Geometrically Nonlinear Dynamic Analysis of Piezoelectric Integrated Thin-Walled Smart Structures

In this work, a fully geometrically nonlinear dynamic finite element (FE) model, which considers the kinematics of small strains but large rotations, is developed for transient analysis of piezolaminated thin-walled structures based on first-order shear deformation (FOSD) hypothesis. Linear electro-mechanically coupled constitutive equations and the assumption of linearly distributed electric potential through the thickness of the piezoelectric layers are employed. An eight-node quadrilateral plate/shell element with five mechanical degrees of freedom (DOFs) per node and one electrical DOF per smart layer is adopted in the finite element formulation. The second order differential dynamic equation is solved by the central difference algorithm. The mathematical method is validated by transient analysis of three different examples of a beam, a plate, and a cylindrical shell. The results illustrate that the geometrical nonlinearity affects the structural dynamic responses significantly.