Date of Award


Degree Name

Doctor of Philosophy


Mechanical and Aerospace Engineering

First Advisor

Dr. Koorosh Naghshineh

Second Advisor

Dr. Judah Ari-Gur

Third Advisor

Dr. James Kamman

Fourth Advisor

Dr. Mitchel Keil


Dimpled, Beams, Vibration, Acoustics, Boundary Value Model. Noise Control


Attention has been given recently to the use of dimples as a means of passively altering the vibroacoustic properties of structures. Because of their geometric complexity, previous studies have modeled dimpled structures using the finite element method. However, the dynamics of dimpled structures are not completely understood. The goal of this study is to provide a better understanding of these structures through the development of a boundary value model (BVM) using Hamilton's Variational Principle. The focus of this study is on dimpled beams, which represent the simplest form of a dimpled structure.

A general model of a beam with N dimples in free vibration is developed. Since dimples formed via a stamping process do not change the mass of the beam, the dimple thickness is less than that of the straight segments. Differential equations of motion that describe the normal and axial motion of the dimpled beams are derived. Their numerical solution yields the natural frequencies and analytical mode shapes of a dimpled beam. The accuracy of this model is checked against those obtained using the finite element method, as well as the analytical studies on the vibrations of arches, and shown to be accurate.

The effect of dimple placement, dimple angle, its chord length, its thickness, as well as beam boundary conditions on beam natural frequencies and mode shapes are investigated. For beams with axially restrictive boundary conditions, the results show that a peak in a natural frequency for certain dimple angles corresponds to a changing mode shape within the dimple. Previous studies had suggested that dimple thinning was the cause of this phenomenon. The natural frequencies also exhibit a greater sensitivity to changes in dimple angle for dimples located at regions of highest modal strain energy (MSE) of a uniform beam. The use of MSE as a design strategy for optimum placement of dimples is demonstrated. Finally, using the MSE in combination with the genetic algorithm (GA), single and multiple dimples are shown to alter beam vibroacoustic properties significantly.

Access Setting

Dissertation-Open Access