A novel analysis method for calculating nonlinear Frequency Response Functions

Abstract

The Frequency Response Functions (FRFs) are the most widely used functions to characterise the dynamic behaviour of structures. The natural frequencies and damping behaviour can be easily and quickly detected from a Bode diagram. The modal properties of FRFs can be evaluated using modal analysis methods, and as the last step, frequency response models can synthesise response functions to verify the robustness of the modal parameters identified by the analysis. The circularity between 1) measurement, 2) identification, 3) regeneration and 4) comparison is ensured on the assumption that transfer functions are measured under linear vibrations, even though mechanical systems are intrinsically non-linear. Some sources of nonlinearity might be excited and revealed, and others not for various reasons. Anyhow, it is unavoidable to measure non-linear vibrations when vibration tests are executed at various levels of excitation forces. Eventually, linear and non-linear vibrations are processed to obtain linear and non-linear FRFs. The linear FRFs are processed using the existing identification methods. The non-linear FRFs are archived or blandly processed to evaluate the level and the type of nonlinearity, such as hardening or softening behaviour. This research aims to (i) formulate a new analysis method to generate nonlinear frequency responses and (ii) formulate a new identification method for extracting amplitude-dependent modal parameters. The first objective will demonstrate that a nonlinear frequency response surface generated by linear FRFs is the solution space of nonlinear FRFs. The second objective will demonstrate that a linear modal analysis method called line-fit, based on the Dobson formulation, allows extracting amplitude-dependent modal parameters from non-linear FRFs.