Master thesis and internship[BR]- Master's thesis : Identification of nonlinear frequency response and backbone curves using phase-locked loop methods[BR]- Integration internship

Abstract

Vibration testing plays an important role in the development of modern engineering structures by revealing their dynamic limitations, providing validation data for numerical models, and serving as a benchmark in standardised testing procedures. While modal analysis of linear systems is a well-established process, with linear systems characterised by constant resonance frequencies regardless of excitation amplitude, the adoption of novel materials and complex structures in the aeronautical industry has led to the increased occurrence of nonlinear phenomena. Such systems may exhibit multiple stable and unstable solutions, superharmonic and subharmonic resonances, and amplitude-dependent frequency responses, thereby challenging classical identification techniques in the reconstruction of complete bifurcation diagrams.

To identify complete frequency response and backbone curves of nonlinear structures, experimental continuation methods have recently gained interest. This thesis investigates the implementation of a phase-locked loop (PLL) algorithm in the LabVIEW FPGA environment to perform real-time tracking of fundamental frequency response and backbone curves, with a view towards industrial application.

The PLL approach is first developed within the Simulink environment as a reference model, and is validated numerically and experimentally. The algorithm is then implemented in LabVIEW, and multiple tests are performed on experimental setups. Results demonstrate that the LabVIEW-based PLL achieves real-time computation of frequency response and backbone curves with an accuracy comparable to that of the Simulink implementation. An industrial application of the present work can be considered to track frequency response and backbone curves of fundamental resonances of nonlinear systems. However, instabilities arising from the inappropriate calibration of controller gains when identifying unstable responses prevent a smooth application of the method, and a robust technique for determining these gains has yet to be established.