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Continuum-based free vibration of circular trigonal and isotropic plates



Ward L. Johnson, Paul R. Heyliger


The free vibration behavior of completely unrestrained elastic circular plates with trig- onal and isotropic material symmetry is studied using approximate solutions to the three- dimensional theory of linear elasticity. Of primary interest are 1) the influence of trigonal material symmetry on the modes of free vibration, and 2) the relative accuracy of thin plate theory as compared to the more exact three-dimensional theory. Frequencies are calculated based on approximations of the weak form of the equations of motion for the plate using the Ritz method formulated in cylindrical coordinates that allows a splitting of the resulting eigenvalue problem using group theory. Representative examples are given and quantitative limits are discussed.
Journal of the Acoustical Society of America


disks, elasticity, group theory, isotropic material, Ritz method, trigonal crystals, trigonal plates, vibrational modes


Johnson, W. and Heyliger, P. (2013), Continuum-based free vibration of circular trigonal and isotropic plates, Journal of the Acoustical Society of America, [online], (Accessed July 14, 2024)


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Created May 28, 2013, Updated June 2, 2021