Abstract:

Curved shells are increasingly utilized in applied engineering due to their shared characteristics with other sandwich structures, flexibility, and attractive appearance. However, the inability of controlling and regulating vibrations and destroying them afterward is a challenge to scientists. In this paper, the curve shell equations and a linear quadratic regulator are adopted for the state feedback design to manage the structure vibrations in state space forms. A five-layer sandwich doubly curved micro-composite shell, comprising two piezoelectric layers for the sensor and actuator, is modeled by the fourth-order shear deformation theory. The core (honeycomb, truss, and corrugated) is analyzed for the bearing of transverse shear forces. The results show that the honeycomb core has a greater effect on the vibrations. When the parameters related to the core and the weight percentage of graphene increase, the frequency increases. The uniform distribution of graphene platelets results in the lowest natural frequency while the natural frequency increases. Furthermore, without taking into account the piezoelectric layers, the third-order shear deformation theory (TSDT) and fourth-order shear deformation theory (FOSDT) align closely. However, when the piezoelectric layers are incorporated, these two theories diverge significantly, with the frequencies in the FOSDT being lower than those in the TSDT.

Key words: vibration and control, doubly curved shell, micro-composite, honeycomb, truss, corrugate core