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Structural Engineering and Mechanics
  Volume 4, Number 3, May 1996, pages 277-301
DOI: http://dx.doi.org/10.12989/sem.1996.4.3.277
 


Eigenvalue analysis of structures with flexible random connections
Matheu EE, Suarez LE

 
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 Ist 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.
 
Key Words
    modal analysis, random eigenvalue problem, flexible connections, finite element modeling
 
Address
Matheu EE, VIRGINIA TECH,DEPT ENGN SCI & MECH,BLACKSBURG,VA 24061
UNIV PUERTO RICO,DEPT GEN ENGN,MAYAGUEZ,PR 00681
 

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