Optimal discrete piezoelectric patch allocation on composite structures for vibration control based on GA and modal LQR

• It is presented a methodology to allocate piezoelectric patches in composite structures.
• A GPL-T9 FE for slender plates and shells is presented and used with LQR modal control.
• An index based on Lyapunov value is proposed to differentiate allocation suitability.
• The GA optimized results have superior performance when compared to examples in the literature.

The optimization of piezoelectric patches allocation in composite structures is analysed in this paper. The finite element method and a linear quadratic regulator are used to study the electro-mechanical behaviour and the gain calculation. Due to the discrete nature of the problem, a simple binary Genetic algorithm is used as an optimization tool. Three examples are presented related to the optimal allocation based on Lyapunov functional. The PSD (Power Spectral Density) of the state space variables as well as input voltages are presented in order to identify the controlled modes and to show the effective attenuation obtained due to control of specific modes.