Doctoral Dissertations
Keywords and Phrases
Balanced Truncation Method
Abstract
We consider model order reduction of a cable-mass system modeled by a one dimensional wave equation with interior damping and dynamic boundary conditions. The system is driven by a time dependent forcing input to a linear mass-spring system at the left boundary of the cable. A mass-spring model at the right end of the cable includes a nonlinear stiffening force. The goal of the model reduction is to produce a low order model that produces an accurate approximation to the displacement and velocity of the mass in the nonlinear mass-spring system at the right boundary. We believe the nonlinear cable-mass model considered here has not been explored elsewhere; therefore, we prove the well-posedness and exponential stability of the unforced linear and nonlinear models under certain conditions on the damping parameters, and then consider a balanced truncation method to generate the reduced order model (ROM) of the nonlinear input-output system. Little is understood about model reduction of nonlinear input-output systems. Therefore, we present detailed numerical experiments concerning the performance of the nonlinear ROM; we find that the ROM is accurate for many different combinations of model parameters. We also prove the well-posedness and exponential stability of other cable-mass problems with unbounded input and output operators, and numerically investigate the behavior of the ROMs for these systems
Advisor(s)
Singler, John R.
Committee Member(s)
Zhang, Yanzhi
He, Xiaoming
Jiang, Nan
Batten, Belinda A.
Department(s)
Mathematics and Statistics
Degree Name
Ph. D. in Mathematics
Publisher
Missouri University of Science and Technology
Publication Date
Summer 2017
Pagination
xi, 115 pages
Note about bibliography
Includes bibliographical references (pages 110-114).
Rights
© 2017 Madhuka Hareena Lochana Weerasinghe, All rights reserved.
Document Type
Dissertation - Open Access
File Type
text
Language
English
Thesis Number
T 11404
Electronic OCLC #
1052767332
Recommended Citation
Weerasinghe, Madhuka Hareena Lochana, "Balanced Truncation Model Reduction of Nonlinear Cable-Mass PDE System" (2017). Doctoral Dissertations. 2713.
https://scholarsmine.mst.edu/doctoral_dissertations/2713