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Dynamic properties of magneto-sensitive elastomer cantilevers as adaptive sensor elements

In engineering applications, one of the actual scientific challenges is a development of sensor systems with complex adaptive behaviour and operating sensitivity. Smart materials like magneto-sensitive elastomers (MSEs) offer great potential for designing such intelligent devices, because they possess unique magnetic-field dependent properties. This paper deals with the investigation of the free vibrational behaviour displayed by cantilever beams made of MSEs containing magnetically soft particles in the presence of a uniform magnetic field. The presented setup is considered as a prototype of a sensitive unit for transforming mechanical stimuli of the base into vibrations of the MSE element, which could be converted in a facile way into electromagnetic signals for measuring and analysing. It is shown experimentally that for the MSE beams of several different lengths and compositions, the first eigenfrequency depends strongly on the strength of the applied magnetic field. The developed theoretical model extends the conventional vibrational dynamics of thin rods to allow for the ponderomotive torque induced by magneto-mechanical interactions experienced by an MSE beam. The model has two adjustable parameters that characterise the geometric configuration of the cantilever beam and its magnetic material properties. It is found that the values of these parameters are ‘universally’ valid, i.e., they provide good agreement between the theoretical eigenfrequency dependencies and the experimental results for all used MSE beams. The evidence presented ensures a good basis for further investigations of the sensitivity and amplitude–frequency characteristics of MSE vibration sensor elements.