Dynamic Response of Systems Subjected to Non-Stationary Random Processes

Introduction

The dynamic behavior of structural and mechanical systems subjected to uncertain dynamic excitations can be described, in general, through random processes. The probabilistic characterization of these random processes can be extremely complex. In this study, the well-established definitions of spectral characteristics for real-valued stationery and non-stationary processes are extended to general complex-valued non-stationary random processes. The spectral characteristics for complex-valued random processes are then evaluated and closed-form solutions for the time-variant statistics of the response of linear single-degree-of-freedom (SDOF) and both classically and non-classically damped multi-degree-of-freedom (MDOF) systems subjected to modulated Gaussian colored noise are obtained. Afterwards, the study presents closed-form solutions for the nongeometric spectral characteristics of nonstationary stochastic processes representing the response of linear elastic structural models subjected to fully nonstationary excitation processes. These spectral characteristics provide a complete description of the nonstationary stochastic processes representing the dynamic response of linear structural models when the input excitation is a Gaussian process. In particular, the nongeometric spectral characteristics can be used to evaluate the time-variant central frequency and bandwidth parameters of nonstationary stochastic processes.

 

Related Publications

  • Barbato M, Conte JP and Peng BF (2004). “Response mean upcrossing rate for linear MDOF systems subjected to fully nonstationary earthquake ground motion model.” Proceedings (full paper), 13th World Conference on Earthquake Engineering (13th WCEE), August 1-6, 2004, Vancouver, British Columbia (Canada). (Link)
  • Barbato M and Conte JP (2008). “Spectral characteristics of non-stationary random processes: theory and applications to linear structural models.” Probabilistic Engineering Mechanics, 23(4):416-426. (Link)
  • Barbato M and Conte JP (2007). “Extension of spectral characteristics to complex-valued random processes and applications in structural reliability.” Proceedings (full paper), 10th International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP10), August 1-3, 2007, Tokyo (Japan).
  • Barbato M and Conte JP (2009). “A new efficient simulation technique for a fully non-stationary stochastic earthquake ground motion.” Proceedings (full paper), 10th International Conference on Structural Safety and Reliability (ICOSSAR 2009), September 13-17, 2009, Osaka (Japan).
  • Barbato M (2009). “Time-variant spectral characteristics of non-stationary random processes: an application to structural reliability and earthquake engineering.” Proceedings (full paper), 2nd International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN 2009), June 22-24, 2009, Rhodes (Greece).
  • Barbato M and Conte JP (2010). “Spectral Characteristics of Non-Stationary Random Processes: Theory and Applications to Linear Structural Models.” Rep. No. SSRP-07/23, Dept. of Structural Engineering, University of California at San Diego, La Jolla, CA (USA). (Link)
  • Barbato M and Vasta M (2010). “Closed-form solutions for the time-variant spectral characteristics of non-stationary random processes.” Probabilistic Engineering Mechanics, 25(1):9-17. (Link)
  • Barbato M and Vasta M (2011). “Time-variant spectral characteristics of non-stationary random processes.” Proceedings (full paper), 6th Computational Stochastic Mechanics (CSM6) Conference, June 13-16, 2010, Rhodes (Greece). (Link)
  • Barbato M, Vasta M and Conte JP (2011). “Closed-form solutions for the spectral characteristics of linear elastic systems subjected to a fully nonstationary earthquake ground motion process.” Proceedings (full paper), 8th International Conference on Structural Dynamics (EURODYN 2011), July 4-6, 2011, Leuven (Belgium).
  • Barbato M and Conte JP (2011). “Structural reliability applications of nonstationary spectral characteristics.” Journal of Engineering Mechanics (ASCE), 137(5):371-382. (Link)
  • Barbato M (2011). “Use of time-variant spectral characteristics of nonstationary random processes in structural reliability and earthquake engineering applications.” Chapter 4 in “Computational Methods in Stochastic Dynamics.” M Papadrakakis, G Stefanou, V Papadopoulos Editors, Computational Methods in Applied Science Series, E. Onate Series Editor, Springer, ISBN: 978-90-481-9986-0. (Link)
  • Barbato M and Conte JP (2013). “Analytical estimates of time-variant failure probability for linear elastic systems subjected to fully non-stationary stochastic earthquake excitation.” Proceedings (full paper), 11th International Conference on Structural Safety and Reliability (ICOSSAR 2013), June 16-20, 2013, Columbia University New York, NY (USA).
  • Barbato M and Conte JP (2015). “Time-variant reliability analysis of linear elastic systems subjected to fully-nonstationary stochastic excitations.” Journal of Engineering Mechanics (ASCE), 04014173, 141(6), June 2015. (Link)

  • Li Y, Conte JP and Barbato M (2016). “Influence of time-varying frequency content in earthquake ground motions on seismic response of linear elastic systems.” Earthquake Engineering and Structural Dynamics, 45(8):1271–1291. (Link)

 

Funded Projects Supporting this Research

  • A probabilistic Performance-Based Approach for Wind-Borne Debris Hazard Mitigation

PI: Barbato, M.

Co-PI: None

Sponsor: LSU College of Engineering, through Longwell’s Family Foundation

Program: Fund for Innovation in Engineering Research (FIER)

Period: March 2008 - May 2010

  • Probabilistic Demand Analysis of Dynamically-Excited Uncertain Structural Systems

PI: Barbato, M.

Co-PI: None

Sponsor: Louisiana Board of Regents, through NSF EPSCoR

Program: Pilot Funding for New Research (Pfund)

Period: May 2008 - July 2009

  • Development of a Novel Record-and-Site-Based Stochastic Model for Generation of Synthetic Ground Motions

PI: Barbato, M.

Co-PI: None

Sponsor: LSU Council on Research Program: 2008 Summer Stipend Program

Period: July 2008

  • A probabilistic performance-based approach for building separation distance decision to mitigate seismic pounding risk

PI: Barbato, M.

Co-PI: None

Sponsor: LSU Council on Research

Program: 2009-2010 Faculty Research Grant Program

Period: August 2010 - July 2011

  • Development of finite elements for response and response sensitivity analysis of reinforced concrete structures retrofitted with externally-bonded fiber reinforced polymers

PI: Barbato, M.

Co-PI: None

Sponsor: Louisiana Board of Regents

Program: RCS Program

Period: August 2010 - July 2013

  • Use of stabilized phosphogypsum as a construction material for artificial reefs

PI: Barbato, M. (35%), Gutierrez-Wing, M.T. (35%),

Co-PI: Rusch, K.A., Seals, R. (10%), Jung, J. (20%)

Sponsor: Louisiana Department of Wildlife and Fisheries

Program: NA

Period: September 2013 - August 2016