Semi-active control of a sandwich beam partially filled with magnetorheological elastomer

• Adaptive control of a sandwich beam is proposed.
• Magnetorheological elastomer reduces amplitudes of displacements.
• Analytical investigations were performed and the control strategy was numerically determined.
• Experimental verification proved the efficiency of the approach.
• Elastomer should act only during a short period on the descending characteristics.

The paper deals with the semi-active control of vibrations of structural elements. Elastomer composites with ferromagnetic particles that act as magnetorheological fluids are used. The damping coefficient and the shear modulus of the elastomer increases when it is exposed to an electro-magnetic field. The control of this process in time allows us to reduce vibrations more effectively than if the elastomer is permanently exposed to a magnetic field.First the analytical solution for the vibrations of a sandwich beam filled with an elastomer is given. Then the control problem is defined and applied to the analytical formula. The numerical solution of the minimization problem results in a periodic, perfectly rectangular control function if free vibrations are considered. Such a temporarily acting magnetic field is more efficient than a constantly acting one. The surplus reaches 20–50% or more, depending on the filling ratio of the elastomer. The resulting control was verified experimentally in the vibrations of a cantilever sandwich beam.The proposed semi-active control can be directly applied to engineering vibrating structural elements, for example helicopter rotors, aircraft wings, pads under machines, and vehicles.