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Plane wave expansion and extended plane wave expansion formulations for Mindlin-Reissner elastic metamaterial thick plates |
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| Authors: | EJP Miranda SF Rodrigues C Aranas JMC Dos Santos |
| Institution: | 1. Federal Institute of Maranhão, IFMA-EIB-DE, Rua Afonso Pena, 174, CEP 65010-030, São Luís, MA, Brazil;2. Federal Institute of Maranhão, IFMA-PPGEM, Avenida Getúlio Vargas, 4, CEP 65030-005, São Luís, MA, Brazil;3. University of Campinas, UNICAMP-FEM-DMC, Rua Mendeleyev, 200, CEP 13083-970, Campinas, SP, Brazil;4. University of New Brunswick, Department of Mechanical Engineering, Fredericton, E3B 5A3, New Brunswick, Canada |
| 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. |
| Keywords: | Fourier series expansion Multiple resonators Evanescent waves Band gaps |
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