Random Vibrations of Plates With Large Amplitudes

[+] Author and Article Information
R. E. Herbert

College of Aeronautics, Cranfield, Bedford, England

J. Appl. Mech 32(3), 547-552 (Sep 01, 1965) (6 pages) doi:10.1115/1.3627257 History: Received April 24, 1964; Revised December 15, 1964; Online September 15, 2011


The theory of the Markoff process and the associated Fokker-Planck equation is used to investigate the large vibrations of beams and plates with arbitrary boundary conditions subjected to while-noise excitation. An expression for the joint probability-density function of the first N-coefficients of series expansions of the middle surface displacements is obtained. Detailed calculations presented for simply supported beams and plates show that the probability-density function of the modal amplitudes is non-Gaussian and statistically dependent. Numerical computations for the plate indicate a significant reduction of the mean-squared displacement for values of the parameters well inside the range of practical considerations. Furthermore, for the square plate, the percent reduction is greatest.

Copyright © 1965 by ASME
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