Electronic Theses and Dissertations

Date

2024

Document Type

Dissertation

Degree Name

Doctor of Philosophy

Department

Mathematical Sciences

Committee Chair

Dr. Irena Lasiecka

Committee Member

Dr. Hongqiu Chen

Committee Member

Dr. Pei-Kee Lin

Committee Member

Dr. Irena Lasiecka

Committee Member

Dr. Roberto Triggiani

Abstract

This dissertation delves into the intricate dynamics of nonlinear oscillations within elastodynamic systems, focusing particularly on the Von Karman evolution equation accounts large displacements in nonlinear elasticity. By comprehensively analyzing the system’s response to both internal and external forces, augmented with frictional damping to induce dissipation, the research endeavors to elucidate mechanisms for suppressing oscillations effectively. Central to this exploration of the sharp regularity of Airy stress inherent in the Von Karman equation, pivotal in establishing the well-posedness of the associated dynamical system. A primary objective of the study is to demonstrate well- posedness of dynamical system in finite energy(weak solution) and existence of global compact attractor which attracts asymptotically all solutions.This is achieving in the following ways: showing the system’s gradient nature, accomplished through the establishment of the existence of a Lyapunov function and asymptotiaclly smoothness of the trajectories. This finite-dimensional asymptotic behavior not only provides insights into the long-term evolution of the system but also facilitates a deeper understanding of its underlying dynamics. The two main difficulty of the system are: (i) Nonlinearity in the equation and (ii)The essential damping active only in a layer of the body. The dissertation offering a comprehensive perspective on the behavior of elastodynamic systems governed by the Von Karman evolution equation. By elucidating the mechanisms underlying oscillation suppression and establishing the system’s stability properties, this research contributes to the broader understanding of nonlinear dynamical systems and their practical implications in engineering and applied mathematics.

Comments

Data is provided by the student.

Library Comment

Dissertation or thesis originally submitted to ProQuest.

Notes

Embargoed until 11-08-2026

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Available for download on Sunday, November 08, 2026

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