beam theory. Through variational formulation and the Hamilton principle the governing differential equations of the free vibration of nonlocal Timoshenko beam and the boundary conditions are derived. The obtained equations are solved by the differential transformation method (DTM) for various frequency modes of beams with different end conditions. In addition, the effects of slenderness and on vibration behavior are presented. It is revealed that the slenderness affects the vibration characteristics slightly whilst the small scale plays a significant role in vibration behavior of the nanobeam.

🏷️ Keywords

free vibrationnanobeamEringen nonlocal elasticity theory
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Citation

Sarah Johnson, Emily Davis, Jessica Brown, Amanda Taylor. (2023). Nonlocal scaling effects on the free transverse vibration characteristics of nanobeams. Cithara Journal, 63(7). ISSN: 0009-7527