Analysis of piezoelastic structures with laminated piezoelectric triangle shell elements

Abstract

In the recent development of active structural systems and microelectromechanical systems, piezoelectrics are widely used as sensors and actuators. Because of the limitations of theoretical and experimental models in design applications, finite element development and analysis are proposed and presented in this paper. A new laminated quadratic C° piezoelastic triangular shell finite element is developed using the layerwise constant shear angle theory. Element and system equations are also derived. The developed piezoelastic triangular shell element is used to model 1) a piezoelectric bimorph pointer and 2) a semicircular ring shell. Finite element (triangular shell finite element) solutions are compared closely with the theoretical, experimental, and finite element (thin solid finite element) results in the bimorph pointer case. Natural frequencies and distributed control effects of the ring shell with piezoelectric actuators of various length are also studied. Finite element analyses suggested that the inherent piezoelectric effect has little effect on natural frequencies of the ring shell. Vibration control effect increases as the actuator length increases, and it starts leveling off at the seven-patch (70%) actuator. Coupling and control spillover of lower natural modes are also observed.