Dynamics and Active Control of Largely Deflected Active Structures Using the Finite Element Technique

This paper focuses on the vibration, sensing and distributed control of laminated electro/elastic nonlinear plate structures based on newly developed nonlinear shell piezoelastic finite elements. The generic governing electromechanical finite element equations for nonlinear piezoelastic shell structures are developed for the curved hexahedral and triangular piezoelectric shell elements based on the layerwise constant shear angle theory. The nonlinear system equations are linearized to enhance computational feasibility. Equations of electric potential output and feedback control force defined in a matrix from are derived. The modified Newton-Raphson method is adopted for nonlinear dynamic analysis of large and complex piezoelectric/elastic/control structures. A finite element code for vibration sensing and control analysis of nonlinear active piezoelectric structronic systems is developed. Standard structural problems involving geometrical nonlinearity are tested to validate the current finite element code and verify the accuracy of the proposed hexahedral and triangular elements. Vibration control of constant-curvature electro/elastic plate structures is studied. Time-history responses of free and controlled largely deflected nonlinear electro/elastic plate systems are presented and nonlinear effects discussed.