LQG vibration control of sandwich beams with transversely flexible core equipped with piezoelectric patches

The purpose of this paper is control of simply supported flexible core sandwich beam's linear vibration equipped with piezoelectric patches under different loads. The effects of external forces imposed on sandwich beam can be reached to a minimum value by designing an appropriate controller and control the beam's vibration. Three-layer sandwich beam theory is used for analytical modeling of sandwich beam vibration. Euler-Bernoulli beam theory and linear displacement field are used for the face-sheets and the soft core, respectively. The piezoelectric stress resultants are expressed in terms of Heaviside discontinuity functions. Governing equations of motion are obtained using Hamilton’s principle. The state space equations of system are derived from governing equations of motion, by defining suitable state variables and using Galerkin’s method. The controller is designed using linear quadratic Gaussian (LQG) technique and Kalman filter is used to estimate the state of the system. The numerical results are compared with those available in the literature. The obtained results show that the controller can play a big role toward damping out the vibration of the sandwich beam. It also shows the difference between the vibration of top face sheets and bottom face sheets because of the flexibility of the core and the situations of sensor and actuator on the top or bottom face sheets have an important role on the dynamic response of sandwich beam.