  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.

Signal Processing