Methods for separating close natural frequencies

Abstract

When close natural frequencies occur, they may cause complications when performing experiments and require special attention and treatment in modelling. It is shown that close and even identical natural frequencies can occur in linear structures. However, these are unlikely to occur if one parameter in the system is varied in an attempt to tune a system. Adding damping to a system with close natural frequencies may result in an adverse result where one mode has reduced damping and another increased damping. A method based on narrow band filtering is presented which enables close modes to be separated so that the natural frequency and damping of each mode can be identified. This method involves reversing the time history of vibration decay prior to filtering. Finally, the effect of nonlinearities is examined. A new algorithm based on barycentric interpolation is demonstrated. This algorithm can be used for model fitting linear or nonlinear systems and is shown to be near perfect. A case is demonstrated that uses the nonlinear model to separate close modes. However, a counter example shows that this may not be generalised.