Dynamic asymptotic homogenization for wave propagation in magneto-electro-elastic laminated composite periodic structure

Abstract

In the present work, anti-plane wave propagation with oblique incidence in a magneto-electro-elastic multi-laminated composite periodic structure with perfect contact is studied. A general asymptotic homogenization method is applied to analyze dispersion phenomena and dynamic process. On assuming the solution having a single-frequency dependency, the higher-order terms for the displacement, electric potential and magnetic potential in asymptotic expansions are studied. Higher order local problems up to a finite order and a generalization of the local problem of infinite order are derived through rigorous calculations satisfying the necessary and sufficient condition for the existence of 1-periodic solutions. The effective equation of motion also known as “Good” Boussinesq equation has been achieved directly which is one of the highlight of the present work. Moreover, closed-form expression of dispersion equation and closed-form solutions of first and second local problems have been obtained. The analytical results have been validated for particular elastic case. Graphical illustrations have been done for tri-laminated magneto-electro-elastic composite periodic structure and the effect of size of unit cell, angle of incidence of wave, volume fraction of the composite and magneto-electric properties on the dispersion curve and also slowness curves have been examined. The numerical results have been validated with previous work and compared with results obtained by other approximation method. The present dynamic homogenization method has been proven to provide a more dispersive system and better approximation.