Tracking of Backbone Curves of Nonlinear Systems Using Phase-Locked-Loops

Abstract

In nonlinear systems the resonance frequency depends on the energy in the system. This change in resonance frequency contains valuable information about the systems behavior and the nonlinear normal modes (NNMs) associated with each point of the backbone curve. This information can e.g. be used for system identification. However, the accurate and efficient measurement of the backbone curve in nonlinear systems is still challenging. This contribution proposes a new method to measure the backbone curve which is based on the control concept of a Phase-Locked-Loop (PLL) which is well known in electronics applications. A properly designed PLL is capable of finding linear resonances but it can also be used for the tracking of energy dependent backbone curves. The new method provides very accurate results by using steady state responses in the nonlinear mode. In contrast to commonly used free decay measurements this approach eliminates transient effects. Yet, it is also very efficient and user friendly as an automated testing can be performed. The method is experimentally demonstrated on a beam structure with cubic nonlinearity. Furthermore the capability of tracking through internal resonant NNMs will be examined and new possibilities for quantitative measurements of these effects will be discussed.