TECHNICAL PAPERS
Sep 1, 2007

Peak Response of a Nonlinear Beam

Publication: Journal of Engineering Mechanics
Volume 133, Issue 9

Abstract

A model for estimating the peak dynamic response distribution of a nonlinear beam, based on a special class of non-Gaussian stochastic processes, is proposed in this paper. It is shown that the stochastic response of a cantilever beam with geometrically nonlinear behavior can be accurately calibrated with translation processes. Different models to describe the significant bimodal features in the marginal probability density functions of the response time histories are proposed. Finally, two of these models are used to estimate the response peak value distributions and the results are compared. This comparison demonstrates the effects of inaccurate models for the parent response processes on the peaks estimation.

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Acknowledgments

This work was supported by MIUR (Italian Ministry of University and Scientific Research–PERBACCO and VinCES Research Programs).

References

Antonini, A., Gioffrè, M., and Gusella, V. (2002). “Geometrically nonlinear cantilever under stochastic loading vectors.” Nonlinear Dyn., 28(1), 83–102.
Bathe, K.-J., and Bolourchi, S. (1979). “Large displacement analysis of three-dimensional beam structures.” Int. J. Numer. Methods Eng., 14(7), 961–986.
Cartwright, D. E., and Longuet-Higgins, M. S. (1956). “The statistical distribution of the maxima of a random function.” Proc. R. Soc. London, Ser. A, 237(1209), 212–232.
Cramér, H., and Leadbetter, M. R. (1967). Stationary and related stochastic processes; Sample function properties and their applications, Wiley, New York.
Davenport, A. G. (1964). “Note on the distribution of the largest value of a random function with application to gust loading.” Proc.-Inst. Civ. Eng., 28, 187–196.
Gioffrè, M. (1998). “Analysis and simulation of non-Gaussian processes with application to wind engineering and reliability.” Ph.D. thesis, Univ. of Florence, Florence, Italy.
Gioffrè, M., Grigoriu, M., Kasperski, M., and Simiu, E. (2000). “Wind-induced peak bending moments in low-rise building frames.” J. Eng. Mech., 126(8), 879–881.
Gioffrè, M., and Gusella, V. (2002). “Numerical analysis of structural systems subjected to non-Gaussian random fields.” Meccanica, 37(1–2), 115–128.
Grigoriu, M. (1984). “Crossings of non-Gaussian translation processes.” J. Eng. Mech., 110(4), 610–620.
Grigoriu, M. (1995). Applied non-Gaussian processes: Examples, theory, simulation, linear random vibration and MATLAB solutions, Prentice-Hall, Englewood Cliffs, N.J.
Rice, S. O. (1944). “Mathematical analysis of random noise.” Bell Syst.Tech. J., 23, 282–332.
Schuëller, G. I., and Bucher, C. G. (1988). “Non-Gaussian response systems under dynamic excitation.” Stochastic structural dynamics: Progress in theory and applications, S. Ariaratnam, G. Schuëller, and I. Elishakoff, eds., Elsevier Applied Science, London, 219–239.
Shock, H. J. (1976). Untersuchungen zur tragfaehigkeit von seilverspannten druckstaeben, Universitat Stuttgart, Stuttgart, Germany.
Soong, T. T., and Grigoriu, M. (1993). Random vibration of mechanical and structural systems, PTR Prentice Hall, Englewood Cliffs, N.J.
Vanmarke, E. (1975). “On the distribution of first-passage time for normal stationary random processes.” ASME J. Appl. Mech., 42(1), 215–220.

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Information

Published In

Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 133Issue 9September 2007
Pages: 963 - 969

History

Received: Aug 4, 2003
Accepted: Feb 27, 2007
Published online: Sep 1, 2007
Published in print: Sep 2007

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Notes

Note. Associate Editor: Arvid Naess

Authors

Affiliations

Massimiliano Gioffrè, Ph.D. [email protected]
Assistant Professor, Dept. of Civil and Environmental Engineering, Univ. of Perugia, Via G.Duranti 93, 06125 Perugia, Italy (corresponding author). E-mail: [email protected]
Vittorio Gusella, Ph.D. [email protected]
Full Professor, Dept. of Civil and Environmental Engineering, Univ. of Perugia, Via G.Duranti 93, 06125 Perugia, Italy. E-mail: [email protected]

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