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Model Reduction of a Nonlinear Cable-Mass PDE System with Dynamic Boundary Input
Proceedings of the 22nd International Symposium on Mathematical Theory of Networks and Systems (2016, Minneapolis, MN)
  • Belinda A. Batten
  • Hesam Shoori
  • John R. Singler, Missouri University of Science and Technology
  • Madhuka H. Weerasinghe
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
7-1-2016
Citation Information
Belinda A. Batten, Hesam Shoori, John R. Singler and Madhuka H. Weerasinghe. "Model Reduction of a Nonlinear Cable-Mass PDE System with Dynamic Boundary Input" Proceedings of the 22nd International Symposium on Mathematical Theory of Networks and Systems (2016, Minneapolis, MN) (2016) p. 327 - 334
Available at: http://works.bepress.com/john-singler/30/