By Wodek Gawronski
The publication provides and integrates the tools of structural dynamics, identity 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 and Active Control of Structures
In the second case we use the system states to describe the dynamics. Structural engineers prefer degrees of freedom and the second-order differential equations of structural dynamics; this is not a surprise, since they have a series of useful mathematical and physical properties. This representation has a long tradition and using it many important results have been derived. The state-space model, on the other hand, is a standard model used by control engineers. Most linear control system analyses and design methods are given in the state-space form.
The input matrix Bo is nd u s , the output displacement matrix Coq is r u nd , and the output velocity matrix Cov is r u nd . The mass matrix is positive definite (all its eigenvalues are positive), and the stiffness and damping matrices are positive semidefinite (all their eigenvalues are nonnegative). 1. Determine the nodal model for a simple system from Fig. 1. 01ki , i = 1, 2, 3, 4. There is a single input force at mass 3, and three outputs: displacement and velocity of mass 1 and velocity of mass 3.
The models can also be represented in the form of a transfer function, after applying the Laplace or Fourier transformation. The state-space representation carries information about the internal structure (represented by states) of the model, while the transfer function describes the model in terms of its input–output properties (although its internal state can be somehow recovered). Also, the statespace models are more convenient and create less numerical difficulties than transfer functions when one deals with high-order models.
Advanced Structural Dynamics and Active Control of Structures by Wodek Gawronski