A novel analysis method for calculating nonlinear Frequency Response Functions.
Abstract
This research presents a novel analysis method for calculating nonlinear Frequency Response Functions from a nonlinear frequency response surface (NFRS). The research aims to provide engineers with a user-friendly technique to evaluate the nonlinear frequency responses when the modal parameters as a function of the vibration amplitude are available. The Frequency Response Functions (FRFs) are the most widely used functions to characterise the dynamic behaviour of structures. The experimental modal analysis stands on four pillars 1) measurement, 2) identification, 3) regeneration, and 4) comparison, and these four steps must be ensured under linear and nonlinear vibrations. However, the nonlinear vibrations are challenging for identifying, regenerating, and comparing nonlinear FRFs.
This research postulates that a nonlinear FRF solves a geometrical intersection between the nonlinear frequency response surface and any constant amplitude force surface. The paper demonstrates the hypothesis with ONE- and TWO-DoF systems with a cubic stiffness nonlinearity by showing how to generate a nonlinear frequency response surface when the force-displacement relationship is calculated. The verification of the proposed formulation is yielded by comparing nonlinear FRFs generated by the new analysis method (NM) to the ones generated by the Harmonic Balance Method and numerical integration. Furthermore, the paper presents a new identification method, based on the Dobson formulation, for extracting amplitude-dependent modal parameters. These parameters generate an NFRS, from which synthesised nonlinear FRFs are evaluated and compared to the experimental ones. The most important innovation of this research is that the four steps listed earlier can quickly be implemented with the proposed technique.