A dynamic homogenization method for elastic wave band gap and initial-boundary value problem analysis of piezoelectric composites with elastic and viscoelastic periodic layers

Abstract

In this paper, we present a dynamic homogenization model for elastic wave propagation analysis in piezoelectric composites with periodic electroelastic and viscoelectroelastic layers. The model is developed using a multiscale homogenization method based on an asymptotic expansion of displacement and electric potential up to the 8th order. By employing the formulation structure of gradient elasticity theory, time-space nonlocal momentum balance equations are derived to predict wave propagation and attenuation in piezoelectric composites more accurately. For verification, we have developed both a plane-wave expansion method and a direct numerical method for comparison, showing that the proposed model is of high accuracy. On this basis, the active control of the band structure in piezoelectric materials is investigated under open and short circuit electric boundary conditions. In addition, the effects of viscoelastic parameters on transient wave propagation and the band gap in a viscoelectroelastic periodic heterogeneous material are analyzed. The developed dynamic homogenization model offers significant computational savings which can be an order higher than the direct numerical solution with an increasing number of microstructures, thus providing an efficient tool for the analysis and design of piezoelectric composite structures under dynamic loading. While we mainly focus on piezoelectric materials in this paper, our model can be readily extended to piezomagnetic materials as summarized in the Appendix.