  Shear modulus is one of the fundamental mechanical properties of materials,
while its quick and accurate measurement is still a challenge. Here we proposed
two methods for shear modulus measurement based on torsional resonance and
torsional wave propagation using a same piezoelectric torsional transducer.
Firstly, the torsional transducer was introduced which consists of two
thickness poled, thickness shear (d15) piezoelectric half-rings. Secondly, the
equivalent circuit of the transducer-cylindrical specimen system is derived and
the shear modulus can be explicitly obtained using the torsional resonance
frequency. The internal friction can also be obtained, which is calculated by
using an approximate formula. Then, the principle of shear modulus and internal
friction measurement based on torsional wave propagation were presented.
Finally, shear modulus and internal friction measurement on four materials
including 1045 steel, aluminum, quartz glass and PMMA, were conducted. Results
indicate that the measured shear moduli using these two methods are very close
to each other, and consistent with the reference values in literatures. The
resonance method is quite convenient and highly repeatable, but is typically
not suitable for long specimens where the first torsional resonance may not be
visible. The wave propagation method is especially suitable for long specimens
and high frequency measurement is suggested. The internal frictions measured by
these two methods were also close to each other, and the simple wave
attenuation method is suggested. The two shear modulus measurement methods
proposed in this work are quite reliable and can be widely used in near future.
