This paper presents a dynamic study of sandwich functionally graded beam with\npiezoelectric layers that are used as sensors and actuators. This study is exploited later in the\nformulation of the active control laws, while using the optimal control Linear Quadratic Gaussian\n(LQG), accompanied by the Kalman filter. The mathematical formulation is based on Timoshenkoâ??s\nassumptions and the finite element method, which is applied to a flexible beam divided into a finite\nnumber of elements. By applying the Hamilton principle, the equations of motion are obtained. The\nvibration frequencies are found by solving the eigenvalue problem. The structure is analytically then\nnumerically modeled and the results of the simulations are presented in order to visualize the states\nof their dynamics without and with active control.
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