A generalized nonlocal elasticity solution for the propagation of longitudinal stress waves in bars

In the present work, the propagation of one dimensional wave along the axial direction of a nano scale bar is investigated using a unified nonlocal elasticity model with two parameters. The present analysis is mainly based on Love rod theory. However, the total elastic strain energy is calculated including the shear stress components by considering Bishop correction. Thus, by applying Hamilton's principle, the explicit generalized nonlocal elasticity solution is obtained, and then, the comparative results of analysis are presented in detail.