Eigenfrequency shift mechanism due to variation in the cross sectional area of a conduit

ABSTRACT

Eigenfrequency (i.e. natural resonant frequency) shift due to variation in the cross sectional area of a conduit is observed in different applications such as vocal tracts, musical instruments and water supply systems. In the context of water supply systems, past research focused on developing inverse problem techniques that use shifts in eigenfrequencies to identify blockages. The goal of this paper is to understand the mechanisms that cause this eigenfrequency shift. Application of the principle of action invariance to a small blockage shows that the eigenfrequency shift is directly related to the change in energy. For a severe blockage, the pipe system is decoupled into two independent subsystems: a subsystem that involves the blockage and another that involves the intact pipe section. The decoupling is lost when the blockage length is such that the fundamental frequencies of the two subsystems are close or equal, resulting in resonance where perturbation theory is successfully used to derive a simple frequency relation.

Keywords:

• Asymptotic approach
• blockage-detection in pipe system
• eigenfrequency shift mechanism
• energy approach
• transient flow
• pipe system

Acknowledgements

The authors thank Dr D.A. McInnis for the technical and editorial suggestions.

Additional information

Funding

This study is supported by the Hong Kong Research Grant Council, (projects 612712 & 612713 & T21-602/15R) and by the Postgraduate Studentship.