Nested Bloch waves in elastic structures with configurational forces



Corso, Francesco Dal, Tallarico, Domenico, Movchan, Natalia V, Movchan, Alexander B and Bigoni, Davide
(2019) Nested Bloch waves in elastic structures with configurational forces. Philosophical Transactions of the Royal Society A (2019) 377: 20190101.

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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.

Item Type: Article
Additional Information: 20 pages, 5 figures
Uncontrolled Keywords: physics.class-ph, physics.class-ph, cond-mat.mtrl-sci
Depositing User: Symplectic Admin
Date Deposited: 11 Sep 2019 07:40
Last Modified: 02 Sep 2022 20:10
DOI: 10.1098/rsta.2019.0101
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3054133