Optimal design in vibration control of adaptive structures using a simulated annealing algorithm

Advanced reinforced composite structures incorporating piezoelectric sensors and actuators are increasingly becoming important due to the development of smart structures. These structures offer potential benefits in a wide range of engineering applications such as vibration and noise suppression, shape control and precision positioning. This paper presents a finite element formulation based on the classical laminated plate theory for laminated structures with integrated piezoelectric layers or patches, acting as sensors and actuators. The finite element model is a single layer triangular nonconforming plate/shell element with 18 degrees of freedom for the generalized displacements, and one additional electrical potential degree of freedom for each surface bonded piezoelectric element layer or patch. The control is initialized through a previous optimization of the core of the laminated structure, in order to minimize the vibration amplitude and maximize the first natural frequency. Also the optimization of the patches position is performed to maximize the piezoelectric actuators efficiency. The simulated annealing algorithm is used for these purposes. To achieve a mechanism of active control of the structure dynamic response, a feedback control algorithm is used, coupling the sensor and active piezoelectric layers or patches, and to calculate the dynamic response of the laminated structures the Newmark method is considered. The model is applied in the optimization of an illustrative adaptive laminated plate case. The influence of the position and number of piezoelectric patches, as well as the control gain, are investigated and the results are presented and discussed.