Modal Contributions and Static Correction
The first part of this class was actually devoted to closing the previous week lesson.
To this effect, we have seen one example on Rayleigh-Ritz procedure, we discussed the Subspace Iteration Method and finally a last exercise on subspace iteration.
The second part was devoted to the analysis of the relative imortance of the different modal contributions to the response.
First, we introduced the modal partecipation factor and from this definition we derived the idea of modal load contributions. Modal partecipation factors depend on the "tuning" between the loading vector and the respective eigenvectors.
Second, we recognized that it is possible, mode for mode, to separate the dynamic response, expressed in terms of a pseudo-displacement, from a pseudo-static response due to the modal load contribution.
Next, we introduced the modal contribution factor, the dynamic response amplification factor and the peak factors.
Finally, we recognized that, for a given response quantity, we have a static response that, mode by mode, is modulated by a a dynamic amplification and a constant modal contribution factor.
The dynamic amplification is null, and the response is essentially static, for modal frequencies much larger than the the excitation frequency.
From this consideration, the static correction procedure insert into the response the higher modes contributions in term of an enveloping of a static response that, surprise, can be computed also in terms of the lower modes characteristics!
Material available for this class:
- the slides i used for my lesson
- a ready to print version of the slides.