Revisiting piezoelectric sensor calibration methods using elastodynamic
stress waves
Abstract
The application of absolutely calibrated piezoelectric (PZT) sensors is
increasingly used to help interpret the information carried by radiated
seismic waves in laboratory and in situ seismology. In this paper, we
revisit the methodology based on the finite element method (FEM) to
characterize PZT sensors. The FEM-based modelling tool is used to
numerically compute the Green’s function between a ball impact source,
and an array of PZT sensors used to detect laboratory-induced elastic
stress wave propagation excited by a unit step force-time function.
Realistic boundary conditions that capture the experimental conditions,
are adopted to physically constrain the problem of elastic wave
propagation, reflection and transmission in/on the elastic medium. The
modelling methodology is first validated against the reference approach
(generalized ray theory) and is then extended down to 1 kHz where
elastic wave reflection and transmission along different types of
boundaries are explored. We find the Green’s functions calculated for
realistic boundaries have distinct differences between commonly employed
2 Wu et al., idealized boundary conditions, especially around the
anti-resonant and resonant frequencies. Unlike traditional methods that
use singular ball drops, we find that each ball drop is only partially
reliable over specific frequency bands. We demonstrate, by adding
spectral constraints, that the individual instrumental responses are
accurately cropped and linked together over 1 kHz to 1 MHz after which
they overlap with little amplitude shift. This study finds that ball
impacts with a broad range of diameters as well as the corresponding
valid frequency bandwidth and equivalent seismic magnitude, are
necessary to characterize broadband PZT sensors from 1 kHz to 1 MHz.
This work bridges the gap between microcrack/damage mechanics and
laboratory/in situ acoustic emissions (AEs) by unraveling sources in
terms of the physics that generates AE signals.