Date of Award
Master of Science (MS)
Mechanical & Aerospace Engineering
While the mathematical foundation for modal analysis of continuous systems has long been established, flexible structures have become increasingly widespread and developing tools for understanding their mechanics has become increasingly important. Cantilever beams and plates, in particular, have been extensively studied due to their practical importance as approximations of more complex structures. The focus of this thesis is on understanding the dynamics of vibrating cantilever beams and plates through analytical and experimental investigation. Various models for the mechanics of these structures, of varying physical fidelity, are described and compared. A fiber optic sensing system is utilized to experimentally acquire distributed strain measurements, which are used to estimate the mode shapes and natural frequencies for the cantilever structures. These experimental estimates are compared with analytical and numerical solutions corresponding to the models previously introduced. Next, a detailed case study is described which demonstrates the nonlinear response in a cantilever beam's first mode and implements an empirical procedure for estimating a variable parameter model which accounts for its varying system parameters. By implementing the described identification methods, parameter variations due to a system's nonlinear response are included in a modified linear model and significantly reduce the errors in predicted response. Based on this research, methods to experimentally estimate and validate the mode shapes and system parameters can be implemented for other beam- and plate-like structures.
Heaney, Patrick S.. "Distributed Sensing and System Identification of Cantilever Beams and Plates in the Presence of Weak Nonlinearities" (2018). Master of Science (MS), thesis, Mechanical & Aerospace Engineering, Old Dominion University, https://digitalcommons.odu.edu/mae_etds/40