Ritz Analysis

A Ritz analysis is a way of calculating approximations to the dynamic modes of a structure, so can appear similar to a modal dynamic analysis, even though the calculation is quite different. A Ritz analysis is based on a set of load dependent vectors derived from gravity loads applied in the three global axis directions. The advantage of a Ritz analysis is that it will recover modes of vibration that are significant in all three directions. This is the case even if the stiffness in one direction is significantly different from the other, which is a challenge form a normal dynamic modal analysis.

Modelling implications

In a Ritz analysis there is a structure mass matrix and structure stiffness matrix, just as with the modal analysis.

A Ritz analysis is set up using the Analysis Wizard from the Analysis | New Analysis Task menu command. Select the Ritz analysis option. The next page allows the user to specify the task name (a name to associate with this modal analysis), the number of Ritz vectors and the “load” direction, and the maximum number of iterations. The number of Ritz vectors determines the number of approximate modes. The number that are required will depend on the structure and what is to be done with the modal results.

Results of Ritz analysis

The results for a Ritz analysis are almost identical to those for a modal analysis. However the mode shapes, represented by the displacements, are in this case only approximations to the true mode shapes. The reliability of the mode shape can be checked by examining the error norm which for an exact calculation of the true mode shape would be zero.

Details of results available and how they can be viewed are in the Results Display Options section.