Improved dynamic response of piezoelectric composite shells using multiobjective optimization and closed loop control

A multiobjective optimization procedure is developed for improving the vibratory response of composite shells with distributed piezoelectric patches under a variety of loading conditions. The objective is to minimize the overall maximum deflection associated with the first five modes of vibration and the static deflection as the shell is subjected to electrical, mechanical and combined loading. Constraints are imposed on the natural frequencies and stresses. The stacking sequence is used as a design variable to investigate the most efficient stiffness distribution. A closed loop control system is designed using Linear Quadratic Gaussian (LQG) controller. The multiple objective function problem is formulated using the Kreisselmeier-Steinhauser (K-S) function approach. Using this approach, the multiobjective constrained optimization problem is reduced to the unconstrained optimization of a single envelope function (the K-S function). A Simulated Annealing algorithm is used as the search algorithm. Numerical results are presented for a variety of loading conditions to show the significant improvements in vibratory response from optimizing the stacking sequence. The influence of the orientation of the piezoelectric patch is also investigated.