Nonlinear Active Vibration Control of Functionally Graded Beam in Presence of Uncertainty under Periodic Load with Different Boundary Conditions

In recent years, the vibrations control of beams has been significantly considered by researchers and a lot of research has been done in this field. Given that the material of studied beams was mostly metal or composite, so in this study, in order to increase the physical and thermal resistance, the studied beam was considered as functional graded (FG). In this paper, the active control of nonlinear vibrations for an FG beam with different boundary conditions under external loading is investigated. Two piezoelectric layers are connected to the upper and lower surfaces of the beam to be used as sensors and actuators. To discretize the equations of motion, Glerkin method is used, and the numerical simulation is utilized to solve the discretized equations. In order to control the vibrations of the beam, the feedback linearization control and the sliding mode methods have been used. The time-amplitude and time-voltage curves are shown for five boundary conditions, including, clamped- clamped, free-clamped, simply-clamped, free-free and simply-supported ends. The results of the mentioned control methods are compared for all boundary conditions in the presence and absence of uncertainty.