MIMO adaptive control for suppression the vibrations of a nonlinear interconnected structure with abrupt changes in...

The presented paper, for the first time, deals with the simultaneous suppression of elastically coupled interconnected Timoshenko beams at different nodes by employing a simple virtual absorber (control algorithm). The main system is discretized into interconnected Timoshenko beams using finite element method with unknown parameters. The system is excited externally by applying harmonic disturbances with unknown amplitudes and uncertain time-varying frequency. The aim of the article is to utilize a virtual absorber with adjustable stiffness which is capable of suppressing the vibration of the elastically coupled model at multiple nodes and also identifying the uncertain frequency of the excitations. In addition, the uncertain parameters and their effects on the behavior of the nonlinear formulations of the MIMO system are, practically, included through the dynamic of the model and the adaptable algorithm (embedded in the virtual controller) is employed to annihilate the nonlinear vibration of such complex system only based on its output. The results demonstrate that the proposed adaptive algorithm is able to simultaneously cease the vertical and rotational oscillations of a nonlinear multi-beam system at a wide range of frequencies.