Double resonating beam force transducer with reduced longitudinal pumping

In a resonator beam having two tines terminating in base regions, a method for minimizing coupling of vibration of the resonator beam into a support structure to which the resonator beam is attached, the method comprising:

• in a model of the resonator beam having one of the base regions fixed and an other of the base regions free, applying a cutout of a predetermined geometry at a predetermined position in an interior portion of each of the base regions;
• computing normal resonance modes of the resonator beam;
• computing a ratio of an amplitude of a longitudinal motion of the free base region to an amplitude of the center of the tines;
• and
• comparing the ratio with a desired minimum value.

In a resonator beam having two tines terminating in base regions, a method for minimizing coupling of vibration of the resonator beam into a support structure to which the resonator beam is attached, the method comprising:

• in a finite element analysis model of the resonator beam having one of the base regions fixed and an other of the base regions free, applying a first cutout of a predetermined size at a predetermined position in an interior portion of a first one of the base regions, and applying a second cutout of a predetermined size at a predetermined position in an interior portion of a second one of the base regions;
• using the finite element analysis model, computing normal resonance modes of the resonator beam;
• using the finite element analysis model, computing an amplitude of a longitudinal motion of the free base region;
• using the finite element analysis model, computing an amplitude of the center of the tines;
• computing a ratio of an amplitude of a longitudinal motion of the free base region to an amplitude of the center of the tines in the mode used for force sensing;
• and
• comparing the ratio to zero.