Date of Award

Summer 2014

Degree Type


Degree Name

Master of Science in Mechanical Engineering (MSME)


Mechanical Engineering

First Advisor

Shirley J. Dyke

Committee Chair

Shirley J. Dyke

Committee Member 1

Arun Prakash

Committee Member 2

Jeffrey F. Rhoads


The study of vibrations in beams has been largely addressed by authors and researchers. However, relatively few researchers have considered the case of unknown boundary conditions, as usually it is reasonable to assume the classical cases such as simply supported, clamped or free. Indeed, there are a wide variety of boundary-condition configurations, each one representing a whole different problem with its own modal characteristics. ^ A method for updating experimental beam models to specifically address the issue of unknown boundary conditions is proposed. This methodology takes advantage of vector comparison techniques such as the modal assurance criterion and the dot product to determine the degree of linear relationship between two mode shapes systematically and iteratively until an acceptable parametric match is found. This thesis includes the phases of development, numerical demonstration and experimental verification. In the section devoted to development, a detailed explanation of the method is given; the numerical demonstration section is intended to demonstrate the capabilities of the method using mathematical models only; and finally, in the experimental verification section, a case study example is developed using real experiment data. ^ At the end of this thesis, a generalized procedure is described so the method can be applied to beam-behaving structures and ultimately any engineering model in which boundary conditions have an important role.