Download e-book for kindle: Advanced Structural Dynamics & Active Control of Structures by Wodek Gawronski

By Wodek Gawronski

ISBN-10: 0387406492

ISBN-13: 9780387406497

The e-book offers and integrates the equipment of structural dynamics, indentification and keep watch over right into a universal framework. It goals to create a typical language among structural and regulate approach engineers.

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Example text

55). 42), respectively, by rearranging the columns of A and C and the rows of A and B. 1. In particular, the first component of the input matrix Bi might not necessarily be zero, unless one finds a unique transformation that preserves the zero entry. 1. m determine the modal model 2 using the modal or nodal data. m determine modal model 1 or 2 using an arbitrary state-space representation. 9. 8. 7370 »¼ >cm1 cm2 cm3 @. 5). In modal coordinates it is, of course, G ( s ) Cm ( sI  Am )1 Bm . 6).

64) Proof. 45) to the definition of the transfer function we obtain 1 G (Z ) Cm ( jZ I  Am ) Bm n ¦ Cmi ( jZ I  Ami ) i 1 1 n Bmi ¦ 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.

Modal models of structures are the models expressed in modal coordinates. Since these coordinates are independent, it leads to a series of useful properties that simplify the analysis (as will be shown later in this book). The modal coordinate representation can be obtained by the transformation of the nodal models. This transformation is derived using a modal matrix, which is determined as follows. , a structure without external excitation (u { 0) and with the damping matrix D = 0. 7) in this case turns into the following equation: Mq + Kq = 0.

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Advanced Structural Dynamics & Active Control of Structures by Wodek Gawronski

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