Laser-based resonant ultrasound spectroscopy in samples with compliant boundary conditions

Laser-based resonant ultrasound spectroscopy (LRUS) is a promising technique for measuring elastic properties in samples of exceedingly miniature sizes where traditional piezoelectric transducers present a limitation. However, the performance of an LRUS system is highly dependent on the geometry and boundary conditions of the specimen. More specifically, samples manufactured from a substrate, such as micro-pillars, have a compliant boundary at the base which needs to be accounted for. In this work, sub-millimeter, free-standing rectangular parallelepipeds were manufactured from tungsten material. These samples provided excellent measurements of resonances as well as mode shapes. A similar pillar was manufactured and left attached to the tungsten block to study the outcome due to alterations on boundary conditions. The results show a significant attenuation on all signal content in modes with higher frequency than the fundamental bending resonance. However, excellent images of mode shapes were obtained once the sample was detached from the substrate. Furthermore, silicon cantilevers were manufactured from wafers, and similar effects were observed. The theoretical justification for poor performance in higher-order modes resulted in sample redesigns that provided superior fidelity resonance measurements.