Natural frequencies of a smart plate with segmented piezoelectric patches

Classical Plate Theory (CPT) has been applied successfully in the past to the plates with distributed piezoelectric patch bonded to the surface or embedded within the layers. In all earlier models the mass and stiffness' contributions from sensor and actuator patches were neglected for estimating the natural frequencies of the smart plate. Also the thickness direction electric fields and strain fields inside the patches are assumed to be constant over the entire area of the patch. The validity of these assumptions depends on the size and relative stiffnesses of the patches and is not investigated before. In this paper the CPT is used to estimate the natural frequencies of a plate structure with surface bonded piezoelectric patches without the above-mentioned assumptions. A detailed modeling of the patches is developed by expressing the electric potential inside the patch as a quadratic function of thickness coordinate. The equations of motion are derived for a generally isotropic plate with surface bonded segmented patches. Solution to the dynamic equation of motion are obtained using Fourier series method for a plate with collocated piezoelectric actuator/sensor patches. The effect of the passive and active stiffness' of the surface bonded actuator and sensor patches on the dynamic characteristics of host plate structure is investigated.

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