A nonlinear theory of laminated piezoelectric plates

A fully nonlinear theory for the dynamics of anisotropic plates with integrated piezoelectric actuators and sensors undergoing large-rotation and small-strain vibrations is presented. The theory accounts for large rotations, continuity o f interlaminar shear stresses, extensionality, orthotropic properties o f piezoelectric actuators, dependence o f piezoelectric strain constants on strains, and arbitrary orientations of the integrated actuators and sensors. Five fully nonlinear partial-differential equations describing the extension-bending-shear vibrations o f plates are obtained, which display l inear elastic and nonlinear geometric couplings among all motions. Extension and shearing forces and bending and twisting moments are introduced onto the plate along the boundaries o f the piezoelectric actuators.