Variational principles and finite element Bloch analysis in couple stress elastodynamics

We address the numerical simulation of periodic solids (phononic crystals) within framework couple stress elasticity. The additional terms in elastic potential energy lead to dispersive behavior shear waves, even absence material periodicity. To study bulk waves these materials, we establish an action principle frequency domain and present a finite element formulation for wave propagation problem related theory subject extended set Bloch-periodic boundary conditions. A major difference from traditional phononic crystals is appearance higher-order derivatives. solve this with use Lagrange-multiplier approach. After presenting variational general treatment, particularize it finding dispersion relations bodies properties. resulting implementation used determine curves homogeneous porous solids, which latter found exhibit interesting bandgap structure.