Energy shares of plane harmonic wave at an interface between two microstructured flexoelectric half-spaces

Abstract

In the present work, we consider a problem of reflection and transmission of plane waves at an interface between two different isotropic dielectric half-spaces by considering the effects of flexoelectricity, micro-inertia and strain gradient elasticity. The plane wave solutions of the governing field equations for such a medium shows the existence of two quasi-plane waves. An incident plane wave at an interface between two dissimilar half-spaces generates two reflected and two transmitted waves. By using the continuous conditions at the interface, the relations between amplitude ratios of reflected and transmitted waves are derived in terms of a transfer matrix. A quantitative example of the model is set up to evaluate numerically the amplitude and energy ratios of various reflected and transmitted waves. The numerical results are validated by the law of energy conservation. The numerical results are illustrated graphically against the angle of incidence to show the effects of flexoelectricity, micro-inertia and strain gradients on the amplitude and energy ratios.