Eigenvalue

Whenever eigenvalue or adaptive pushover analyses need to be run, users may choose between two different eigensolvers, the Lanczos algorithm presented by Hughes [1987] or the Jacobi algorithm with Ritz transformation, in order to the determine the modes of vibration of a structure. When the automatic option is selected the most suitable eigensolver will be used depending on the number of the degrees of freedom of the building. The input for each algorithm is described in detail hereafter:

Lanczos algorithm
The following parameters are used to control the way in which this eigensolver works:

  • Number of eigenvalues. The maximum number of eigenvalue solutions required by the user. The default value is 10 which normally guarantees that, at least for standard structural configurations, all modes of interest are adequately captured. Users might wish to increase this parameter when analysing 3D irregular buildings and bridges, where modes of interest might be found beyond the 10th eigensolution.
  • Maximum number of steps. The maximum number of steps required for convergence to be reached. The default value is 50, sufficiently large to ensure that, for the vast majority of structural configurations, solutions will always be obtained.

Jacobi algorithm with Ritz transformation
The user may specify:

  • Number of Ritz vectors (i.e. modes) to be generated in each direction (X, Y and Z). This number cannot exceed the number of dof.
  • Maximum number of steps. The default value of 50 may, in general, remain unchanged.

Notes

  1. Since the Lanczos algorithm implemented in SeismoStruct may struggle to converge with small models featuring a limited number of degrees of freedom (i.e. 1 to 3), users are advised to instead employ the Jacobi-Ritz option for such cases.
  2. When running an eigenvalue analysis using Lanczos algorithm, user may be presented with a message stating: "could not re-orthogonalise all Lanczos vectors", meaning that the Lanczos algorithm could not calculate all or some of the vibration modes of the structure. This behaviour may be observed in either (i) models with assemblage errors (e.g. unconnected nodes/elements) or (ii) complex structural models that feature links/hinges etc. If users have checked carefully their model and found no modelling errors, then they may perhaps try to "simplify" it, by removing its more complex features until the attainment of the eigenvalue solutions. This will enable a better understanding of what might be causing the analysis problems, and thus assist users in deciding on how to proceed. This message typically appears when too many modes are sought, e.g. when 30 modes are asked in a 24 DOF model, or when the eigensolver cannot simply find so many modes (even if DOFs > modes).