Nested Bloch waves in elastic structures with configurational forces

Abstract

Small axial and flexural oscillations are analyzed 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 non-linear 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.

20 pages, 5 figures

References in corpus (14)

• Mechanical modeling of innovative metamaterials alternating pentamode lattices and confinement plates
• Eshelby-like forces acting on elastic structures: theoretical and experimental proof
• Tilted resonators in a triangular elastic lattice: chirality, Bloch waves and negative refraction
• Vibrations and elastic waves in chiral multi-structures
• Interfacial waveforms in chiral lattices with gyroscopic spinners
• Transition wave in a supported heavy beam
• Configurational forces and nonlinear structural dynamics
• An Elastica Arm Scale
• Development of configurational forces during the injection of an elastic rod
• Edge waves and localisation in lattices containing tilted resonators
• On the planar elastica, stress, and material stress
• Asymptotic self-restabilization of a continuous elastic structure
• Propagation and filtering of elastic and electromagnetic waves in piezoelectric composite structures
• Partial constraint singularities in elastic rods

Cited by in corpus (3)

• Design of tunable acoustic metamaterials with periodic piezoelectric microstructure
• The elastica sling
• Configurational forces on elastic structures