Nested Bloch waves in elastic structures with configurational forces

Small axial and flexural oscillations are analysed for a periodic and infinite structure, constrained by sliding sleeves and composed of elastic beams. A nested Bloch–Floquet technique is introduced to treat the nonlinear coupling between longitudinal and transverse displacements induced by the configurational forces generated at the sliding sleeve ends. The action of configurational forces is shown to play an important role from two perspectives. First, the band gap structure for purely longitudinal vibration is broken so that axial propagation may occur at frequencies that are forbidden in the absence of a transverse oscillation and, second, a flexural oscillation may induce axial resonance, a situation in which the longitudinal vibrations tend to become unbounded. The presented results disclose the possibility of exploiting configurational forces in the design of mechanical devices towards longitudinal actuation from flexural vibrations of small amplitude at given frequency. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 1)’.

Atomistic Study for the Vibrational Properties on Σ5 Symmetric Tilt Bicrystal Copper Nanowires

In this study, an atomistic simulation was performed to investigate intrinsic resonance propensity of clamped-clamped copper nanowires with Σ5 (310)/[001] symmetric tilt grain boundary. Grain boundary energy γGB for bicrystal structure was calculated based on an iterative approach. The stable atomic configuration was then doubly clamped and excited via flexural oscillation under varied temperatures. From the result, the appearance of grain boundary significantly alters the resonance properties of Cu nanowires. Greater attenuation in kinetic energy can be observed with increased temperature. Quality factors attains Q ~ 1/T0.7144 and 1/T0.7249 with temperatures from kinetic energy and centroid root mean square spectrum, respectively, where the former seems more reliable to employ at elevated temperatures.