Natural frequencies of laminated piezoelectric plates with internal electrodes
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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.