By Wodek Gawronski

The booklet provides and integrates the equipment of structural dynamics, identity and regulate right into a universal framework. It goals to create a standard language among structural and keep an eye on procedure engineers.

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Extra resources for Advanced Structural Dynamics and Active Control of Structures

Example text

Although input–output relations remain invariant, it makes a difference for system analysis or controller design what state or representation is chosen. 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.

5: if uncontrolled, it can rotate freely with respect to the azimuth (vertical) axis and its dish can freely rotate with respect to the elevation (horizontal) axis. Modal analysis for such structures shows that they have zero natural frequency, and that the corresponding natural mode shows structural displacements without flexible deformations. A mode without flexible deformations is called a rigid-body mode. Corresponding zero frequency implies that the zero frequency harmonic excitation (which is a constant force or torque) causes rigid-body movement of the structure.

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. The importance of distinguishing it from “regular” modes is the fact that they make a system unstable, thus a system that requires special attention. 1. 1 assuming that k1 0 .

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