Natural frequencies of laminated piezoelectric plates with internal electrodes

Natural vibrations of laminated piezoelectric plates with internal electrodes are analyzed using the transfer matrix method and the asymptotic expansion method. The steady-state equations of three-dimensional linear piezoelectricity reduce to a hierarchy of two-dimensional equations of the same homogeneous operator. The leading-order equations are easily solvable, whereas the higher-order equations may contain secular terms and are not straightforward to find their solutions. The solvability condition is established to calculate higher-order frequency parameters. The present theoretical formulation is used to provide new results by calculating fundamental frequencies of a rectangular laminated plate with two surface-affixed piezoelectric actuators, a parallel bimorph, a four-layered multimorph and a functionally graded plate attached with an actuator. © 2006 WILEY-VCH Verlag GmbH & Co. KGaA.