Structural Engineering and Mechanics

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Eigenvalue analysis of structures with flexible random connections

  • Matheu, E.E. (Department of Engineering Science and Mechanics, Virginia Tech.) ;
  • Suarez, L.E. (Department of General Engineering, University of Puerto Rico)
  • Published : 1996.05.25
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Abstract

A finite element model of a beam element with flexible connections is used to investigate the effect of the randomness in the stiffness values on the modal properties of the structural system. The linear behavior of the connections is described by a set of random fixity factors. The element mass and stiffness matrices are function of these random parameters. The associated eigenvalue problem leads to eigenvalues and eigenvectors which are also random variables. A second order perturbation technique is used for the solution of this random eigenproblem. Closed form expressions for the 1st and 2nd order derivatives of the element matrices with respect to the fixity factors are presented. The mean and the variance of the eigenvalues and vibration modes are obtained in terms of these derivatives. Two numerical examples are presented and the results are validated with those obtained by a Monte-Carlo simulation. It is found that an almost linear statistical relation exists between the eigenproperties and the stiffness of the connections.

Keywords

References

  1. Boyce, W.E. and Goodwin, B.E. (1964), "Random transverse vibrations of elastic beams", SIAM Journal, 12, 613-629.
  2. Boyce, W.E. (1968), Random Eigenjvalue Problems, Probabilistic Methods in Applied Mathematics, A.T. Barhucha-Reid ed., Academic Press, New York, NY, 1, 1-73.
  3. Collins, J.D. and Thomson, W.T. (1969), "The eigenvalue problem for structural systems with statistical properties", AIAA Journal, 7(4), 642-648. https://doi.org/10.2514/3.5180
  4. Haines, C.W. (1965), An Analysis of Stochastic Eigenvalue Problems, Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy, NY.
  5. Hart, G.C. (1973), "Eigenvalue uncertainty in stressed structures", Journal of the Engineering Mechanics Division, ASCE, 99(EM3), 481-494.
  6. Hasselman, T.K. and Hart, G.C. (1972), "Modal analysis of random structural systems", Journal of the Engineering Mechanics Division, ASCE, 98(EM3), 561-579.
  7. Iyengar, R.N. and Manohar, C.S. (1989), "Probability distribution of the eigenvalues of the random string equation", Journal of Applied Mechanics, ASME, 56, 202-207. https://doi.org/10.1115/1.3176047
  8. Ross, S.M. (1987), Introduction to Probability and Statistics for Engineers and Scientists, John Wiley & Sons, New York, NY.
  9. Scheidt, J. and Purkert, G.M. (1983), Random Eigenvalue Problems, North-Holland, New York, NY.
  10. Shinozuka, M. and Astill, C.J. (1972), "Random eigenvalue problems in structural analysis", AIAA Journal, 10(4), 456-462. https://doi.org/10.2514/3.50119
  11. Soong, T.T. (1981), Probabilistic Modeling and Analysis in Science and Engineering, John Wiley & Sons, New York, NY.
  12. Suarez, L.E. and Matheu, E.E. (1992), Joint Flexibility Effects on the Dynamic Response of Structures, Part I: Deterministic Analysis, Technical Report, College of Engineering, University of Puerto Rico, Mayaguez,, PR.

Cited by

  1. Formulation of a generalized beam element on a two-parameter elastic foundation with semi-rigid connections and rigid offsets vol.80, pp.25, 2002, https://doi.org/10.1016/S0045-7949(02)00226-2
  2. Generalized beam-column finite element on two-parameter elastic foundation vol.21, pp.5, 2005, https://doi.org/10.12989/sem.2005.21.5.519