Doctoral Dissertations

Keywords and Phrases

Balanced Truncation Method


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


Singler, John R.

Committee Member(s)

Zhang, Yanzhi
He, Xiaoming
Jiang, Nan
Batten, Belinda A.


Mathematics and Statistics

Degree Name

Ph. D. in Mathematics


Missouri University of Science and Technology

Publication Date

Summer 2017


xi, 115 pages

Note about bibliography

Includes bibliographical references (pages 110-114).


© 2017 Madhuka Hareena Lochana Weerasinghe, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Thesis Number

T 11404

Electronic OCLC #


Included in

Mathematics Commons