Strongly nonlinear multi-degree of freedom systems

Abstract

Lightweight structures, once ubiquitous in specific sectors such as aeronautics and space sectors, in recent years, have increasingly attracted the attention of industries that, historically, have not been particularly concerned with structural weight. Ample examples are provided by the civil and automotive industry, in which the paradigm shift towards lower carbon footprint and sustainability prompted new trends characterised by mass reduction, the use of novel materials, and the accounting for large deformations. However, accurately modelling the dynamic behaviour of such structures requires nonlinear mathematical models, which are not widely used in common industrial practices. Reduced-Order Models (ROMs) have emerged as a popular alternative to computationally expensive Finite Element (FE) models, nonetheless, there is still a need to evaluate their effectiveness in accurately modelling strongly nonlinear behaviours. This study investigates the capacity of multiple-degree-of-freedom (MDOF) ROMs to capture and predict the nonlinear behaviour of lightweight structures subjected to large deformations. A novel identification procedure, built on existing linear and nonlinear identification methods, is used to identify an ROM from numerical and experimental data. Being based on the separation of the linear and nonlinear restoring force contributions, the proposed method can be easily embedded in the current industrial practices for the identification of mechanical systems, paving the way to an integrated usage of linear and nonlinear dynamic models. To validate the identified MDOF-ROM, a lightweight structure composed of lumped masses and nonlinear elastic connections is experimentally studied and the numerical and experimental results are compared at different excitation conditions. We demonstrated that the existence of the Nonlinear Restoring Force (NLRF) surface in a reduced subspace corresponds to the presence of local active nonlinearities in the experimental model. This information permits simplifying the nonlinear restoring force function of the ROM, improving the overall identification process. Finally, we showed that the identified ROM accurately represents the nonlinear dynamic behaviour of the experimental test rig and correctly predicts the passage from high-amplitude response to low-amplitude response (jumps) when different levels of excitation are applied to the system, demonstrating the effectiveness of the proposed procedure.