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Introduction to Random Vibration and Stochastic Analysis

In: Stochastic Analysis of Offshore Steel Structures

Author

Listed:
  • Halil Karadeniz

    (Delft University of Technology)

  • Mehmet Polat Saka

    (Middle East Technical University)

  • Vedat Togan

    (Karadeniz Technical University)

Abstract

This chapter is included to provide basic information and essential formulation of random vibration and stochastic analysis that needed in the offshore structural analysis. It contains seven sections. The first section describes briefly random vibration and its occurrence in practice. The second section explains some definitions in the probability theory and presents their formulations that to be used in the probabilistic analysis. The third section explains calculation of probability moments of random variables and random functions. Then, commonly used probability distribution models are presented. In the fourth section, random processes, ensemble averages and expected values, stationary and ergodic processes are explained, and then differentiation of stochastic processes are summarized. In the fifth section, spectral analysis is explained with emphasis on band-limited, narrow-banded and broad-banded processes, crossing analysis and probability distribution of maxima. The sixth section presents input–output relations of stochastic processes and transfer functions. In the seventh section, some illustrative examples are provided.

Suggested Citation

  • Halil Karadeniz & Mehmet Polat Saka & Vedat Togan, 2013. "Introduction to Random Vibration and Stochastic Analysis," Springer Series in Reliability Engineering, in: Stochastic Analysis of Offshore Steel Structures, edition 127, chapter 0, pages 121-176, Springer.
    • Handle: RePEc:spr:ssrchp:978-1-84996-190-5_2
    DOI: 10.1007/978-1-84996-190-5_2
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