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.

Nonlinear wave propagation in locally dissipative metamaterials via Hamiltonian perturbation approach

“…Alternative to multi-phase material approaches, innovative materials possessing periodic cellular structures are being explored in the literature [9][10][11] with the objective of tailoring the dynamic properties of the unit cells toward increased vibration absorption properties or the creation of bandgaps which can stop the propagation of waves across targeted frequency bands and wavelengths. These materials, also known as mechanical metamaterials, are macro/microarchitected media characterized by non-conventional features and designed for advanced applications such as passive attenuation of elastic waves [12], broadband sound absorption and low-frequency noise filtering [13][14][15][16][17] or other unusual dynamic properties [18,19]. The growing success of mechanical metamaterials is also sustained by the recent extraordinary developments in the technical and technological fields of highfidelity computational mechanics, micro-engineering design and high-precision additive manufacturing [20].…”

Configurational Forces on Elastic Structures

“…2. Moreover, it has also been proven that configurational forces acting at the ends of an elastic rod can strongly influence band gaps in the wave dispersion diagram and introduce a nonlinear coupling between longitudinal and transverse displacements [13]. In this article, the effects of configurational forces on one-dimensional elastic structures are reviewed, together with applications to soft devices (the elastica arm scale, the dripping of an elastic rod, and the torsional actuator), implications on stability (the penetration on an elastic blade), and connections with limbless locomotion (the snaking rod).…”

Free and forced wave propagation in beam lattice metamaterials with viscoelastic resonators

“…Within this stimulating framework, composite materials and metamaterials with periodic cellular microstructure are being purposely designed to achieve superior effective properties, outperforming the elasto-dynamic characteristics of the ingredient materials building each microstructured cell [12], [13], [14]. Significant achievements have been obtained in tailoring unusual properties or exotic performances, including for instance super lightness-to-strength ratios, strong auxeticity, synclastic bending curvatures, giant hysteresis, morphing and multistability, negative indexes of dynamic refraction, non-reciprocal vibration propagation, broadband sound absorption, controllable wave guiding, obstacle cloaking, low-frequency noise filtering, energy focusing or harvesting [15], [16], [17], [18], [19], [20], [21], [22], [23], [24].…”