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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Random Vibrations of Plates With Large Amplitudes
R. E. Herbert
College of Aeronautics, Cranfield, Bedford, England
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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