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Structural Engineering and Mechanics Volume 15, Number 6, June 2003 , pages 705-716 DOI: https://doi.org/10.12989/sem.2003.15.6.705 |
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Dynamic analysis of gradient elastic flexural beams |
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S. Papargyri - Beskou, D. Polyzos and D. E. Beskos
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| Abstract | ||
| Gradient elastic flexural beams are dynamically analysed by analytic means. The governing equation of flexural beam motion is obtained by combining the Bernoulli-Euler beam theory and the simple gradient elasticity theory due to Aifantis. All possible boundary conditions (classical and non-classical or gradient type) are obtained with the aid of a variational statement. A wave propagation analysis reveals the existence of wave dispersion in gradient elastic beams. Free vibrations of gradient elastic beams are analysed and natural frequencies and modal shapes are obtained. Forced vibrations of these beams are also analysed with the aid of the Laplace transform with respect to time and their response to loads with any time variation is obtained. Numerical examples are presented for both free and forced vibrations of a simply supported and a cantilever beam, respectively, in order to assess the gradient effect on the natural frequencies, modal shapes and beam response. | ||
| Key Words | ||
| beams; gradient elasticity; flexural vibrations; non-classical boundary conditions; free vibrations; forced vibrations. | ||
| Address | ||
| General Department, School of Technology, Aristotle University of Thessaloniki, GR-54006 Thessaloniki, Greece Department of Mechanical and Aeronautical Engineering, University of Patras, GR-26500 Patras, Greece Department of Civil Engineering, University of Patras, GR-26500 Patras, Greece | ||