Session: 17-01-01 Research Posters

Paper Number: 74215

Start Time: Thursday, 02:25 PM

74215 - Elastic Wave Propagation in Metamaterial Thin Plates With Periodic Shunted Piezo-Patches 

Periodic structures known as phononic crystals and mechanical metamaterials are artificial structures designed to open up Bragg-type and/or locally resonant band gaps. In these ranges of frequency, there are no propagating waves, only evanescent waves. Such periodic structures are being applied in many branches of science, and have many applications, e.g., passive/active vibration control, acoustic barriers/filters, metamaterials-based enhanced energy harvesting, waveguides, among others. More recently, periodic structures with shunt circuits, named piezoelectric metamaterials, have been proposed for vibration attenuation in low frequencies. These piezoelectric structures exhibit abnormal properties, different from those found in nature, through the artificial design of the topology or exploring the shunt circuit parameters. In this study, the wave propagation in a 2-D elastic metamaterial thin plate with periodic arrays of shunted piezo-patches is investigated. This piezoelectric metamaterial plate is capable of filtering the propagation of flexural elastic waves over a specified range of frequency.

The most common strategy to analysis the wave attenuation behaviour in a metamaterial is to compute the complex dispersion relation. There are many methods used to calculate the complex values of wave numbers, for instance the multiple scattering theory (MST), spatial Laplace transform for complex wave number, wave finite element (WFE), finite element (FE), multipole expansion, finite difference time domain (FDTD), transfer matrix (TM), extended Bloch mode synthesis, state-space formulation, plane wave expansion (PWE), extended plane wave expansion (EPWE), among others. In this study, the complex dispersion diagrams are obtained by the PWE and EPWE approaches.

The dispersion relation computed by using the PWE and EPWE approaches presents similar result as methods based on finite elements, but with a considerably lower computational cost, thus indicating its advantage for the use in optimization problems. Furthermore, the analysis of the dispersion relation using different approaches has become an interesting topic for both mathematical community and engineering applications.

The PWE and EPWE approaches are considered as semi-analytical methods and can also be used to calculate the wave shapes of phononic crystals and metamaterials. The advantage of using EPWE over PWE is that evanescent modes are obtained naturally, thus the complex band structure can be investigated. In PWE, it is assumed that the Bloch wave vector is real. In addition, EPWE method is not restricted to the first Brillouin zone (FBZ). Moreover, the evanescent modes obtained by EPWE obey Floquet-Bloch's theorem.

The comparison between these methods shows good agreement. The Bragg-type and locally resonant band gaps are opened up. The shunt circuits influence significantly the propagating and the evanescent modes. The results can be used for elastic wave attenuation using piezoelectric periodic structures.

Keywords: periodic structures, band gaps, shunt circuits, complex dispersion diagram.

Presenting Author: Edson Jansen Pedrosa de Miranda Jr. Federal Institute of Maranhão (IFMA)

Authors:

Edson Jansen Pedrosa de Miranda Jr. Federal Institute of Maranhão (IFMA)
José Maria Campos Dos Santos University of Campinas (UNICAMP)