Dispersion properties of guided elastic waves in micropolar plates

The free propagation of harmonic guided waves in homogeneous isotropic micropolar plates is investigated. The physical-mathematical model treats the micropolar plates as finite-thickness layers of linearly elastic Cosserat continuum, bounded by traction-free parallel planes. Initially, the partial differential equations governing free undamped motion are formulated for the unbounded three-dimensional micropolar continuum. Their analytical solutions are obtained by an original spectral decomposition of the acoustic tensor in the frequency domain. The resulting dispersion spectrum is endowed with spectral branches-absent in the classical Cauchy continuum-, which are associated with microrotational waveforms and characterized by distinct cutoff frequencies. A novel energy-based criterion is proposed to classify and quantify the waveform polarization. Subsequently, the partial wave method is employed to enforce boundary conditions and to construct semi-analytical solutions for the elastodynamic problem of harmonic guided waves propagating in infinite plates. This analysis enables a comprehensive characterization of the dispersion properties for both in-plane and out-of-plane uncoupled problems. From a mechanical perspective, the parametric analyses of the in-plane problem solutions reveal significant qualitative and quantitative effects of micropolarity on wave dynamics. In addition to the spectral enrichment due to micropolar branches, several distinctive dynamic phenomena are identified and parametrically described. These include frequency hardening, non-dispersive behavior in the limits of long/short wavelengths, asymptotic coalescence of phase/group speeds, proliferation of internal resonances, crossing and veering of spectral branches, hybridization of quasi-resonant translational and microrotational wavemodes. Mathematical conditions for the occurrence of frequency veering and modal hybridization are established.