On the forced vibration of the fiber partially immersed in fluid

In this paper an experimental and theoretical investigation of the forced vibration of a partially immersed fiber has been carried out. An optical method utilizing a forward light scattering pattern has been used to detect a small (<1.0 μm) vibration amplitude of the fiber. The physical and mathematical model of the partially immersed fiber vibration has been put forward. Based on an analytical solution of the model, natural frequencies of the partially immersed fiber vibration have been found; they are consecutive positive roots of the transcendental equation. An “effective” speed of the wave propagation over the fiber has been introduced, which allows one to find the physical meaning of normal modes of the partially immersed fiber vibration. Theoretical predictions agree well with experimental data. The sensor exhibits an excellent sensitivity and could be used for measuring physical properties of fluids and liquid level.