Model Reduction of a Nonlinear Cable-Mass PDE System with Dynamic Boundary Input
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.
B. A. Batten et al., "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), pp. 327-334, Regents of the University of Minnesota, Jul 2016.
22nd International Symposium on Mathematical Theory of Networks and Systems (2016: Jul. 11-15, Minneapolis, MN)
Mathematics and Statistics
Center for High Performance Computing Research
Article - Conference proceedings
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