The title problem is analyzed when nodal lines are concentric ellipses by using boundary characteristic orthonormal polynomials in Rayleigh-Ritz method for Winkler foundation where quadratically varying thickness is controlled by two independent taper constants. Numerical results for frequencies, nodal ellipses and mode shapes for first four modes of vibration are presented for plates of free, simply-supported and clamped edge conditions for various values of aspect ratio, taper, orthotropy and foundation parameters.
Vibration of Rectangular Orthotropic Elliptic Plates of Quadratically Varying Thickness Resting on Elastic Foundation
Contributed by the Technical Committee on Vibration and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 2002; Revised May 2003. Associate Editor: B. Yang.
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Gupta, A. P., and Bhardwaj, N. (February 26, 2004). "Vibration of Rectangular Orthotropic Elliptic Plates of Quadratically Varying Thickness Resting on Elastic Foundation ." ASME. J. Vib. Acoust. January 2004; 126(1): 132–140. https://doi.org/10.1115/1.1640654
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