Passive linearization of nonlinear resonances

Abstract

The objective of this paper is to demonstrate that the addition of properly-tuned nonlinearities to a nonlinear system can increase the range over which a specific resonance responds linearly. Specifically, we seek to enforce two important properties of linear systems, namely the force-displacement proportionality and the invariance of resonance frequencies. Numerical simulations and experiments are used to validate the theoretical findings.

A fully passive nonlinear piezoelectric vibration absorber

“…As shown theoretically and numerically for mechanical absorbers by Habib et al [24,26], the introduction of a nonlinear component into the tuned vibration absorber counteracts the effect of the nonlinearity of the primary system. According to the so-called 'principle of similarity', the absorber should be governed by equations similar to those of the primary system.…”

“…The experimental set-up in figure 4a is made of a 700 mm long cantilever beam of cross-sectional area 14 × 14 mm [26,30,31]. This beam has been covered with an array of 2 mm thick PZT-5A bimorph patches for the implementation of an NPTVA.…”

A Multimodal Nonlinear Tuned Vibration Absorber

“…They designed a nonlinear vibration absorber able to maintain equal peaks over a broader range of forcing amplitude than when using a linear vibration absorber. This same principle of similarity was recently used by Habib and Kerschen [7] to modify the characteristics of multiple nonlinear resonances. By introducing and properly tuning nonlinearities in a structure, they were able to linearise its dynamics.…”

“…The same formalism as Habib and Kerschen [7] is used in the following. The nonlinear equations of motion of the structure and of the nonlinear absorbers attached to it are given by…”

“…Their functional form is chosen according to a principle of similarity. The same formalism as [7] is used to impose equal peaks in the nonlinear frequency response function. With this new design, the working range of vibration absorbers can be extended to higher forcing amplitudes.…”