Modeling of a clamped-clamped beam vibrating in a fluid for viscosity and density sensing regarding compressibility

摘要

A clamped-clamped beam vibrating in a compressible fluid for the measurement of the fluid's density and viscosity is modeled using the Bernoulli-Euler equation for the beam and the linearized Navier-Stokes equations for the fluid. The adiabatic compressibility coefficient was used to characterize the pressure-density coupling. Based on the method of moments, the flow around the beam and the associated resistance of the fluid on the beam were computed using a 2D-approximation. Hydrodynamic resistance coefficients are determined and compared to the known resistance coefficients for a cylinder vibrating in an incompressible fluid. The influence of the fluid's compressibility on the resistance on the beam is examined and a critical value of the vibration frequency is determined, over which the beam experiences excessive damping due to the excitation of pressure waves. (c) 2007 Elsevier B.V. All rights reserved.