PROPAGATION OF STRESS WAVE IN A FUNCTIONALLY GRADED NANO-BAR BASED ON MODIFIED COUPLE STRESS THEORY

Abstract

In this paper, propagation of a one-dimensional elastic stress wave in a functionally graded (FG) nano-bar is analysed based on the modified couple stress theory. It is assumed that the material properties of FG bar are distributed as an exponential function along the axial direction. The two main advantages of the modified couple stress theory over the classical couple stress theory are the inclusion of a symmetric couple stress tensor and the involvement of only one material length scale parameter. According to the modified couple stress theory, only one material length scale parameter is used to describe the size effect in nano-bar. Also, the shear stress components come from the lateral inertia effect are considered in the elastic strain energy relation. Then, the governing equations are derived using Hamilton's principle and are generally solved. Finally, effects of length scale parameter, material inhomogeneity constant and Poisson's ratio on stress wave propagation velocity and harmonic behavior of stress wave are evaluated and can be observed that using the classical continuum theory leads to considerable errors in analysis of stress wave propagation.