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By Wodek Gawronski

The e-book provides and integrates the tools of structural dynamics, indentification and keep an eye on right into a universal framework. It goals to create a standard language among structural and keep an eye on approach engineers.

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Impulse responses of (a) first mode; (b) second mode; and (c) third mode. All show single frequency time histories. 1). Recall that a set of the three state-space parameters ( A, B, C ) is called the state-space representation, and x is the state vector, u is the input, and y is the output. Again, the representation depends on the choice of the state vector, while the input and output remain invariant. It makes a difference what state representation is chosen for system analysis or for controller design.

The value of the transfer function at the ith resonant frequency is approximately equal to the value of the ith mode transfer function at this frequency: ( jcmqi  Zi cmvi )bmi G (Zi ) # Gmi (Zi ) 2] iZi2 . 64) Proof. 45) to the definition of the transfer function we obtain G (Z ) Cm ( jZ I  Am ) 1 Bm n ¦ i 1 Cmi ( jZ I  Ami ) 1 Bmi n ¦ Gmi (Z ), i 1 which proves the first part. The second part follows from the first part by noting that, for flexible structures with distinct natural frequencies and low damping, Gmj (Zi )  Gmi (Zi ) 2 2 for i z j.

3 Special Models ª how to describe less-common structures Do not quench your inspiration and your imagination; do not become the slave of your model. —Vincent van Gogh Models described in the previous chapter include typical structural models, which are continuous-time, stable, and with proportional damping. In this chapter we consider models that are not typical in the above sense but, nevertheless, often used in engineering practice. Thus, we will consider models with rigid-body modes (which are unstable), models with nonproportional damping, discrete-time structural models, models with acceleration measurements, and generalized structural models.

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