Abstract
In this study, we investigate random vibration of vehicle model exhibiting repeated natural frequencies. It is shown that the cross-correlations have crucial effect, and their neglect may lead to considerable error in the evaluation of mean-square values of the response. In addition, we revisit some discrete systems with coinciding natural frequencies.
Similar content being viewed by others
References
Elishakoff I.: On the role of cross-correlations in the random vibrations of shells. J. Sound Vib. 50, 239–252 (1977)
Elishakoff I., van Zanten A.T., Crandall S.H.: Wide-band random axisymmetric vibration of cylindrical shells. ASME J. Appl. Mech. 46, 417–423 (1979)
Elishakoff, I., Ducreux, B.: Dramatic effect of cross-correlations in random vibration of point-driven spherically curved panel. Arch. Appl. Mech. pp. 1–18 (2013)
Dahlberg T.: Modal cross-spectral terms may be important and an alternative method of analysis be preferable. J. Sound Vib. 84, 503–508 (1982)
Crandall S.H.: Modal-sum and image-sum procedures for estimating wide-band random response of structures. Probab. Eng. Mech. 8, 187–196 (1993)
Elishakoff I.: Probabilistic Methods in the Theory of Structures, pp. 317–380. Wiley, New York (1983)
Lubliner E., Elishakoff I.: Random vibration of system with finitely many degrees of freedom and several coalescent natural frequencies. Int. J. Eng. Sci. 24, 461–470 (1986)
Elishakoff I.: Random Vibration-Status and Recent Developments: The Stephen Harry Crandall Festschrift, pp. 101–112. Elsevier Science Ltd, Amsterdam (1986)
Friswell M.: The derivatives of repeated eigenvalues and their associated eigenvectors. ASME J. Vib. Acoust. 118, 390–397 (1996)
Zuo L., Nayfeh S.A.: Structured H2 optimization of vehicle suspensions based on multi-wheel models. Veh. Syst. Dyn. 40, 351–371 (2003)
Kim H., Yoon Y.S.: Semi-active suspension with preview using a frequency-shape performance index. Veh. Syst. Dyn. 24, 759–780 (1995)
Zuo L., Nayfeh S.A.: H2 optimal control of disturbance-delayed systems with application to vehicle suspensions. Veh. Syst. Dyn. 45, 233–247 (2007)
Li L., Hu Y., Wang X.: A parallel way for computing eigenvector sensitivity of asymmetric damped systems with distinct and repeated eigenvalues. Mech. Syst. Signal Process. 30, 61–77 (2012)
Xu Z., Wu B.: Derivatives of complex eigenvectors with distinct and repeated eigenvalues. Int. J. Numer. Meth. Eng. 75, 945–963 (2008)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Long, X.Y., Elishakoff, I., Jiang, C. et al. Notes on random vibration of a vehicle model and other discrete systems possessing repeated natural frequencies. Arch Appl Mech 84, 1091–1101 (2014). https://doi.org/10.1007/s00419-014-0865-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-014-0865-7