Camillacci, R., Ferguson, N.S. and White, P.R.
Simulation and experimental validation of modal analysis for non-linear symmetric systems
Mechanical Systems and Signal Processing, 19, (1), . (doi:10.1016/j.ymssp.2004.05.002).
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A dual approach, direct and inverse, is proposed for the study of a subset of discrete mechanical non-linear systems. Applying the definition of a "mode" for a non-linear system, the response calculation is refined for a class of mechanical systems possessing elastic restoring forces proportional to the cube of the displacement. The relationship between the modal natural frequencies and modal amplitudes of oscillation is analytically computed using the Harmonic Balance Method. An identification method, which operates on the free response of the system, is presented and it is shown to be capable of recovering these functional relationships. Comparisons of the analytical approximation and identification solutions are made in order to evaluate the method's effectiveness and its range of application. This comparison is achieved through numerical simulation.
An experiment performed on a physical mechanical system exhibiting non-linear behaviour is then presented. For such a system, the analytical relationships between modal natural frequencies and modal amplitudes of oscillation are calculated using its mechanical parameters. These relationships are compared with those identified experimentally and finally the results and possible extensions to the work are discussed.
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