Small-Amplitude Free-Vibration Analysis of Piezoelectric Composite Plates Subject to Large Deflections and Initial Stresses

A coupled theoretical and computational framework is presented for analyzing the small amplitude-free vibrational response of composite laminated plates with piezoelectric actuators and sensors, subject to nonlinear effects due to large rotations and initial stresses. Coupled laminate mechanics incorporating nonlinear governing equations with mixed-field shear-layerwise assumptions for the piezoelectric laminate are implemented. A finite element method is formulated to yield the linearized discrete dynamic equations of a piezocomposite plate on top of its nonlinear electrostatic response, and a novel eight-node coupled nonlinear plate finite element forms the basis of numerical analyses. The natural frequencies in a beam with a piezoceramic actuator and sensor subject to in-plane mechanical loading, high enough to induce buckling and postbuckling are also experimentally characterized, and comparisons to numerical results show excellent correlation. Additional numerical evaluations quantify the active shifting of natural frequencies in adaptive beams and plates subject to high out-of-plane and in-plane electromechanical loading, and the variation of modal frequencies during buckling and postbuckling response. Finally, the possibility to detect and actively manage buckling in adaptive piezocomposite plates is illustrated.