Download Advanced Structural Dynamics and Active Control of by Wodek Gawronski PDF

By Wodek Gawronski

The ebook provides and integrates the tools of structural dynamics, identity and keep watch over right into a universal framework. It goals to create a typical language among structural and regulate method engineers.

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This is a variable that satisfies the following equation: q )qm . 7) by )T , obtaining )T M )qm  )T D) qm  )T K ) qm y Coq )qm  Cov )qm . 16) we obtain the above equation in the following form: M m qm  Dm qm  K m qm )T Bo u , y Coq )qm  Cov )qm . Next, we multiply (from the left) the latter equation by M m1 , which gives M m1)T Bo u , qm  M m1Dm qm  M m1K m qm y Coq )qm  Cov )qm . The obtained equations look quite messy, but the introduction of appropriate notations simplifies them, qm  2 =:qm  : 2 qm Bm u , y Cmq qm  Cmv qm .

However, in some cases, it is possible to obtain Dm diagonal. In these cases the damping matrix is called a matrix of proportional damping. The proportionality of damping is commonly assumed for analytical convenience. This approach is justified by the fact that the nature of damping is not known exactly, that its values are rather roughly approximated, and that the off-diagonal terms in most cases—as will be shown later—have negligible impact on the structural dynamics. 17) where D1 and D 2 are nonnegative scalars.

However, in some cases, it is possible to obtain Dm diagonal. In these cases the damping matrix is called a matrix of proportional damping. The proportionality of damping is commonly assumed for analytical convenience. This approach is justified by the fact that the nature of damping is not known exactly, that its values are rather roughly approximated, and that the off-diagonal terms in most cases—as will be shown later—have negligible impact on the structural dynamics. 17) where D1 and D 2 are nonnegative scalars.

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