By Wodek Gawronski
The ebook provides and integrates the tools of structural dynamics, indentification and keep watch over right into a universal framework. It goals to create a standard language among structural and regulate method engineers.
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Extra info for Advanced Structural Dynamics & Active Control of Structures
42 Chapter 3 We obtain the rigid-body modes by solving the same eigenvalue problem as presented for the standard models. , the stiffness matrix becomes singular. The corresponding rigid-body mode Irb is the one that satisfies the equation KIrb 0. 3) n y ¦ yi . 54) by assuming Zi 0 . 62) for Zi 0, Gmi (Z ) (cmqi jZ cmvi )bmi Z2 . 5) For an experienced engineer rigid-body frequency and mode are not difficult to determine: rigid-body frequency is known in advance, since it is always zero, and rigid-body mode can be predicted as a structural movement without deformation.
For example, some representations have useful physical interpretations; others are more convenient for analysis and design. 2 Transfer Function Besides the state-space representation a linear system can be alternatively represented by its transfer function. 5) where y(s) and u(s) are the Laplace transforms of the output y(t) and input u(t), respectively. 1) for the zero initial condition, x(0) = 0, we express the transfer function in terms of the state parameters (A,B,C), G ( s ) C ( sI A) 1 B.
In generic coordinates each state depends on itself (through the gain Ami shown in Fig. 9 with a solid line) and on other states (through the gains Amij shown in Fig. 9 with a dashed line). In modal coordinates the cross-coupling gains Amij are zero, thus each state is independent and depends only on itself. 9. Block diagram of the state-space representation of a structure with two modes: The modal cross coupling (marked with a dashed line) is nonexistent. We consider three modal representations in this book.