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.
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September 1965
Research Papers
Random Vibrations of Plates With Large Amplitudes
R. E. Herbert
R. E. Herbert
College of Aeronautics, Cranfield, Bedford, England
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R. E. Herbert
College of Aeronautics, Cranfield, Bedford, England
J. Appl. Mech. Sep 1965, 32(3): 547-552 (6 pages)
Published Online: September 1, 1965
Article history
Received:
April 24, 1964
Revised:
December 15, 1964
Online:
September 15, 2011
Citation
Herbert, R. E. (September 1, 1965). "Random Vibrations of Plates With Large Amplitudes." ASME. J. Appl. Mech. September 1965; 32(3): 547–552. https://doi.org/10.1115/1.3627257
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