This　work　is　devoted　to　study　the　dynamic　problems　of　periodic　piezoelectric　structures　by　using　the　spectral　element　method　(SEM).　The　dynamic　stiffness　matrix　of　the　piezoelectric　square　lattice　is　formulated　by　this　method.　Highly　accurate　frequency-domain　solutions　of　the　lattices　with　and　without　piezoelectric　beams　are　obtained.　Band　gap　properties　of　the　piezoelectric　square　lattices　are　investigated　and　the　influences　of　the　different　contents　of　piezoceramic　layers　are　analyzed.　The　behaviors　of　the　waveguide　due　to　material　defects　are　demonstrated.　Lattice　structures　with　different　central　and　peripheral　parts　are　designed　and　their　unique　dynamic　characteristics　are　also　analyzed.　(C)　2014　Elsevier　Ltd.　All　rights　reserved.