SYMPOSIA PAPER Published: 01 January 1990

Resonating-Orthotropic-Cube Method for Elastic Constants


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 Cij. 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 Cij within a given tolerance ϵi: λi(Cij)-λi¯=ϵi. (No sum on i.) Here ƛi relates to the measured resonance frequencies, and λi 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.

Author Information

Heyliger, P
Ledbetter, H
Austin, M
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Developed by Committee: E28
Pages: 100–109
DOI: 10.1520/STP24618S
ISBN-EB: 978-0-8031-5111-6
ISBN-13: 978-0-8031-1291-9