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Bernoulli-Euler finite-element modelling of vibration modes on axisymmetric containers for level measurement

Liquid level measurement inside closed containers is an essential process in control systems, quality control, and many real scenarios in the daily life. In this work, an analysis of vibration modes behavior of two axisymmetric containers and an immersed beam, aiming to liquid level measurement using acoustic resonance, is presented. In acoustic resonance, the vibration pattern produced in the container when it is excited by an external force is related to the liquid level and its physical characteristics. Vibration modes are analyzed using Bernoulli-Euler approach and finite-element modelling (FEM) in COMSOL. Results show a good correspondence of normalized frequency vibration modes shifting vs liquid level. Experimental results are consistent with theoretical and simulated FEM analysis, with an error lower than 1% in the first longitudinal vibration mode.