Graduate Studies

 

First Advisor

Joseph Turner

Second Advisor

Keegan J. Moore

Degree Name

Doctor of Philosophy (Ph.D.)

Committee Members

Daniel Linzell, Mehrdad Negahban

Department

Mechanical Engineering

Date of this Version

8-2025

Document Type

Dissertation

Citation

A dissertation presented to the Graduate College of the University of Nebraska in partial fulfillment of requirements for the degree of Doctor of Philosophy

Major: Mechanical Engineering and Applied Mechanics

Under the supervision of Professors Joseph Turner and Keegan J. Moore

Lincoln, Nebraska, August 2025

Comments

Copyright 2025, Manal Mustafa. Used by permission

Abstract

This dissertation examines the role of mass in nonlinear systems, uncovering its role in enabling passive energy redistribution and robust vibration control in both idealized and real-world structures. Focusing on a strongly nonlinear two-degree-of-freedom system, it investigates how changes in mass ratio influence the dynamics of energy transfer, nonlinear normal modes (NNMs), and dissipation behavior.

A number of significant contributions are introduced in this work beginning with the introduction of the frequency-energy-peaks (FE-pks) plot, a novel tool that visualizes how energy flows through the system, revealing transient resonance orbits, internal resonance effects, and effectively capturing the different nonlinear phenomena with ease. This method proved highly sensitive and efficient, even at low excitation levels and large mass ratios, capable of detecting subtle nonlinear behaviors that might otherwise be misinterpreted as noise in experimental data. Another key finding is the establishment of settling time as a practical and interpretable metric. It not only quantifies energy transfer efficiency but also serves multiple diagnostic roles: distinguishing between regular and chaotic behavior, pinpointing the energy threshold for the 1:3 internal resonance loop of the first NNM, and enabling the identification of NNMs when used for different sets of initial conditions. Another novel contribution is the isolation of early frequency content as a predictor for the onset of chaos, providing a new window for early detection and control of instabilities.

The study reveals promising future directions. Investigating the frequency content governing chaos onset could improve early prediction and control in nonlinear systems. Using image processing techniques to analyze the FE-pks plots may allow automated detection and tracking of transient resonance orbits, enhancing understanding of their behavior and role in energy transfer. Analyzing different system configurations and parameter variations could broaden the understanding of nonlinear behavior. Building a structured database of dynamic regimes, energy paths, and critical thresholds could guide the design of systems for targeted energy transfer. Additionally, further exploration of the forced response is recommended to complement free-damped analysis and reveal resonance-driven behaviors under harmonic excitation.

Advisors: Joseph Turner and Keegan J. Moore

Download

Share

COinS