Experimental modal analysis of nonlinear systems using force-controlled harmonic testing

This paper presents the Force-Controlled Testing-Harmonic Force Surface (FCT-HFS) framework, a novel approach for experimental modal analysis that identifies nonlinear modal models using standard force-controlled testing. Based on single nonlinear normal mode theory and quasi-linearisation in experimental analysis of nonlinear systems, the framework represents nonlinearities as response-amplitude-dependent modal parameters. The framework involves conducting a series of force-controlled frequency response tests to construct a three-dimensional HFS. By slicing this surface at constant response amplitude planes, quasi-linear frequency response functions (FRFs) are extracted, allowing the identification of amplitude-dependent modal parameters through established linear modal identification techniques. The proposed framework is validated through numerical simulations and experimental investigations of two benchmark structures: the length-modified Brake-Reuß beam and the Orion beam. It is observed that the accuracy of synthesised responses is highly sensitive to the density of forcing levels and to the interpolation techniques employed during both HFS construction and modal-parameter curve fitting. Numerical and experimental results demonstrate that the proposed framework accurately captures the nonlinear modal model of nonlinear systems, provided that no unstable branch exists in the frequency response. Consequently, the framework is well-suited for weakly nonlinear systems and systems with strong nonlinear damping where a jump does not occur. The FCT-HFS framework eliminates the need to measure quasi-linear FRFs through response-controlled testing using specialised control systems, enabling the use of well-established force-controlled harmonic testing methods and equipment while still capturing the key benefits of the response-controlled nonlinear modal analysis approach when there is no unstable branch in the frequency response. Graphical abstract