Vibration analysis of a partially treated multi-layer beam with magnetorheological fluid

Semi-active vibration control based on magnetorheological (MR) materials offers excellent potential for high bandwidth control through rapid variations in the rheological properties of the fluid under varying magnetic field. Such fluids may be conveniently applied to partial or more critical components of a large structure to realize more efficient and compact vibration control mechanism with variable damping. This study investigates the properties and vibration responses of a partially treated multi-layer MR fluid beam. The governing equations of a partially treated multi-layered MR beam are formulated using finite element method and Ritz formulation. The validity of the proposed finite element formulations is demonstrated by comparing the results with those obtained from the Ritz formulation and the experimental measurements. The properties of different configurations of a partially treated MR-fluid beam are evaluated to investigate the influences of the location and length of the MR-fluid for different boundary conditions. The properties in terms of natural frequencies and loss factors corresponding to various modes are evaluated under different magnetic field intensities and compared with those of the fully treated beams. The effect of location of the fluid treatment on deflection mode shapes is also investigated. The forced vibration responses of the various configurations of partially treated MR sandwich beam are also evaluated under harmonic force excitations. The results suggest that the natural frequencies and transverse displacement response of the partially treated MR beams are strongly influenced not only by the intensity of the applied magnetic field, but also by the location and the length of the fluid pocket. The application of partial treatment could also alter the deflection pattern of the beam, particularly the location of the peak deflection.