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An optimal shape for internal friction measurements using a dual cantilevered beam is described. The new shape is analyzed by a finite element method, in order (a) to optimize its parameters to reduce parasitic interactions with the sample holder, and (b) to calculate the stress distribution in the vibrating sample. The numerical analysis shows that the interactions between the sample and its holder are much weaker for the new shape than for the classical flexural vibration of a simple cantilevered beam. The predictions of the numerical analysis are compared to experimental results on a niobium sample at low temperature.