Vibrating beams and application to viscometers
Résumé
This paper presents a finite element model of an apparatus based on the phenomenon of resonance, for measuring the viscosity of Newtonian fluids. The study is based on a cantilever beam in a viscous fluid excited by an electromagnetic force. The Bernoulli-Euler equation is used to model the beam and linearized Navier-Stokes equations for the fluid. The Maxwell equations are used for the magnetic-structure interaction. The action of the fluid on the beam is replaced by the known hydrodynamic resistance coefficients. A semi numerical model of a vibrating beam is obtained and results are used to model a semi numerical vibrating viscometer.
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