Control of Transverse Vibrations in Functional Gradient Beams with Magnetostrictive Layers of Terfenol-D Resting on a Winkler Foundation

In this study, we focus on the analysis of the transverse vibratory motion of a Functional Gradient Material (FGM) beam equipped with magnetostrictive layers, for use in vibration control. The differential equation of motion governing the vibratory behaviour of this beam is solved using the finite element method. The solutions obtained from these equations give natural frequencies and damping factors comparable to those obtained from the literature. To ensure the accuracy of our formulation and the finite element solution, we have carefully examined the convergence behaviour of the natural frequency for four combinations of FGM materials, and we present extensive comparative studies between our approach and the DQ method. Finally, our paper also explores the impact of magnetostrictive layers, material properties, control parameters and the effect of the elasticized foundation on the effectiveness of vibration suppression. These results are essential to guide the future development of vibration control systems in structures, with potentially revolutionary implications for many industrial and technological applications.