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Stochastic Analysis of Linear Systems

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Encyclopedia of Earthquake Engineering

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Synonyms

Evolutionary frequency response function; Evolutionary power spectral density function; Gaussian zero-mean random models of seismic accelerations; Non-geometric spectral moments; Stochastic analysis

Introduction

The stochastic analysis of structural vibrations deals with the description and characterization of structural loads and responses that are modeled as stochastic processes. The probabilistic characterization of the input process could be extremely complex in time domain where the probability density functions depend on the autocorrelation functions which experimentally have to be specified over given set points. Since this approach is difficult to be used in applications, stochastic vibration analysis of structural linear systems subjected to Gaussian input processes is quite often performed in the frequency domain by means of the spectral analysis. This analysis is a very powerful tool for the analytical and experimental treatment of a large class of physical as well...

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References

  • Borino G, Muscolino G (1986) Mode-superposition methods in dynamic analysis of classically and non-classically damped linear systems. Earthq Eng Struct Dyn 14:705–717

    Article  Google Scholar 

  • Conte JP, Peng B-F (1997) Fully nonstationary analytical earthquake ground-motion model. J Eng Mech (ASCE) 123:15–24

    Article  Google Scholar 

  • Corotis RB, Vanmarcke EH, Cornell CA (1972) First passage of nonstationary random processes. J Eng Mech (ASCE) 98:401–414

    Google Scholar 

  • Di Paola M (1985) Transient spectral moments of linear systems. SM Arch 10:225–243

    MathSciNet  MATH  Google Scholar 

  • Di Paola M, Petrucci G (1990) Spectral moments and pre-envelope covariances of nonseparable processes. J Appl Mech (ASME) 57:218–224

    Article  MathSciNet  MATH  Google Scholar 

  • Fan FG, Ahmadi G (1990) Nonstationary Kanai-Tajimi models for El Cento 1940 and Mexico City 1985 earthquakes. Probab Eng Mech 5:171–181

    Article  Google Scholar 

  • Harichandran RS, Vanmarcke EH (1986) Stochastic variation of earthquake ground motion in space and time. J Eng Mech (ASCE) 112:154–174

    Article  Google Scholar 

  • Hsu T-I, Bernard MC (1978) A random process for earthquake simulation. Earthq Eng Struct Dyn 6:347–362

    Article  Google Scholar 

  • Jennings PC, Housner GW, Tsai C (1969) Simulated earthquake motions for design purpose. In: Proceedings of the 4th world conference earth engineering, Santiago, A-1, pp 145–160

    Google Scholar 

  • Langley RS (1986) Structural response to non-stationary non-white stochastic ground motion. Earthq Eng Struct Dyn 14:909–924

    Article  Google Scholar 

  • Li J, Chen JB (2009) Stochastic dynamics of structures. Wiley, Singapore

    Book  MATH  Google Scholar 

  • Lin YK (1976) Probabilistic theory of structural dynamics. Krieger, Huntington

    MATH  Google Scholar 

  • Lutes LD, Sarkani S (2004) Random vibrations – analysis of structural and mechanical vibrations. Elsevier, Boston

    Google Scholar 

  • Michaelov G, Sarkani S, Lutes LD (1999a) Spectral characteristics of nonstationary random processes – a critical review. Struct Saf 21:223–244

    Article  Google Scholar 

  • Michaelov G, Sarkani S, Lutes LD (1999b) Spectral characteristics of nonstationary random processes – response of a simple oscillator. Struct Saf 21:245–267

    Article  Google Scholar 

  • Muscolino G (1991) Nonstationary pre-envelope covariances of nonclassically damped systems. J Sound Vib 149:107–123

    Article  MathSciNet  Google Scholar 

  • Muscolino G, Palmeri A (2005) Maximum response statistics of MDOF linear structures excited by non-stationary random processes. Comput Method Appl Mech Eng 194:1711–1737

    Article  MATH  Google Scholar 

  • Priestley MB (1999) Spectral analysis and time series. Academic, London

    Google Scholar 

  • Shinozuka M, Sato Y (1967) Simulation of nonstationary random process. J Eng Mech (ASCE) 93:11–40

    Google Scholar 

  • Spanos P, Solomos GP (1983) Markov approximation to transient vibration. J Eng Mech (ASCE) 109:1134–1150

    Article  Google Scholar 

  • Vanmarcke EH (1972) Properties of spectral moments with applications to random vibrations. J Eng Mech (ASCE) 98:425–446

    Google Scholar 

  • Vanmarcke EH (1975) On the distribution of the first-passage time for normal stationary random processes. J Appl Mech (ASME) 42:215–220

    Article  MATH  Google Scholar 

  • Zerva A (1991) Effect of spatial variability and propagation of seismic ground motions on the response of multiply supported structures. Probab Eng Mech 6:212–221

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Ingegnria Civile, Informatica, Edile, Ambientale e Matematica Applicata, Università degli Studi di Messina, Villaggio Sant’Agata, 98166, Messina, Italy

    Giuseppe Muscolino

Authors
  1. Giuseppe Muscolino
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Corresponding author

Correspondence to Giuseppe Muscolino .

Editor information

Editors and Affiliations

  1. Institute for Computer Science in Civil Engineering, Gottfried Wilhelm Leibniz, University Hannover, Hannover, Germany

    Michael Beer

  2. Department of Civil Engineering & Engineering Mechanics, Columbia University, New York, NY, USA

    Ioannis A. Kougioumtzoglou

  3. Institute for Risk & Uncertainty and Centre for Engineering Sustainability, Liverpool, UK

    Edoardo Patelli

  4. Institute for Risk & Uncertainty and Centre for Engineering Dynamics, Liverpool, UK

    Siu-Kui Au

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Muscolino, G. (2015). Stochastic Analysis of Linear Systems. In: Beer, M., Kougioumtzoglou, I.A., Patelli, E., Au, SK. (eds) Encyclopedia of Earthquake Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35344-4_335

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