摘要
By incorporating the strain gradient elasticity into the classical Bernoulli-Euler beam and Timoshenko beam models, the size-dependent characteristics of wave propaga- tion in micro/nanobeams is studied. The formulations of dis- persion relation are explicitly derived for both strain gradi- ent beam models, and presented for different material length scale parameters （MLSPs）. For both phenomenological size- dependent beam models, the angular frequency, phase veloc- ity and group velocity increase with increasing wave num- ber. 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.
By incorporating the strain gradient elasticity into the classical Bernoulli-Euler beam and Timoshenko beam models, the size-dependent characteristics of wave propaga- tion in micro/nanobeams is studied. The formulations of dis- persion relation are explicitly derived for both strain gradi- ent beam models, and presented for different material length scale parameters （MLSPs）. For both phenomenological size- dependent beam models, the angular frequency, phase veloc- ity and group velocity increase with increasing wave num- ber. 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.
基金
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)
Independent Innovation Fund of Shandong University(2011GN055)
National Science Foundation(CMMI-0643726),DARPA(W91CRB-11-C-0112)
Changjiang Scholar Program from Ministry of Education of China
