title: Dispersion relations of elastic waves in one-dimensional piezoelectric/piezomagnetic phononic crystal with functionally graded interlayers.
abstract: The effects of functionally graded interlayers on dispersion relations of elastic waves in a one-dimensional piezoelectric/piezomagnetic phononic crystal are studied in this paper. First, the state transfer equation of the functionally graded interlayer is derived from the motion equation by the reduction of order (from second order to first order). The transfer matrix of the functionally graded interlayer is obtained by solving the state transfer equation with the spatial-varying coefficient. Based on the transfer matrixes of the piezoelectric slab, the piezomagnetic slab and the functionally graded interlayers, the total transfer matrix of a single cell is obtained. Further, the Bloch theorem is used to obtain the resultant dispersion equations of in-plane and anti-plane Bloch waves. The dispersion equations are solved numerically and the numerical results are shown graphically. Five kinds of profiles of functionally graded interlayers between a piezoelectric slab and a piezomagnetic slab are considered. It is shown that the functionally graded interlayers have evident influences on the dispersion curves and the band gaps.
authors.affiliation: Department of Applied Mechanics, University of Science and Technology Beijing, Beijing 100083, China.
authors.forename: Xiao
authors.initials: X
authors.lastname: Guo
authors.affiliation: Department of Applied Mechanics, University of Science and Technology Beijing, Beijing 100083, China. Electronic address: weipj@ustb.edu.cn.
authors.forename: Peijun
authors.initials: P
authors.lastname: Wei
authors.affiliation: Department of Mathematics and Science, Luoyang Institute of Science and Technology, Luoyang 471000, China.
authors.forename: Man
authors.initials: M
authors.lastname: Lan
authors.affiliation: Department of Mathematics, Qiqihar University, Qiqihar 161006, China.
authors.forename: Li
authors.initials: L
authors.lastname: Li
keywords: Bloch wave; Dispersion relations; Functionally graded interlayer; Phononic crystal; Piezoelectric slab; Piezomagnetic slab; Transfer matrix