Corrigendum to “Eigenvector method, consistency test and inconsistency repairing for an incomplete fuzzy preference relation” [Applied Mathematical Modelling 37(2013) 5171–5183]

This paper presents a novel semi-analytical method to consider complex dispersion relations and evanescent wave characteristics in periodic magneto-electro-electric curved phononic crystal plates, based on the plate theory and Bloch-Floquet theorem. Generalized elastodynamic wave equation considering the magneto-electric effects in cylindrical coordinate system is established and discretized with the curved higher-order spectral elements. Then, the proposed approach is validated by the analysis of accuracy and convergence. The influence of magneto-electro coupling effect on dispersion relations are discussed. Significant parameters of the periodic curved phononic crystal are studied systematically, which fundamentally determines the tunability of complex dispersion relations of various guided wave modes including propagative wave modes, purely evanescent wave modes, evanescent edge wave modes, and complex wave modes. It is witnessed that propagative wave modes lead the bandgap to the emergence, variation, and closure with the change of significant parameters. And evanescent wave modes dominate two individual patterns of bandgaps. When the radius angle or curvature changes, the polarization of bandgaps appears. Furthermore, complex wave modes are generated with the increase of curvature resulting in strengthening the attenuation of propagative wave modes. The variation of lattice ratio can separate the intersection point of two propagative wave modes, which induces the opening of two bandgaps and the attenuation of evanescent wave modes. The results of this work provides may benefit the multi-functional development and application of smart materials and structures.