Nonlinear force appropriation in the presence of mode interactions

不断提高航空系统效率的驱动力导致结构越来越非线性。预测这种结构行为的数学模型的发展和验证需要新的实验测试方法，可以提取足够的非线性振动数据。这个项目的目标就是发展这样的方法。我们将首先推导几何非线性模型（冯·卡门运动学）的概念简单的学术结构（悬臂梁和横梁），然后用简化的几何形状（不受任何知识产权）建模航空发动机叶片。借助解析和数值方法，如范式和数值延拓，我们将研究所开发的模型，以确定在实验测试中必须使用的激励的适当分布，以提取非线性振动模态。然后，该项目将开发新的实时控制算法，如自适应和比例积分导数（PID），以在测试期间直接调整激励频率和达到非线性谐振所需的多谐波、多点激励幅度。在进行理论研究之后，将对梁和叶片结构进行制造，并对所提出的方法进行实验验证。控制器将使用MATLAB/Simulink实现，并部署在dSpace实时控制器平台上。这些结构将使用电动振动筛进行激励，并使用加速度计测量其响应。收集的数据将与模型预测进行比较，并有助于模型验证。

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 andnumerical 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.