Nonlinear damping quantification from phase-resonant tests under base excitation

TL;DR

This paper introduces a novel response-only method for quantifying nonlinear damping from phase-resonant tests under base excitation, eliminating the need for force measurement and demonstrating high robustness and accuracy.

Contribution

The work develops and validates a new response-only approach for damping quantification in phase-resonant tests with base excitation, avoiding force measurement.

Findings

Method is highly robust and accurate.

Validated in virtual and physical experiments.

Effective with a limited number of sensors.

Abstract

The present work addresses the experimental identification of amplitude-dependent modal parameters (modal frequency, damping ratio, Fourier coefficients of periodic modal oscillation). Phase-resonant testing has emerged as an important method for this task, as it substantially reduces the amount of data required for the identification compared to conventional frequency-response testing at different excitation/response levels. In the case of shaker-stinger excitation, the applied excitation force is commonly measured in order to quantify the amplitude-dependent modal damping ratio from the phase-resonant test data. In the case of base excitation, however, the applied excitation force is challenging or impossible to measure. In this work we develop an original method for damping quantification from phase-resonant tests. It relies solely on response measurement; it avoids the need to resort to force measurement. The key idea is to estimate the power provided by the distributed inertia force imposed by the base motion. We develop both a model-free and a model-based variant of the method. We validate the developed method first in virtual experiments of a friction-damped and a geometrically nonlinear system, and then in a physical experiment involving a thin beam clamped at both ends via bolted joints. We conclude that the method is highly robust and provides high accuracy already for a reasonable number of sensors.