A size-dependent model for wave propagation in timoshenko nanobeam

By incorporating the strain gradient elasticity into the Timoshenko nanobeam, a size-dependent model for wave propagation in such nanobeam is developed. The formulations of dispersion relation are explicitly derived for strain gradient nanobeam and presented for different material length scale parameters (MLSPs). The size-dependent characteristics of wave propagation in Timoshenko nanobeam are then studied. The results show that the angular frequency, phase velocity and group velocity increase with increasing wave number. However, the velocity ratios approach different values for different beam modes, indicating an interesting behavior of the asymptotic velocity ratio.