Master thesis and internship[BR]- Master's thesis : Derivative-less control-based nonlinear vibration testing[BR]- Internship

Abstract

Characterizing the vibrational response of structures is essential for ensuring safety and integrity under dynamic loads, or "excitations". Linear systems resonate only at their natural frequencies, known as fundamental resonances, and obey the principle of superposition. Real-world structures exhibit nonlinear behavior, and the same excitation frequency can lead to multiple stable or unstable solutions, with possible jumps between solutions. In addition to their fundamental resonance, nonlinear systems can resonate at any multiple or fraction of the excitation frequency, a phenomenon known as superharmonic or subharmonic resonance. Experimental modal analysis, based on linear assumptions, fails to characterize nonlinear responses. New approaches have been developed for more systematic and reliable testing of nonlinear structures. This thesis investigates a recently introduced derivative-free method for experimental arclength control-based continuation (ACBC). The study focuses on a one-degree-of-freedom system with cubic nonlinearity, known as the Duffing oscillator. Both a numerical Duffing oscillator and an experimental setup involving an electronic circuit simulating the Duffing oscillator’s behavior are considered. The ACBC method is applied to identify the frequency response of both numerical and electronic Duffing oscillators. While their fundamental resonance is fully identified, superharmonic and subharmonic resonances remain challenging to identify completely. To address these limitations, a new double-sweep strategy is introduced into the existing ACBC method. This approach successfully identifies superharmonic and subharmonic resonances, including isolated responses. Furthermore, the double-sweep strategy effectively detects isolated responses experimentally. It opens the door to advancing the study of secondary resonances, enhancing the design of mechanical structures to avoid unexpected failures and ensure long-term reliability.