Modeling and intelligent control of vibration of cantilever composite plate embedded with shape memory alloy wires

The purpose of this study is controlling the forced vibration of a layered composite cantilever plate embedded with shape memory alloys wires using classical and fuzzy controllers. The governing equations of motion of the composite plate including shape memory alloy wires are calculated using the classical laminated plate theory and the Hamilton principle. The Liang formula is also used to model the thermo-mechanical behavior of the shape memory alloys wire actuators. Then, the free vibration solution for the layered composite plate is calculated using semi-analytical Rayleigh-Ritz method and then is compared with experimental method. Comparison between the obtained natural frequencies of the composite plate and those of published experimental results confirms the accuracy of the purposed modeling and solution. Finally, three controlling system are designed to reduce the amplitude of vibrational displacement of the structure against forced vibrational excitations including PID controller, Fuzzy controller and PID-Fuzzy controller. Finally, the genetic algorithm is used to optimize the gain coefficients of the classic controller and the rules and parameters of the fuzzy controller to reduce the vibrational displacement amplitude of the plate. The obtained results show that the all designed controllers can reduce the steady-state vibrational displacement amplitude of the plate significantly, but the PID-Fuzzy controller has the best performance.