A new way for harmonic probing of hysteretic systems through nonlinear smooth operators.

Highlights • Nonlinear operators are used to smooth a hysteretic system with rate-independent hysteresis property. • It is applied the harmonic probing method on the equivalent system that carries the nonlinear smooth operator. • Analytical expressions to the higher-order frequency response functions are derived to evaluate a hysteretic system. • The analytical approach proposed can reproduce the hysteresis loop of a benchmark involving a Bouc-Wen oscillator for narrow-banded input conditions. Abstract This paper proposes a new way to approach hysteresis with the rate-independent property through an analytical response for the non-smooth hysteresis loop using frequency response approximations. The method consists of rewriting the loading and unloading loop using smooth operators and after applying a harmonic probing in the equivalent system to obtain the higher-order frequency response functions computed by Volterra series. The novelty of this paper lies on predicting analytically, through closed-form equations of the Volterra kernels, the output and the hysteresis loop from a non-smooth system. To illustrate the applicability of the proposed approach, a challenging benchmark with hysteretic damping, described by the Bouc-Wen model, is simulated through a numerical integration scheme. The hysteresis loops, as well as the outputs, are compared to the analytical approach proposed here. The results show that the Volterra model is able to predict the hysteretic outputs when the excitation amplitude is weak and the hysteresis draws a single loop in the restoring force × displacement plane. The higher-order FRFs are given as a function of the model parameters. This framework could turn into an alternative tool to perform nonlinear modal analysis on a hysteretic system. [ABSTRACT FROM AUTHOR]