2 research outputs found
Balanced Truncation Model Reduction of a Nonlinear Cable-Mass PDE System with Interior Damping
We consider model order reduction of a nonlinear cable-mass system modeled by
a 1D 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 one boundary. 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 opposite
boundary. We first prove that the linearized and nonlinear unforced systems are
well-posed and exponentially stable 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 known
about model reduction of nonlinear input-output systems, and so 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
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