The Study of Using External Fluid Loading on a Vibrating Rectangular Plate for Suspended Sediment Concentration in Water

Abstract

This paper presents the result of a theoretical study on a new fluid den- sity measuring concept which uses the effect of external fluid loading on a vibrating thin plate. The underling physical principle of this concept is that the resonance frequencies of an immersed vibrating plate change with the surface impedance changes caused by the mass density variations of the external fluid. In this paper, the analytical solutions of resonance frequencies with specific gravity are demon- strated by a COMSOL the finite element simulation. The theoretical analysis pre- sented in this paper shows that the resonance frequencies of an immersed vibrating thin plate affect significantly with surrounding fluid loading, which is loaded as an extra added mass. The resonance frequencies shifted to lower frequencies when the fluid specific gravity increased. For the resonance frequency ratio applied to the specific gravity estimation of onsite measurement, the increases in this coeffi- cient are directly proportional to the increase with the specific gravity. In addition, size effect on the thin plate is also presented. The results show that the thickness of the thin plate is the most important factor for this resonance frequency ratio. Finally, the preliminary experiment of the thin plate immersed in the various fluid loading is also accomplished. The comparison shows that the experimental results agree reasonably well with the finite element simulation. Based on these results of the theoretical analysis and the experiment in this paper, using the loading by the external fluid on the vibrating thin plate is feasible.