Date of Award

8-2016

Document Type

Thesis

Degree Name

Master of Science (MS)

Legacy Department

Mechanical Engineering

Committee Member

Dr. Mohammed Daqaq, Committee Chair

Committee Member

Dr. Gang Li

Committee Member

Dr. Lonny Thompson

Abstract

Most of the previous research studies that discuss the influence of surface tension on the nonlinear planar sloshing of incompressible fluids in rectangular containers focused on the deep water scenario where internal resonances among the sloshing modes of the fluid column cannot be easily activated. Very few, if any, have investigated how surface tension influences the dynamics of the surface waves in the vicinity of an internal resonance. To fill this gap in the current knowledge, this thesis aims at investigating the influence of surface tension on the nonlinearity of the sloshing modes and the potential activation of internally-resonant multi-mode sloshing motions. The thesis addresses only weak surface tension effects by assuming a 90◦ contact angle between the fluid and the containers side walls and free slipping at the contact line. To achieve the thesis objectives, we develop a nonlinear model governing the dy-namics of the system assuming an inviscid, incompressible, and irrotational fluid sloshing inside a rectangular container. We obtain an approximate analytical solution of the model using perturbation methods, namely the method of multiple scales, for the free and forced surface response. We utilize the resulting solution to study the influence of the bond number and the ratio between the fluid height and the container’s width on the modal frequencies. We use the resulting understanding to construct a map in the design parameters’ space to highlight regions of possible nonlinear internal resonances among the sloshing modes up to fifth mode. Subsequently, we study the influence of surface tension on the effective non-linearity of the sloshing modes away from any internal resonances. We also investigate the influence of surface tension on the response of the sloshing waves near internal resonances of the two-to-one type. Finally, we study the influence of surface tension on the primary resonance behavior of the sloshing modes with and without a two-to-one internal resonance energy pump. Results indicate that surface tension has a dramatic influence on the re-gions where internal resonances can be activated and on the softening/hardening nonlinear characteristics of a given sloshing mode.

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