This paper presents a numerical study on optimal voltages and optimal placement of piezoelectric actuators for shape control of beam structures. A finite element model, based on Timoshenko beam theory, is developed to characterize the behavior of the structure and the actuators. This model accounted for the electromechanical coupling in the entire beam structure, due to the fact that the piezoelectric layers are treated as constituent parts of the entire structural system. A hybrid scheme is presented based on great deluge and genetic algorithm. The hybrid algorithm is implemented to calculate the optimal locations and optimal values of voltages, applied to the piezoelectric actuators glued in the structure, which minimize the error between the achieved and the desired shape. Results from numerical simulations demonstrate the capabilities and efficiency of the developed optimization algorithm in both clamped？free and clamped？clamped beam problems are presented.
Mota Silva, S.; Ribeiro, R.R.; Rodrigues, J.D.; Vaz, M.A.P.; Monteiro, J.M. The application of genetic algorithms for shape control with piezoelectric patches—An experimental comparison. Smart Mater. Struct. 2004, 13, 220–226.
Hadjigeorgiou, E.P.; Stavroulakis, G.E.; Massalas, C.V. Shape control and damage identification of beams using piezoelectric actuation and genetic optimization. Int. J. Eng. Sci. 2006, 44, 409–421, doi:10.1016/j.ijengsci.2006.02.004.
Thomas, O.; Deü, J.F.; Ducarne, J. Vibrations of an elastic structure with shunted piezoelectric patches: Efficient finite element formulation and electromechanical coupling coefficients. Int. J. Numer. Meth. Eng. 2009, 80.2, 235–268, doi:10.1002/nme.2632.
Kendall, G.; Mohamad, M. Channel Assignment in Cellular Communication Using a Great Deluge Hyper？Heuristic. In Proceedings of 12th IEEE International Conference on Networks, Berlin, Germany, 16–19 November 2004; pp. 769–773.