Date of Award
Master of Science (MS)
A theoretical model is developed for the resonant frequencies and mode shapes of pinned edge surface waves on a viscoelastic fluid contained in a finite depth cylindrical container. A boundary integral approach is used to map the governing equations to the domain boundary. The surface waves obey an eigenvalue operator equation that depends on four dimensionless parameters: the cylinder aspect ratio, the Bond number, the Ohnesorge number, and the elastocapillary number. A solution is constructed using a Rayleigh-Ritz variational procedure over a constrained function space, which is able to effectively incorporate the pinned edge boundary condition. Mode shapes are defined by the mode number pair (n,m), where n is the radial mode number and m is the azimuthal mode number. The focus is on irrotational motions, but we show that rotational effects only affect the dissipation in the system. The theoretical predictions agree well with related experiments over a wide range of material parameters.
Wilson, Phillip, "Model of Surface Waves on a Viscoelastic Material in a Cylindrical Container with Edge Constraints" (2023). All Theses. 4199.