Ritz vs. Eigen vectors
An overview of Ritz and Eigen vectors, taken from the CSI Analysis Reference Manual (Modal Analysis > Overview, page 323), is given as follows:
- Eigenvector analysis determines the undamped free-vibration mode shapes and frequencies of the system. These natural modes provide an excellent insight into the behavior of the structure.
- Ritz-vector analysis seeks to find modes that are excited by a particular loading. Ritz vectors can provide a better basis than do Eigenvectors when used for response-spectrum or time-history analyses that are based on modal superposition.
The user should determine the type of modes which are the most appropriate.
Eigenvectors
Eigen modes are most suitable for determining response from horizontal ground acceleration, though a missing-mass (residual-mass) mode may need to be included to account for missing high-frequency effects. Mass participation is a common measure for determining whether or not there are enough modes, though it does not provide information about localized response.
Eigen analysis is useful for checking behavior and locating problems within the model. Another benefit is that natural frequencies indicate when resonance should be expected under different loading conditions. Users may control the convergence tolerance. Orthogonality is strictly maintained to within the accuracy of the machine (15 decimal digits). Sturm sequence checks are performed and reported to avoid missing Eigen vectors when using shifts. Internal accuracy checks are performed and used to automatically control the solution. Ill-conditioned systems are detected and reported, then still produce Eigen vectors which may be used to trace the source of the modeling problem.
Ritz vectors
Load-dependent Ritz vectors are most suitable for analyses involving vertical ground acceleration, localized machine vibration, and the nonlinear