Vibration analysis on electromagnetic-resonance-ultrasound microscopy (ERUM) for determining localized elastic constants of solids

In this paper we present a new acoustic-resonance microscopy, Electromagnetic-Resonance-Ultrasound Microscopy (ERUM), to measure the localized elastic stiffness of a solid material. It visualizes the resonance-frequency shift of vibrating piezoelectric crystal (langasite, La3Ga5SiO14) excited by an electric field from a solenoid coil. The acoustic coupling is made only at the tip of the crystal touching the specimen surface. Being based on the calibration for the specimen's effective stiffness, the local elasticity is determined from the resonance frequencies of the crystal with the Rayleigh-Ritz method. An approximate model for the specimen's effective stiffness predicts the shift of resonance frequencies, for which the conventional Hertz-contact model is improved. As an illustrating example, the mapping of Young's modulus of a duplex stainless steel is presented, which shows good agreement with the existing study.