Dynamic control of Euler Bernoulli FG porous beam under thermal loading with bonded piezoelectric materials

In order to develop a mathematical modeling of the smart structure, the study consists of using, in first time, the finite element method and Euler-Bernoulli theory applied to a flexible beam divided into a finite number of elements. For this purpose, we define the beam represented by the imperfect FG material, partially bonded on both surfaces, four thin layers of piezoelectric materials used as sensors/actuators. The effects of temperature and porosity on the dynamics and the active control are studied and discussed. The equations of motion are obtained via Hamilton principle. The structure is modeled analytically and numerically and the optimal LQG control with Kalman filtering is applied. The results of the simulation are presented to visualize the states of the dynamics of the several cases.