# Nested Bloch waves in elastic structures with configurational forces

## TL;DR

This paper introduces a nested Bloch-Floquet method to analyze how configurational forces affect wave propagation in elastic structures, revealing new ways to control vibrations and resonance in mechanical systems.

## Contribution

The study presents a novel nested Bloch-Floquet technique to account for non-linear coupling caused by configurational forces in periodic elastic structures.

## Key findings

- Configurational forces break the band gap for longitudinal waves.
- Flexural oscillations can induce axial resonance.
- Configurational forces enable new control strategies for vibrations.

## 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.