Wave propagation characteristics of a twisted micro scale beam

Abstract

Twisted structural elements are inherently complex and their use in engineering systems requires deeper understanding. In this paper, starting with the modified couple stress theory, the elastodynamics governing partial differential equations of motion for the transverse dynamics of a twisted micro scale beam is derived. A micro scale beam of rectangular cross-section, for which the rate of twist introduced a bending–bending coupling effect, is considered. The presented governing equation of motion is used to address the effects of the rate of twist and the material length scale on the bending wave propagation characteristics of the micro scale beam. Results are presented for the spectrum curve, the cut-off frequency, the phase speed and the group velocity of a propagating harmonic wave profile in the twisted micro scale beam. It is observed that the rate of twist bifurcates the spectrum curve of the micro scale beam within a given frequency range, while the material length scale improves the dispersion of the traveling wave. The cut-off frequency is found to be independent of the material length scale, but proportional to the fourth power of the rate of twist. Increasing the material length scale is further observed to increase the group velocity of the wave, while a high rate of twist lowers the wave speeds.