Nonlinear force appropriation in the presence of mode interactions

The constant drive to make aeronautic systems more efficient is leading to structures that are increasingly nonlinear. The development and validation of mathematical models predicting the behaviour of such structures requires new experimental testing methods that can extract the adequate nonlinear vibration data. The objective of this project is to develop such methods. We will first derive geometrically nonlinear models (Von Karman kinematics) of conceptually simple academic structures (cantilever and cross beams) before modelling an aero-engine blade with a simplified geometry (free from any intellectual property). With the help of analytical and numerical methods, such as Normal Forms and
numerical continuation, we will study the developed models to determine the appropriate distribution of the excitation that must be used in experimental tests to extract nonlinear vibration modes. The project will then develop new real-time control algorithms, such as adaptive and proportional-integral-derivative (PID), to adjust directly during tests the excitation frequency and the multi-harmonic, multi-point excitation amplitudes required to reach nonlinear resonance. Following the theoretical investigations, the beam and blade structures will be manufactured and the proposed methods validated experimentally. Controllers will be implement using MATLAB/Simulink and deployed on the dSpace real-time controller platform. The structures will be excited using electrodynamic shakers and their response measured using accelerometers. Collected data will be compared with model predictions and help with model validation.