Plane wave reflection in micro-structural piezomagnetic-flexomagnetic solid with impedance boundary conditions

Abstract

The second-order gradient theory is reliable to predict the behavior of mechanical phenomena such as wave scattering, vibration, and buckling in nano/micro-structures. This theory incorporates size-dependent effects including strain-gradient elasticity and micro-inertia, crucial for constitutive modeling of piezomagnetic-flexomagnetic crystals. These small-scale size effects can have significant impact on the sensing mechanism of nanoscale transducers used in structural health monitoring (SHM) and nondestructive testing (NDT). In this article, we address the scattering of a plane wave (P-type longitudinal wave) in a piezomagnetic-flexomagnetic solid halfspace after it reflects from an open surface. The secular equation of quasi plane ( qP ) wave and multiple wave modes generated after reflection have been obtained analytically using non-classical governing equations. Impedance boundary conditions have been considered and conventional stress-free boundary conditions have been obtained as its case. Unlike a conventional piezomagnetic medium, five different wave modes have been traced after reflection (two different surface wave modes are present due to the gradient elasticity and micro-inertia effect). Closed expressions of amplitude ratios and energy flux ratios of reflected waves have been formulated from the system of linear equations. By taking a suitable numerical example, amplitude ratios and energy flux ratios for reflected waves have been plotted with respect to incidence angle. Detailed discussions have been made to understand the influence of impedance boundary and flexomagnetic effect on those ratios. The numerical results have been validated by energy conservation law. This investigation may provide necessary guidelines to understand the plane wave characteristics in micro-structural smart solid structures.