Theoretical and experimental characterisation of a Weisbord mass

Damping is a crucial aspect for resonant sensors. A bending beam is investigated, which oscillates with a characteristic resonance frequency and its fundamental mode shape. Due to its deflection a moment and shear force are induced at the clamp. Weisbord proposed for resonant force sensors the design of a mass attached to the beam. According to Weisbord the resulting moment becomes zero if the centre of gravity of the Weisbord mass has a certain distance to the clamping of the beam at the Weisbord mass, called “Weisbord distance”. A reduced energy loss and thus an increased quality factor would be the result. This could not be verified experimentally. Therefore, we analysed the Weisbord system by analytical modal analysis and compared those results with a Finite Element (FE) modal analysis. The result was that the centre of gravity has only marginal effects on the compensation of clamp reactions. We found that only the distance between Weisbord mass clamping and the beam clamping determines the reaction forces.