Non-linear system identification in structural dynamics: advances in characterisation of non-linearities and non-linear modal analysis

Abstract

Many new methods for theoretical modelling, numerical analysis and experimental testing have been developed in non-linear dynamics in recent years. Although the computational power has greatly improved our ability to predict non-linear behaviour, non-linear system identification, a central topic of this thesis, still plays a key role in obtaining and quantifying structural models from experimental data.

The first part of the thesis is motivated by the industrial needs for fast and reliable detection and characterisation of structural non-linearities. For this purpose a method based on the Hilbert transform in the frequency domain is proposed. The method detects and characterises structural non-linearities from a single frequency response function and does not require a priori knowledge of the system.

The second part of the thesis is driven by current research trends and advances in non-linear modal analysis and adaptive time series processing using the Hilbert-Huang transform. Firstly, the alternatives of the Hilbert transform, which is commonly used in structural dynamics for the estimation of the instantaneous frequency and amplitude despite suffering from a number of numerical issues, are compared to assess their potential for non-linear system identification. Then, a possible relation between the Hilbert-Huang transform and complex non-linear modes of mechanical systems is investigated. Based on this relation, an approach to experimental non-linear modal analysis is proposed. Since this approach integrates the Hilbert-Huang transform and non-linear modes, it allows not only to detect and characterise structural non-linearities in a non-parametric manner, but also to quantify the parameters of a selected model using extracted non-linear modes. Lastly, a new method for the identification of systems with asymmetric non-linear restoring forces is proposed. The application of all proposed methods is demonstrated on simulated and experimental data.