Studies in Hydroelastodynamics: Singing and Swimming

Abstract

In this thesis we describe two instances of the nonlinear interaction between a fluid and an elastic solid to mimic or explain some phenomenon seen in nature. We focus on the phenomena of singing of small song birds and swimming of small fish. Song birds show a versatile range of tones and compositions that have highly complex spectral structure, while fish cut through water with amazing ease. The complexity of the Navier Stokes Equations that describe the fluid coupled with large deformation elasticity equations, makes analytic attempts intractable. Hence experiments were carried out with simple physical models to explain these observations. In the first case a cylindrical elastic tube (2.5cm long, 2.5mm diameter) was used to model the vocal organ, the syrinx, of a song bird. Muscle action was mimicked using a linear motor that implemented a squeezing action and the action of the lungs was modeled by a constant source of air flow. The combined fluid-elastic system behaved like a nonlinear dynamical system and produced sound under certain conditions of external parameters. Moreover the structure of the sound created depended sensitively on the control parameters, which in this case was dominated by the position of the linear motor. The motor was dynamically controlled to produce a range of songs from simple tonal ones of the Vireo to the complex chaotic songs of the Zebra Finch. In the second instance, a cantilever (5cm long, 1cm wide)suspended between and driven by magnetic coils arranged in an anti-Helmholtz configuration, was used to mimic the dynamics of the caudal fin of a small fish. Three different gaits were observed as a function of the control parameter, the drive frequency. One of these gaits maximized thrust and hydrodynamic efficiency, and velocities unto 6 body lengths per second were measured.