Journal
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 462, Issue 2074, Pages 2977-2995Publisher
ROYAL SOC
DOI: 10.1098/rspa.2006.1712
Keywords
nano-to-micron scale beams; non-local elasticity theory; integral equation method
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In the present work, the integral equation approach and the non-local elasticity theory are employed to investigate the free transverse vibrations of nano-to-micron scale beams. The frequency equation is analytically formulated into an eigenvalue problem of a matrix with an infinite order. The numerical calculation is implemented by truncating this matrix to a finite order one. It is found that the impact of the non-local effect on the natural frequencies and vibrating modes is negligible for the beams with micrometre scale length. But when the length of beams reaches the nanoscale, the non-local effect becomes important; especially for the high-order natural frequencies and vibrating modes.
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