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On the maximum of gaussian fourier series emerging in the analysis of random vibrations

Published online by Cambridge University Press:  14 July 2016

Enzo Orsingher
Enzo Orsingher*
Affiliation:
University of Salerno
*
∗Postal address: Dipartimento di Informatica ed Applicazioni, University of Salerno, 84100 Salerno, Italy.
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Abstract

In this paper we study the maximum of Gaussian Fourier series emerging in the analysis of random vibrations of a finite string. Evaluating the distribution of the maximal displacement corresponds to the analysis of the maximum for the related Gaussian Fourier series with independent coefficients.

When vibrations are triggered by an initial white noise disturbance (where the instantaneous form of the vibrating string is composed of three processes pieced together) we give upper bounds for the maximal displacement.

In the last section we consider forced vibrations at special instants where the instantaneous form of the vibrating string has the structure of a Brownian bridge. This enables us to give the exact distribution of the maximum for the related sine series.

Keywords

WHITE NOISEMAXIMUM OF GAUSSIAN PROCESSESGREEN'S FUNCTIONBROWNIAN BRIDGE
Type
Short Communications
Information
Journal of Applied Probability , Volume 26 , Issue 1 , March 1989 , pp. 182 - 188
Copyright
Copyright © Applied Probability Trust 1989 

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References

Cabaña, E. M. (1972a) On barrier problem for the vibrating string. Z. Wahrscheinlichkeitsth. 22, 13–24.Google Scholar
Cabaña, E. M. (1972b) On barrier problem for sine series with independent Gaussian coefficients. Z. Wahrscheinlichkeitsth. 24, 215–219.Google Scholar
Orsingher, E. (1982) Randomly forced vibrations of a string. Ann. Inst. H. Poincaré B18, 367–394.Google Scholar
Orsingher, E. (1984) Damped vibrations excited by white noise. Adv. Appl. Prob. 16, 562–584.Google Scholar
Shorrock, G. F. and Wellner, J. A. (1986) Empirical Processes with Applications to Statistics. Wiley, New York.Google Scholar