Plane wave expansion and extended plane wave expansion formulations for Mindlin-Reissner elastic metamaterial thick plates

• DOI: 10.1016/j.jmaa.2021.125503
• Publication Date: 2021-07-19T21:29:02Z
• Authors: E.J.P. Miranda; S.F. Rodrigues; C. Aranas; J.M.C. Dos Santos
• Keywords: 0103 physical sciences; 02 engineering and technology; 0210 nano-technology; 01 natural sciences

Abstract The plane wave expansion (PWE) and the extended plane wave expansion (EPWE) formulations are derived in order to obtain the complex dispersion relation of flexural waves in a metamaterial Mindlin-Reissner thick plate with multiple periodic resonators. These new formulations are useful to obtain more accurate results at higher frequencies than those based on Kirchhoff-Love thin plate theory. Multiple periodic resonators with multiple degrees of freedom (M-DOF) attached to metamaterial thick plates broaden the applications for wave attenuation in high frequencies.