Development of nonlinear resonant ultrasound spectroscopy

2014 Fiscal Year Final Research Report

• Project/Area Number: 23686024
• Research Category: Grant-in-Aid for Young Scientists (A)
• Allocation Type: Single-year Grants
• Research Field: Materials/Mechanics of materials
• Research Institution: Osaka University
• Principal Investigator: TARUMI Ryuichi 大阪大学, 工学(系)研究科(研究院), 准教授 (30362643)
• Project Period (FY): 2011-04-01 – 2015-03-31
• Keywords: 超音波共鳴法 / 弾性定数 / 非線形弾性理論 / 固体力学

Outline of Final Research Achievements

The second-order elastic constants (SOECs) of a solid can be determined from free-vibration acoustic resonance (FVAR) frequencies of the medium. This method, called resonant ultrasound spectroscopy, is the state-of-the-art technique for measuring the SOECs. The aim of this study is to generalize the theory of FVAR so as to determine the third-order elastic constants (TOECs) in addition to SOECs. First, we developed the theory of nonlinear FVAR for two-dimensional isotropic medium. It revealed that there exists a new type of vibration symmetry, called the colour symmetry, in nonlinear FVAR modes. We also revealed that the vibration modes can be classified on the basis of magnetic point groups rather than conventional irreducible representations of a point group. We then developed quasilinear FVAR theory for three-dimensional and anisotropic elastic medium. Numerical analysis revealed that nearly the entire TOECs can be determined from pressure dependence of FVAR frequencies.

Free Research Field

弾性理論、固体力学、材料科学