MS09.4: Nonlinear Dynamics in Engineering Systems

This study is concerned with a minimal model of a bowed string instrument, derived through a modal decomposition of the linear Kirchhoff-Carrier PDE with a Coulomb friction force that is subsequently regularized for the sake of numerical conditioning. A bifurcation analysis of the regularized model provides a cartography of the different sound regimes in the parameter space. These results are then compared with time-domain simulations of the unregularized Coulomb friction, to evaluate whether the regularized dynamics can converge to the unregularized dynamics.

This paper proposes the preliminary results on a new method for solving inverse dynamics in Reconfigurable Underactuated Cable-Driven Parallel Robots. Given a prescribed trajectory, imposed to a subset of the end-effector coordinates, the goal is to evaluate the motor torques that are required to properly adjust the cable lengths as well as to compute the commanded trajectories of the movable exit-points. The developed technique is based on the input-output normal form of the nonlinear dynamic model of the unconstrained end-effector and, as it is usual in non-flat underactuated systems, it exploits both algebraic and differential equations, leading to a numerical approach. Some mild simplifications are proposed to reduce the computational effort. Numerical validation is proposed.

A computationally efficient method for nonlinear dynamic analysis of a rotor system with textured journal bearings is presented. The homogenization approach of the bearing undulation applied to the Reynolds equation is coupled with a numerical continuation tool to analyze the dynamic stability of a rotor-bearing coupled system.