Experimental Vibration Testing for Nonlinear System Identification

The CISM Advanced Course on Experimental Vibration Testing for Nonlinear System Identification aims to provide doctoral students and researchers from academia and industry with cutting-edge knowledge for the dynamic characterization of nonlinear structural and mechanical systems. Although mechanical vibrations are a common topic in engineering curricula, they are usually presented from theoretical and numerical perspectives, while experimental aspects are often briefly covered and limited to the linear domain. In contrast, engineering and industrial systems exhibit nonlinear behavior due to material and geometric effects, contact, and damage, leading to complex dynamic responses, including amplitude-dependent resonances, jumps, hysteresis, and chaotic behavior.

This course aims to bridge this gap by presenting state-of-the-art experimental methods and recent research advances in vibration testing of nonlinear systems, combining classical testing and linear signal processing with modern measurement and identification techniques. Advanced sensing technologies, including radar interferometry, nonlinear ultrasonics, optical fibers and video analysis, are introduced together with recent tools for measuring and identifying nonlinear responses. These include experimental continuation for tracking solution branches, as well as data assimilation and AI-based methods such as physics-informed neural networks.

The first topic of the course addresses the vibrational response of structures. Participants will be introduced to the fundamentals of Operational Modal Analysis, signal processing, and Computer Vision applied to structural vibrations. The lectures will further explore structural response under seismic loading, nonlinear vibration phenomena, and hysteretic behavior.

The second topic focuses on advanced sensing and measurement technologies for structural dynamics. Both non-contact techniques, such as radar interferometry, nonlinear ultrasonics, and camera-based measurements, and minimally invasive contact sensors, including fiber optic and motion capture systems, will be presented. Their principles will be illustrated through experimental applications on real-world and large-scale nonlinear structures.

The third part addresses experimental methods for nonlinear dynamical systems. It explores vibration testing for systems exhibiting strong nonlinearities, with particular emphasis on contact dynamics and hysteresis. Recent developments in experimental continuation methods and signal processing techniques for diagnostics will be detailed. Testing procedures for hysteretic devices will also be presented.

The fourth topic focuses on parameter identification and model updating. It covers dynamic damage identification, hysteretic model formulation, parameter identification, data assimilation, and model calibration for seismic response. Advanced computational tools, including finite element model updating and physics-informed neural networks, will be introduced to support nonlinear analysis and predictive modeling.

Some practical sessions with programming exercises will complement the lectures. A poster session will be held on the afternoon of the second day.