Mapping nonlinear forces with congruent vibration functions

This paper considers a new nonparametric identification method for vibration systems. The novelty of the identification is that an unknown arbitrary internal force not separated for stiffness and damping is assumed a priori. A nonlinear vibration structure is decomposed in a number of subsystems, each with its own vibration frequency solution, amplitude and phase as functions of time. Multiple frequency components included in the solution composition can be uncovered by the Hilbert vibration decomposition and subsequent congruent aggregation. The unknown internal acting force is estimated by the displacement–acceleration phase angle and the special partial analytical methods.The developed identification methods were successfully applied to a simulated signal obtained from different nonlinear vibration models, among them the Duffing model, dry friction, combined nonlinearities in backlash stiffness with turbulent quadratic damping, and the van der Pol oscillator.

► A nonlinear structure is decomposed in a number of subsystems of different frequencies.
► Each subsystem is identified non-parametrically by the displacement–acceleration phase.
► The subsystem forces are aggregated congruently in the required nonlinear model.
► An inseparable stiffness/damping internal force is identified by a partial analytic method.