A Method for Double Random Vibration Analysis


Article Preview

A numerical procedure to compute the mean and covariance matrix of the random response of stochastic structures modeled by FE models is presented. With the help of Gegenbauer polynomial approximation, the calculation of dynamic response of random parameter system is transformed into an equivalent certainty expansion order system's response calculation. Non-stationary, non-white, non-zero means, Gaussian distributed excitation is represented by the well-known Karhunen-Loeve (K-L) expansion. The Precise Integration Method is employed to obtain the K-L decomposition of the non-stationary filtered white noise random excitation. A very accurate result is obtained by a small amount of K-L vectors with the vector characteristic of energy concentration, especially for the small band-width excitation. Correctness of the method is verified by the simulations.



Edited by:

Kuang-Chao Fan




J. Liao et al., "A Method for Double Random Vibration Analysis", Applied Mechanics and Materials, Vol. 577, pp. 119-124, 2014

Online since:

July 2014




* - Corresponding Author

[1] ASTILL C, IMOSSEIR S, SHINOZUKA M. Impact loading on structures with random properties [J]. Journal of Structural Mechanics, 1972, 1(1): 63-77.

DOI: https://doi.org/10.1080/03601217208905333

[2] CONTRERAS H. The stochastic finite-element method [J]. Computers & Structures, 1980, 12(3): 341-8.

[3] SUN T. A finite element method for random differential equations with random coefficients [J]. SIAM Journal on Numerical Analysis, 1979, 16(6): 1019-35.

DOI: https://doi.org/10.1137/0716075

[4] GHANEM R, SPANOS P. Polynomial chaos in stochastic finite elements [J]. Journal of Applied Mechanics, 1990, 57(1): 197-202.

DOI: https://doi.org/10.1115/1.2888303

[5] JENSEN H. Response of systems with uncertain parameters to stochastic excitation [J]. Journal of Engineering Mechanics, 1992, 118(1012.

[6] LI J. The expanded order system method of combined random vibration analysis [J]. ACTA Mechanica Sinica-Chinese Edition-, 1996, 28(3): 66-75.

[7] SCHU LLER G I, PRADLWARTER H J. On the stochastic response of nonlinear FE models [J]. Archive of Applied Mechanics (Ingenieur Archiv), 1999, 69(9): 765-84.

DOI: https://doi.org/10.1007/s004190050255

[8] SCHU LLER G I, PRADLWARTER H J, SCHENK C A. Non-stationary response of large linear FE models under stochastic loading [J]. Computers and structures, 2003, 81(8-11): 937-47.

DOI: https://doi.org/10.1016/s0045-7949(02)00473-x

[9] SCHENK C A, PRADLWARTER H J, SCHUELLER G I. On the dynamic stochastic response of FE models [J]. Probabilistic Engineering Mechanics, 2004, 19(1-2): 161-70.

DOI: https://doi.org/10.1016/j.probengmech.2003.11.013

[10] LI J, LIAO S T. Response analysis of stochastic parameter structures under non-stationary random excitation [J]. Computational Mechanics, 2001, 27(1): 61-8.

DOI: https://doi.org/10.1007/s004660000214

[11] XIU D. Numerical methods for stochastic computations: a spectral method approach[M]. Princeton University Press, (2010).

[12] MA X, LENG X, MENG G, et al. Evolutionary earthquake response of uncertain structure with bounded random parameter[J]. Probabilistic Engineering Mechanics, 2004, 19(3): 239-246.

DOI: https://doi.org/10.1016/j.probengmech.2004.02.007

[13] ZHONG W. On precise integration method [J]. Journal of Computational and Applied Mathematics, 2004, 163(1): 59-78.

[14] GHANEM R G, SPANOS P D. Stochastic finite elements: a spectral approach [M]. Dover Pubns, (2003).

[15] CLOUTH RW, PENZIEN J. Dynamics of structures, 2nd ed. New York: McGraw-Hill; (1993).