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

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.