Abstract
The study aims at investigating the effect of a generic state of prestress on the passbands and bandgaps of a phononic crystal plate. To this end, an Updated Lagrangian scheme is developed, which consists of two steps: first, a static geometrically nonlinear analysis of a representative unit cell undergoing the action of an applied external load is conducted and then the Floquet-Bloch decomposition is applied to the linearized equations of the acousto-elasticity for the unit cell in the deformed configuration. In addition, a formula for the calculation the energy velocity is proposed. In the case of an epoxy plate with cylindrical steel inclusions, it is shown that, even in the case of prestress inducing full reversible deformation state, the band gap experiences a shift towards higher frequencies when the cell is subjected to a compressive prestress, whereas a frequency downshift is registered when the cell is subjected to traction. In particular, it is demonstrated that the frequency downshift of the bandgap for the phononic plate undergoing a tensile prestress is approximately 3.5\% with respect to the case of the phononic plate under compression. The results presented herein provide insights in the behavior of phononic crystal plates with tunable dispersive properties, and suggest new leverages for wave manipulation valuable in many application fields such as wave filters, waveguiding and beam splitting, sensing devices, and vibration shielding.
Highlights
The propagation of elastic waves in periodic structures is governed by the elastomorphic and material parameters of its unit cell (Kushwaha and Halevi, 1994; Sainidou et al, 2005)
On the other hand, when the cell is subjected to traction, the lower bound of the bandgap is observed at 68.3 kHz while its upper bound at 84.3 kHz, which corresponds to a frequency downshift of approximately 3.5% of the bandgap with respect to the case of the phononic crystal (PC) plate under compression
An Updated Lagrangian computational scheme has been presented for the calculation of the band diagrams of phononic crystal plates subjected to a generic state of prestress
Summary
The propagation of elastic waves in periodic structures is governed by the elastomorphic and material parameters of its unit cell (Kushwaha and Halevi, 1994; Sainidou et al, 2005) Conceiving their design in terms of size, shape, and arrangement, as well as choosing their density and elastic properties demonstrated great potential for attaining exceptional dynamic behavior, such as frequency bandgaps (Kushwaha and Halevi, 1994; Mártinez-Sala et al, 1995; Liu et al, 2000; Miniaci et al, 2018a), negative refraction (Morvan et al, 2010; Zhu et al, 2014; Zhu and Semperlotti, 2016), topological protection (Mousavi et al, 2015; Süsstrunk and Huber, 2015; Pal et al, 2016; Miniaci et al, 2018b), etc.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
