Model Reduction of a Nonlinear Cable-Mass PDE System with Dynamic Boundary Input

Abstract

We consider the motion of a flexible cable attached to a mass-spring system at each end. The input to the system is the driving force to the mass-spring system at the left end, and the output of interest is the displacement and velocity of the mass at the right end. We model the system by a 1D damped wave equation coupled to second order oscillators holding on the boundaries. The mass-spring model at the right end includes a nonlinear stiffening force. We prove the linearized system is well-posed and exponentially stable. We perform balanced truncation model reduction of the linearized system, and use the resulting modes to obtain a nonlinear reduced order model. We numerically compare the input-output response of the nonlinear PDE system and the nonlinear reduced order model for various driving forces and model parameters.

Meeting Name

22nd International Symposium on Mathematical Theory of Networks and Systems (2016: Jul. 11-15, Minneapolis, MN)

Department(s)

Mathematics and Statistics

Research Center/Lab(s)

Center for High Performance Computing Research

Document Type

Article - Conference proceedings

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2016 Regents of the University of Minnesota, All rights reserved.

Publication Date

01 Jul 2016

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