Anisotropic Elastic Constants: Measurement by Impact Resonance
Publication: Journal of Materials in Civil Engineering
Volume 13, Issue 5
Abstract
Modes of unrestrained free vibration of rectangular parallelepipeds are excited by impact and combined with solutions to the weak form of the equations of motion corresponding to the 3D equations of elasticity and periodic motion to provide estimates for the elastic constants of anisotropic materials. This method has been previously applied to isotropic materials based on analytic approximations for the relationship between elastic constants and resonant frequencies. The present approach extends this procedure to account for material anisotropy and variance in specimen dimension, and we apply this technique to several specimens of differing material type, constitution, and shape to compute various components of the elastic stiffness tensor. Our results are in very good agreement with those found by other techniques.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
American Society for Testing and Materials (ASTM). ( 1998). Annual book of ASTM standards, West Conshohocken, Pa.
2.
Bodig, J., and Jayne, B. A. ( 1993). Mechanics of wood and wood composites, Krieger, Malabar, Fla.
3.
Cramer, S. M., Hermanson, J. C., and McMurty, W. M. ( 1996). “Crush performance and redwood for developing design procedures for impact limiters.” Proc., 11th Int. Conf. on Packaging and Transp. of Radioactive Mat., Vol. 2, Social and Scientific Systems, Inc., Bethesda, Md., 875–882.
4.
Demarest, H. H. ( 1971). “Cube resonance method to determine elastic constants of solids.” J. Acoustical Soc. Am., 49, 768–775.
5.
Foster, K., et al. ( 1999). “Acoustic study of texture in polycrystalline brass.” J. Accoustical Soc. Am., 105, 2663–2668.
6.
Heyliger, P., Jilani, A., Ledbetter, H., Leisure, R. G., and Wang, C.-L. ( 1993). “Elastic constants of isotropic cylinders by resonant ultrasound.” J. Acoustical Soc. Am., 94, 1482–1487.
7.
Ledbetter, H., Fortunko, C., and Heylinger P. ( 1995a). “Elastic constants and internal friction of polycrystaline copper.” J. Mat. Res., 10, 1352–1353.
8.
Ledbetter, H., Fortunko, C., and Heyliger, P. ( 1995b). “Orthotropic elastic constants of B/AL fiber-reinforced composite: Ultrasonic–spectroscopy study.” J. Appl. Phys., 78, 1542–1546.
9.
Maynard, J., McKenna, M., Migliori, A., and Visscher, W. ( 1992). “Ultrasonic measurements of elastic constants in single-crystals of La2CuO4” Ultrasonics of high-Tc and other unconventional superconductors, Academic, Boston.
10.
Meirovitch, L. ( 1980). Computational methods in structural dynamics. Sijthoff and Noordhoff, Alphen aan den Rijn, The Netherlands.
11.
Migliori, A., and Sarrao, J. L. ( 1997). Resonant ultrasound spectroscopy, Wiley, New York.
12.
Migliori, A., et al. ( 1993). “Resonant ultrasound spectroscopic techniques for measurement of elastic moduli of solids.” Physica B, 183, 1–24.
13.
Ohno, I. ( 1976). “Free vibration of rectangular parallelepiped crystal and its application to determination of elastic constants of orthorhombic crystal.” J. Phys. of the Earth, 24, 355–379.
14.
Pickett, G. ( 1945). “Equations for computing elastic constants from flexural and torsional resonant frequencies of vibration of prisms and cylinders.” Proc., ASTM, 45, 846–865.
15.
Reddy, J. N. ( 1984). Energy and variational methods in applied mechanics, Wiley, New York.
16.
Schreiber, E., Anderson, O., and Soga, N. ( 1973). Elastic constants and their measurements, McGraw–Hill, New York.
17.
Spinner, S., and Tefft, W. E. ( 1961). “Method for determining mechanical resonance frequencies and for calculating elastic moduli from these frequencies.” Proc., ASTM, 61, 1221–1238.
18.
Spinner, S., Reichard, T. W., and Tefft, W. E. ( 1960). “Comparison of experimental and theoretical relations between Young's modulus and the flexural and longitudinal resonance frequencies of uniform bars.” J. Res. Nat. Bureau of Standards-A. Phys. and Chem., 64A, 147–155.
19.
Sumino, Y., Ohno, I., Goto, T., and Kumazawa, M. ( 1976). “Measurement of elastic constants and internal frictions on single-crystal MgO by rectangular parallelepiped resonance.” J. Phys. of the Earth, 24, 263–273.
20.
Visscher, W. M., Migliori, A., Bell, T. M., and Reinert, R. A. ( 1991). “On normal modes of free vibration of inhomogeneous and anisotropic elastic objects.” J. Acoustical Soc. Am., 90, 2154–2162.
Information & Authors
Information
Published In
Journal of Materials in Civil Engineering
Volume 13 • Issue 5 • October 2001
Pages: 356 - 363
History
Received: Oct 15, 1998
Published online: Oct 1, 2001
Published in print: Oct 2001
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.