Abstract
Abstract In this paper, additional small-scale boundary effects on the free vibration of single-walled carbon nanotubes under various boundary conditions are investigated using an analytical nonlocal Euler-beam model. From the numerical results, it seems that the various beam boundary conditions due to local and nonlocal elasticity are equivalent. For simplicity, local boundary conditions can still be used even for the free end. It is convenient to analyze the vibration of single-walled carbon nanotubes under various types of boundary conditions. In addition, Hamilton's energy function, which can be explicitly expressed by transverse displacement, has also been derived to explain the boundary equivalence of nonlocal and local beams.
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