Criteria for mode shape tracking in Micropolar-Cosserat periodic panels

Abstract

This study communicates the dispersion nature and motion of propagating waves on the periodic panels resulting from the variation of the Micropolar-Cosserat (MC) parameters such as characteristic length-scale and Cosserat shear modulus. The non-dimensionalization of the system determines the independent parameters for the MC beam model in order to examine the motion of the micro-rotational as well as flexural wave modes. A periodic boundary condition based on Bloch-Floquet’s theorem is employed on the unit cell to maintain the periodicity and assess the eigenvalue domain within the transfer matrix approach. A significant part of this enlightening theoretical comprehension regarding veering, locking, and coupling is elucidated by tracking the mode shapes within the Modal Assurance Criteria (MAC), which is the prime novelty of this research. Periodically pass-band and partial bandwidth are also examined to build up confidence concerning the complex and real wave modes, respectively. A slight variation of MC parameters can dramatically alter the emergence of veering, locking, and coupling phenomena, even 1% only. The band gap (BG) calculated through the two-dimensional (2-D) Finite Element Analysis (FEM) corroborates well with the reduced one-dimensional (1-D) MC periodic panels.