Resonant ultrasound spectroscopy in shear mode

Abstract

We present an enhancement of the resonant ultrasound spectroscopy method for the determination of elastic and viscoelastic properties. By using shear transducers rather than the usual compressional ones, signal strength for the fundamental is enhanced by one to three orders of magnitude. This enables simplified determination of shear modulus and damping tan ␦ with off-the-shelf electronics.Moreover, the polarization of the shear transducers can be used to identify modes of vibration. © 2003 American Institute of Physics. ͓DOI: 10.1063/1.1535739͔Resonant ultrasound spectroscopy ͑RUS͒ involves scanning the resonance structure of a compact specimen such as a cube, parallelepiped, sphere or short cylinder 1-3 with the aim of determining mechanical properties. Typically, a sample is supported by piezoelectric ultrasonic transducers, one a transmitter, and one a receiver, at opposite corners in the case of a cube or at opposite edges for a short cylinder. Corners provide elastically weak coupling to the transducers, hence minimal perturbation to the vibration, minimal shift in resonant frequency, and minimum parasitic damping. The RUS approach has the advantage of simplicity in that no gluing, clamping, or painstaking alignment of the specimen is required since it is held by contact force. Both large and small samples are readily accommodated in RUS. RUS differs from conventional pulsed wave ultrasound as follows. Plane wave approximations are used to obtain the governing equations for pulsed ultrasound; these approximations limit the sample size and test frequency. Pulsed ultrasound attenuation measurements usually involve corrections for diffraction and transducer properties. No such corrections are needed for RUS. The complexity of the usual RUS method enters in the data reduction procedure, which makes use of fast computers to infer elastic moduli from the resonant frequencies. One can obtain all the elastic moduli C i jkl of a single specimen of an anisotropic material at ultrasonic frequency. A substantial challenge in this approach is that some of the resonant modes are missing in a typical scan.2,3 The reason is that a mode which gives rise to corner motion parallel to a compressional transducer will not be observed. If the specimen is remounted at a slightly different angle, the missing mode may appear. However such iterations detract from the elegance and simplicity of the method. Moreover, if one minimizes the contact force to improve accuracy of modulus and damping measurement, angulation is limited by the tendency of the specimen to slip. The torsion and shear modes are valuable for interpretation and verification, since an exact analytical solution is available for them. However these modes are weak or absent in a standard RUS implementation since cube corner motion for them is largely tangential to the transducer face.It is possible to determine material damping tan ␦ with RUS by measuring the width of resonance curves. Since higher modes are closely spaced, it is impractical to determine tan ␦ above 0....

Conductive Blended Polymer MEMS Microresonators

“…From the results of the low crosslinker concentration samples (PMEMS13) the average mechanical loss is around 0.0054 (1/185) in the MHz range. This value is comparable to results obtained by resonant ultrasound spectroscopy (RUS) [46] and broadband viscoelastic spectroscopy (BVS) methods [47]. These results suggest that the mechanical losses of PMMA decrease with increasing frequency in the frequency range from 1 to .…”

“…The insert shows the peaks of a strongly cross-linked sample PMEMS15 for different measurement temperatures . When increases from room temperature to 47 , a significant decrease of is observed for all the polymer samples ( 10%) while for the Si-based microstructure the change in is below 0.5%. In addition, the for the weakly cross-linked sample (PMEMS-13) decreases more rapidly with than the strongly cross-linked sample (PMEMS 15) for the same temperature range.…”

On the use of hollow tube geometries for resonant ultrasound spectroscopy

“…To avoid the use of inverse methods, further analysis is required. (19). Numerical results are shown as solid diamonds for the F1 mode, solid squares for the F1-1 mode, and solid circles for the F1-2 mode.…”

“…The analytical solutions listed as Eqs. (14)- (19), describe similar deformation modes though for different mechanical systems, and were compared to the present numerical results.…”

Viscoelastic measurement techniques

“…30 One may also optically monitor the vibration using laser interferometry to identify the mode 31,32 and avoid the need for a good initial guess of properties. If shear piezoelectric transducers 33 are used rather than the usual compressional ones, one can identify some modes via the polarization of shear vibration; moreover, signal amplitude for the fundamental is enhanced by one to three orders of magnitude. One can perform RUS studies with off-the-shelf electronics, e.g., a function generator capable of sweeps, broadband ultrasonic transducers, and a digital oscilloscope.…”