### STP1045: Resonating-Orthotropic-Cube Method for Elastic Constants

Heyliger, P

*assistant professorresearch metallurgistmaterials research engineer, Colorado State UniversityNISTNBS, Fort CollinsBoulder, ColoradoColorado*

Ledbetter, H

*assistant professorresearch metallurgistmaterials research engineer, Colorado State UniversityNISTNBS, Fort CollinsBoulder, ColoradoColorado*

Austin, M

*assistant professorresearch metallurgistmaterials research engineer, Colorado State UniversityNISTNBS, Fort CollinsBoulder, ColoradoColorado*

Pages: 10 Published: Jan 1990

**Abstract**

Following studies by Demarest (1969) and by Ohno (1976), we describe measurements and analysis that yield, from a single cube-shape specimen, in a single measurement, the complete set of anisotropic elastic-stiffness constants, the C^{ij}. Experimentally, we place a cubic specimen between two piezoelectric transducers, which excite and detect the cube's macroscopic free-vibration (fundamental-mode) frequencies, up to 10 MHz. From the specimen's shape, size, and mass, and from the measured resonance-frequency spectrum, we analyze for the C^{ij} within a given tolerance ϵ^{i}: λi(Cij)-λi¯=ϵi. (No sum on i.) Here ƛ^{i} relates to the measured resonance frequencies, and λ^{i} represents eigenvalues calculated by a Rayleigh-Ritz method using Legendre-polynomial approximating functions. Legendre-polynomial orthogonality ensures a diagonal mass matrix [m], which simplifies the resulting eigenvalue problem: ([k]-λ[m]){x}={0}. For materials with certain symmetries, the coefficient matrix [k] reduces to a block-diagonal matrix, which reduces computational effort and simplifies vibration-mode identification.

**Keywords:**

anisotropic media, elastic constants, Rayleigh—Ritz method, resonating-cube method, vibrational modes

**Paper ID:** STP24618S

**Committee/Subcommittee:** E28.03

**DOI:** 10.1520/STP24618S

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