EMA 611, Lab 5--Resonant ultrasound spectroscopy (RUS)
Advanced Mechanical Testing of Materials
Department of Engineering Physics, Engineering Mechanics Program, University of Wisconsin-Madison

    Lab 5--Resonant ultrasound spectroscopy (RUS)
Further links are at left of EMA 611 page.
RUS cylinder vibration mode

Vibration mode structure of cubes, spheres, and compact cylinders. Determination of moduli. Determination of mechanical damping. We focus on isotropic materials for which the lowest mode frequency reveals the shear modulus, the resonance peak width reveals the mechanical damping, and frequencies of several higher modes reveal Poisson's ratio. Poisson's ratio is extracted by comparing frequencies from experiment with frequencies provided on graphs generated numerically. Frequencies are normalized to the fundamental frequency to allow comparison. This is a graphical approach.

Resources. Lab 5 guide pdf
RUS method pdf
tone bursts, sweeps, pdf
  RUS diagram
setup image
Scope scan, PMMA 10-110 kHz
Scope scan Al alloy 50-150 kHz
Modes of isotropic cube, after Demarest
Modes of isotropic cube, full range of Poisson's ratio
Modes of isotropic sphere , after Yaoita et al.
Modes of isotropic cylinders, after Jaglinski et al.
Physics Today article by Julian Maynard pdf

Videos of vibration modes of isotropic cylinder with length equal diameter, after T. Jaglinski
mixed bend,
symmetric axial.

Software to interpret RUS scans is available here. Though it is not obvious, the assumed units for moduli are 10^12 dynes/cm^2. The software allows the user to invert RUS frequency scans to obtain anisotropic elastic moduli. Many modes are needed. The material needs to be of low damping so that the higher mode peaks are sufficiently sharp to distinguish them. Study of anisotropic crystals via RUS has a substantial learning curve and is beyond the scope of Lab 5 but it could be suitable for a project.