A principle of similarity for nonlinear vibration absorbers

TL;DR

This paper introduces a principle of similarity for designing nonlinear vibration absorbers, showing that matching the nonlinearity form to the primary system enhances vibration mitigation, with a derived formula for nonlinear coefficients.

Contribution

It proposes a principle of similarity for nonlinear absorber design and derives a universal formula for nonlinear coefficients based on system parameters.

Findings

The NLTVA should have the same nonlinearity form as the primary system.

A compact analytical formula for nonlinear coefficients is valid for polynomial nonlinearities.

The principle of additivity allows independent calculation of nonlinear coefficients in multi-nonlinearity systems.

Abstract

This paper develops a principle of similarity for the design of a nonlinear absorber, the nonlinear tuned vibration absorber (NLTVA), attached to a nonlinear primary system. Specifically, for effective vibration mitigation, we show that the NLTVA should feature a nonlinearity possessing the same mathematical form as that of the primary system. A compact analytical formula for the nonlinear coefficient of the absorber is then derived. The formula, valid for any polynomial nonlinearity in the primary system, is found to depend only on the mass ratio and on the nonlinear coefficient of the primary system. When the primary system comprises several polynomial nonlinearities, we demonstrate that the NLTVA obeys a principle of additivity, i.e., each nonlinear coefficient can be calculated independently of the other nonlinear coefficients using the proposed formula.