Date of Award

12-2016

Degree Name

Master of Science in Engineering

Department

Mechanical and Aerospace Engineering

First Advisor

Dr. Koorosh Naghshineh

Second Advisor

Dr. Rick Meyer

Third Advisor

Dr. Kyle R. Myers

Access Setting

Masters Thesis-Open Access

Abstract

Structures such as beams and steel plates can produce potentially high levels of unwanted vibrations and noises in the environment. A method of improving the vibration and acoustic characteristics of beams based on introducing dimples on its surfaces will be presented in this study. This method focuses on creating two dimples in the same and opposite direction on beam’s surface where the effect of dimples on the change in beam’s natural frequencies is the problems of interest.

A boundary value model (BVM) is developed for a beam with two dimples and subjected to various boundary conditions using Hamilton’s Variational Principle. Differential equations that describe the equations of motion of each segment are derived. Beam natural frequencies and mode shapes are obtained using a numerical solution of the differential equations. Four examples will be presented in this research. Two cases will be presented, first case is by creating two dimples in the same direction on beam’s surface and the other case is by creating another beam model with two dimples in the opposite direction. A finite element method (FEM) is used to model the dimpled beam and verify the natural frequencies of the BVM. Both methods are also validated experimentally. The experimental results show a good agreement with the BVM and FEM results.

The change in the natural frequencies of the beam with two dimples in the same direction exhibits a different trend than positioning two dimples in the opposite direction. Various boundary conditions are studied, and the effect of dimple locations and angles are investigated. Earlier studies demonstrated that the natural frequencies of each model represent a greater sensitivity to changes in dimple angle for dimples placed at high modal strain energy regions of a uniform beam. This study confirms the same behavior for both cases (beams with dimples in the same and opposite directions). Finally, conclusions have been drawn from both the analytical and experimental results for the two cases.

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