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Description
Mechanical structures are becoming lighter and thinner, saving resources and space. However, thin-walled structures are more prone to vibrations and emit more noise. Such thin-walled structures are used also in atomic force microscopes for sensing. A cantilever is employed as the structure. The cantilever must remain in a static rest position for accurate measurements. Non-linear structural dynamics are utilized to achieve vibration reduction. The finite element method is applied to model the beam. A time-periodic electromagnetic actuator damps the beam. The optimization of the actuator is carried out through a parameter study. In this study, the position and the time-periodic force exerted by the actuator on the beam are varied, among other factors. This variation achieves adjustable stiffness. The applied force transforms the system into a time-periodic system, and the Floquet theorem is employed. Stability channels are identified by applying the Floquet theorem and varying the parameters. These stability channels indicate the extent of vibration reduction. By optimizing the parameter combination, the decay time can be significantly reduced. The dependence of the achievable decay time is examined through parameter studies of stability maps. This concept can be applied to atomic force microscopes to enable faster measurements with the same sensor sensitivity by reducing the decay time without altering the beam dynamics.
