By incorporating the strain gradient elasticity into the classical Bernoulli-Euler beam and Timoshenko beam models, the size-dependent characteristics of wave propagation in micro/nanobeams is studied. The formulations of dispersion relation are explicitly derived for both strain gradient beam models, and presented for different material length scale parameters (MLSPs). For both phenomenological sizedependent beam models, the angular frequency, phase velocity and group velocity increase with increasing wave number. However, the velocity ratios approach different values for different beam models, indicating an interesting behavior of the asymptotic velocity ratio. The present theory is also compared with the nonlocal continuum beam models. © The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag Berlin Heidelberg 2012.
Bibliographical noteThe project was supported by the National Natural Science Foundation of China (11202117, 11272186, 11172231 and 50928601), the Postdoctoral Science Foundation of China (2012M521326), the Natural Science Fund of Shandong Province (ZR2012AM014 and BS2012ZZ006), and Independent Innovation Fund of Shandong University (2011GN055), National Science Foundation (CMMI-0643726), DARPA (W91CRB-11-C-0112) and Changjiang Scholar Program from Ministry of Education of China.
- Bernoulli-Euler beam theory
- Strain gradient elasticity theory
- Timoshenko beam theory
- Wave propagation