Identifying Localised Nonlinearities: Nonlinear Restoring Force Surface in Piecewise Multi-degree-of-freedom Systems

The presence of contact and backlash often leads to complex and rich dynamic responses in mechanical structures. This typically occurs in systems such as jointed structures and geared mechanisms, where the inherent complexity leads to responses which are difficult to predict. In particular, identifying models capable of performing reliable predictions is extremely challenging, both for the definition of the equations of motion and for the characterisation of their parameters. In this chapter, we present a systematic approach based on the restoring force surface method for analysing and identifying the localised piecewise nonlinear characteristics in multi-degree-of-freedom systems. Our approach builds on the knowledge of the underlying linear system and outlines a procedure to identify equivalent nonlinear characteristics via a graphic representation of the piecewise restoring forces. The approach is validated against experimental measurements of a test rig representative of a two-degree-of-freedom system with a localised nonsmooth characteristic. The reconstruction of the nonsmooth restoring force, identification of the piecewise characteristics, and the validation of the model against experimental time histories are performed following our systematic procedure, proving the flexibility of this practical approach.