Second Order Statistics of Dynamic Response of Structures Using Gamma Distributed Damping Parameters
This article presents the main results of a numerical
investigation on the uncertainty of dynamic response of structures
with statistically correlated random damping Gamma distributed. A
computational method based on a Linear Statistical Model (LSM) is
implemented to predict second order statistics for the response of a
typical industrial building structure. The significance of random
damping with correlated parameters and its implications on the
sensitivity of structural peak response in the neighborhood of a
resonant frequency are discussed in light of considerable ranges of
damping uncertainties and correlation coefficients. The results are
compared to those generated using Monte Carlo simulation
techniques. The numerical results obtained show the importance of
damping uncertainty and statistical correlation of damping
coefficients when obtaining accurate probabilistic estimates of
dynamic response of structures. Furthermore, the effectiveness of the
LSM model to efficiently predict uncertainty propagation for
structural dynamic problems with correlated damping parameters is
demonstrated.
[1] A. Kareem and K. Gurley, “Damping in structures: evaluation and
treatment of uncertainty”. Journal of Wind Engineering & Industrial
Aerodynamics. Vol. 59, 1996, pp. 131-157.
[2] S. Q. Li, J. Q. Fang, A. P. Jeary and C. K. Wong, “Full scale
measurements of wind effects on tall buildings”. Journal of Wind
Engineering & Industrial Aerodynamics. Vol 74-76, 1998, pp. 741-750. [3] J. Q. Fang, Q. S. Li, A. P. Jeary and D. K. Liu “Damping of tall
buildings: its evaluation and probabilistic characteristics”. Structural
Design of Tall Buildings. Vol. 8, 1999, pp. 145-153
[4] B. Tiliouine and M. Belghenou “The significance of damping variability
and its effects on seismic response of building structures”. International
Conference on Earthquake Engineering. (SE- 50EEE). Skopje.
Macedonia, 2013
[5] E. Vanmarcke, Random fields Analysis and synthesis. World scientific,
2010
[6] A. K. Chopra, Dynamics of Structures: Theory and Applications to
Earthquake Engineering. Prentice Hall, 2007.
[7] R. Havilende, “A study of uncertainties in fundamental translational
periods and damping values for real buildings’, Res, Rep. R76-12, Dept
of civil engineering. MIT. Cambridge. 1976.
[8] C. Seung-Kyum, V. G. Ramana and A. C. Robert, Reliability-based
Structural Design, Springer, 2007.
[9] S. Sumen, L. Rajan and D. Norou, “A Bivariate Distribution with
Conditional Gamma and its Multivariate Form” Journal of Modern
Applied Statistical Methods. Vol 13, Nov 2014, pp. 169-184.
[10] B. Tiliouine and B. Chemali “On the sensitivity of dynamic response of
structures with random damping”. 21ème Congrès Français de
Mécanique. Bordeaux, 2013
[11] M. M. Putko, P. A. Newman, A. C. Taylor. III and L. L. Green (2001).
“Approach for Uncertainty Propagation and Robust Design in CDF
Using Sensitivity Derivatives”. AAIA Journal. 2001, pp. 2001-2528.
[1] A. Kareem and K. Gurley, “Damping in structures: evaluation and
treatment of uncertainty”. Journal of Wind Engineering & Industrial
Aerodynamics. Vol. 59, 1996, pp. 131-157.
[2] S. Q. Li, J. Q. Fang, A. P. Jeary and C. K. Wong, “Full scale
measurements of wind effects on tall buildings”. Journal of Wind
Engineering & Industrial Aerodynamics. Vol 74-76, 1998, pp. 741-750. [3] J. Q. Fang, Q. S. Li, A. P. Jeary and D. K. Liu “Damping of tall
buildings: its evaluation and probabilistic characteristics”. Structural
Design of Tall Buildings. Vol. 8, 1999, pp. 145-153
[4] B. Tiliouine and M. Belghenou “The significance of damping variability
and its effects on seismic response of building structures”. International
Conference on Earthquake Engineering. (SE- 50EEE). Skopje.
Macedonia, 2013
[5] E. Vanmarcke, Random fields Analysis and synthesis. World scientific,
2010
[6] A. K. Chopra, Dynamics of Structures: Theory and Applications to
Earthquake Engineering. Prentice Hall, 2007.
[7] R. Havilende, “A study of uncertainties in fundamental translational
periods and damping values for real buildings’, Res, Rep. R76-12, Dept
of civil engineering. MIT. Cambridge. 1976.
[8] C. Seung-Kyum, V. G. Ramana and A. C. Robert, Reliability-based
Structural Design, Springer, 2007.
[9] S. Sumen, L. Rajan and D. Norou, “A Bivariate Distribution with
Conditional Gamma and its Multivariate Form” Journal of Modern
Applied Statistical Methods. Vol 13, Nov 2014, pp. 169-184.
[10] B. Tiliouine and B. Chemali “On the sensitivity of dynamic response of
structures with random damping”. 21ème Congrès Français de
Mécanique. Bordeaux, 2013
[11] M. M. Putko, P. A. Newman, A. C. Taylor. III and L. L. Green (2001).
“Approach for Uncertainty Propagation and Robust Design in CDF
Using Sensitivity Derivatives”. AAIA Journal. 2001, pp. 2001-2528.
@article{"International Journal of Architectural, Civil and Construction Sciences:71204", author = "B. Chemali and B. Tiliouine", title = "Second Order Statistics of Dynamic Response of Structures Using Gamma Distributed Damping Parameters", abstract = "This article presents the main results of a numerical
investigation on the uncertainty of dynamic response of structures
with statistically correlated random damping Gamma distributed. A
computational method based on a Linear Statistical Model (LSM) is
implemented to predict second order statistics for the response of a
typical industrial building structure. The significance of random
damping with correlated parameters and its implications on the
sensitivity of structural peak response in the neighborhood of a
resonant frequency are discussed in light of considerable ranges of
damping uncertainties and correlation coefficients. The results are
compared to those generated using Monte Carlo simulation
techniques. The numerical results obtained show the importance of
damping uncertainty and statistical correlation of damping
coefficients when obtaining accurate probabilistic estimates of
dynamic response of structures. Furthermore, the effectiveness of the
LSM model to efficiently predict uncertainty propagation for
structural dynamic problems with correlated damping parameters is
demonstrated.", keywords = "Correlated random damping, linear statistical model,
Monte Carlo simulation, uncertainty of dynamic response.", volume = "9", number = "11", pages = "1429-7", }