Longitudinal vibration analysis for microbars based on strain gradient elasticity theory
JOURNAL OF VIBRATION AND CONTROL, vol.20, no.4, pp.606-616, 2014 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 20 Issue: 4
- Publication Date: 2014
- Doi Number: 10.1177/1077546312463752
- Journal Name: JOURNAL OF VIBRATION AND CONTROL
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.606-616
- Keywords: Free vibration, micro-sized bar, size effect, strain gradient theory, WALLED CARBON NANOTUBES, NONLOCAL CONTINUUM MODELS, DEFORMABLE SHELL-MODEL, DYNAMIC-ANALYSIS, WAVE-PROPAGATION, FORCED VIBRATION, LENGTH SCALE, BEAM, MICROTUBULES, PLASTICITY
- Akdeniz University Affiliated: Yes
Abstract
The longitudinal free vibration problem of a micro-scaled bar is formulated using the strain gradient elasticity theory. The equation of motion together with initial conditions, classical and non-classical corresponding boundary conditions for a micro-scaled elastic bar is derived via Hamilton's principle. The resulting higher-order equation is solved for clamped-clamped and clamped-free boundary conditions. Effects of the additional length scale parameters on the frequencies are investigated. It is observed that size effect is more significant when the ratio of the microbar diameter to the additional length scale parameter is small. It is also observed that the difference between natural frequencies predicted by current and classical models becomes more prominent for both lower values of slenderness ratio of the microbar and for higher modes.