• dynamic stiffness;
  • stochastic finite element method;
  • random frames;
  • random matrices;
  • frequency response function


The forced harmonic vibration analysis of portal frames consisting of viscously damped beams with spatial stochastic variation of mass and stiffness properties is considered. The analysis is based on the assembly of element stochastic dynamic stiffness matrices. The solution involves inversion of the global dynamic stiffness matrix, which, in this case, turns out to be a complex-valued symmetric random matrix. Three alternative approximate procedures, namely, random eigenfunction expansion method, complex Neumann expansion method and combined analytical and simulation method are used to invert the matrix. The performance of these approximate procedures is evaluated using Monte Carlo simulation results. Copyright © 1999 John Wiley & Sons, Ltd.