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.
Probability Density Function Probability Density Function Joint Moment Rayleigh Distribution Joint Probability Density Function
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.
Crandall SH, Mark WD (1963) Random vibration in mechanical systems. Academic Press, New YorkGoogle Scholar
Newland DE (1984) An introduction to random vibrations and spectral analysis, 2nd edn. Longman, LondonzbMATHGoogle Scholar
Yang CY (1986) Random vibration of structures. Wiley, New YorkGoogle Scholar
Roberts JB, Spanos PD (1990) Random vibration and statistical linearization. Wiley, ChichesterzbMATHGoogle Scholar
Soong TT, Grigoriu M (1993) Random vibration of mechanical and structural systems. PTR Prentice-Hall, Englewood CliffsGoogle Scholar
Preumont A (1994) Random vibration and spectral analysis. Kluwer Academic Publishers, DordrechtzbMATHGoogle Scholar
Paz M, Leigh W (2004) Structural dynamics: theory and computation, 5th edn. Kluwer Academic Publishers, BostonGoogle Scholar
Wijker J (2009) Random vibrations in spacecraft structures design. Theory and Applications. Springer, DordrechtCrossRefGoogle Scholar