Active vibration control and optimal position of MFC actuator for the bistable laminates with four points simply support

Bistable laminates (BSLs) are prone to vibration and dynamical snap-through behavior (STB) under the action of external environment. To control them, active vibration control using smart material is a terrific choice because it can minimize the impact on the stable configuration and properties of bistable laminate. This paper focuses on the active vibration control of rectangular asymmetric and anti-symmetric cross-ply bistable laminates under impact loadings using piezoelectric macro-fiber composite (MFC) whose size and position of paste are optimized instead of pasting randomly or middle of the laminate. The bistable laminated structures are simply supported at four selected points, while all the edges of them are free. With the aid of energy principle, governing equations of vibration of the bistable laminated structure are acquired with regard to two principal curvatures. The accuracy and validation of present formulation are verified by comparison studies of stable configurations and snap-through voltage of MFC. Then, the positions and geometric dimensions of piezoelectric macro-fibers are optimized by using genetic algorithm. The active vibration control of the bistable laminated structures subjected to step loading, decreasing loading, increasing loading and sinusoidal loading is studied for various control gains, geometries and different simply supported points.