Discuss about Eigen Vector and Ritz Vector?
Eigenvector analysis determines
the undamped free-vibration mode shapes and frequencies of the system. These
natural modes provide an excellent insight into the behaviour of the structure.
Ritz-vector the analysis seeks to find modes that are excited by a 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.
Eigenvectors
Eigenmodes 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 there are enough modes, though it does not provide
information about the localized response.
Eigen analysis is useful for
checking behaviour 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 Eigenvectors which may be used to
trace the source of the modelling problem.
Ritzvectors
Load-dependent
Ritz vectors are most suitable for analyses involving vertical ground
acceleration, localized machine vibration, and the nonlinear FNA method. Ritz
vectors are also efficient and widely used for dynamic analyses involving
horizontal ground motion. Their benefit here is that, for the same number of
modes, Ritz vectors provide a better participation factor, which enables the
analysis to run faster, with the same level of accuracy.
Further, missing-mass modes are automatically
included, there is no need to determine whether there are enough modes, and
when determining convergence of localized response with respect to the number
of modes, Ritz vectors converge much faster and more uniformly than do Eigen
vectors. Ritz vectors are not subject to convergence questions, though strict
orthogonality of vectors is maintained, like Eigenvectors.
Related Articles
What is stiffness modifiers?
Shell or area element has two types of stiffnesses i.e. in-plane stiffness refers to f11, f22 and f12 and out-of-plane stiffness refers to m11, m22 and m12. Refer to the below Figure which shows the direction of local axes and their corresponding ...