Continuum-based free vibration of circular trigonal and isotropic plates.
The free vibration behavior of completely unrestrained elastic circular plates with trigonal and isotropic material symmetry is studied with an approach involving approximate continuum 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 accuracy of thin plate theory relative to the more exact three-dimensional theory. Resonant frequencies are calculated from the weak form of the equations of motion for the plate through the use of approximation functions and the Ritz method formulated in cylindrical coordinates. This approach enables the resulting eigenvalue problem to be split through group-theoretical symmetry analysis. Representative examples are given and quantitative limits are discussed.
Department of Civil and Environmental Engineering, Colorado State University, Fort Collins, Colorado 80523, USA.
Paul R
PR
Heyliger
Ward
W
Johnson
D000162:Acoustics / Q000295:instrumentation*; D004548:Elasticity; D004867:Equipment Design; D005583:Fourier Analysis; D016014:Linear Models; D009038:Motion; D011312:Pressure; D013016:Sound; D013997:Time Factors; D014732:Vibration