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A Area ! Undetermined coefficients of the transverse ai ! displacement shape function Undetermined coefficients of the electric disbi ! placement shape function D Electric displacement ! Plate flexural rigidity DP ! d Piezoelectric coefficient ! Nodal electric displacement di ! E Young’s modulus of elasticity ! Electric field E ! e Piezoelectric material constant relating stress to ! electric field Transverse displacement and electric displaceHw,HD ! ment interpolation functions respectively Wave number, component of wave number in x k, kxky ! and y-directions respectively Element bending, electric, and displacementkb,kD,kbD ! electric coupling stiffness matrices respectively Element bending and electric mass matrices remb,mD ! spectively Lateral displacement and electric displacement Nw,ND ! shape functions respectively Q Plane stress plane strain constitutive relation ! T Kinetic energy ! U Potential energy ! V Volume ! W External work ! w Transverse displacement ! Nodal transverse and electric displacements rewb,wD ! spectively ! " 1/" First variation #(!) ! Strain $ ! Shear strain %x y ! Curvature & ! The propagation constant ' ! Mass density ( ! Stress ) ! Wave propagation angle * ! Poisson’s ratio + ! Frequency , ! Dielectric constant " ! Phase angle !

Experimental and Spectral Finite Element Study of Plates with Shunted Piezoelectric Patches