By Wodek Gawronski
The ebook offers and integrates the tools of structural dynamics, indentification and regulate right into a universal framework. It goals to create a standard language among structural and keep watch over approach engineers.
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Extra resources for Advanced Structural Dynamics & Active Control of Structures
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. 4) into the above equation. 2 Second-Order Structural Models In this and the following sections we will discuss the structural models. One of them is the second-order structural model. It is represented by the second-order linear differential equations, and is commonly used in the analysis of structural dynamics. Similarly to the state-space models the second-order models also depend on the choice of coordinates.
9) This is a set of homogeneous equations, for which a nontrivial solution exists if the determinant of K Z 2 M is zero, det( K Z 2 M ) 0. 10) The above determinant equation is satisfied for a set of n values of frequency Z. , n d nd . The frequency Zi is called the ith natural frequency. ,In ` that satisfy this equation. The ith vector Ii corresponding to the ith natural frequency is called the ith natural mode, or ith mode shape. The natural modes are not unique, since they can be arbitrarily scaled.
2(b) presents the modal displacement (rigid-body rotation with respect to the azimuth axis) from the side view, Fig. 2(c) presents the initial position from the top view, and Fig. 2(d) presents the modal displacement from the top view. Note that there are no structural deformations, only displacements. 2. Antenna in neutral position (a) and (c); and rigid-body mode of the antenna (b) and (d); where no flexible deformations are observed. 2 Models with Accelerometers Accelerometers are frequently used as structural sensors due to their simplicity, and because they do not require a reference frame.