By Wodek Gawronski
The ebook offers 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 keep an eye on process engineers.
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Additional info for Advanced Structural Dynamics & Active Control of Structures
1. 1 assuming that k1 0 . The latter assumption causes the structure to float (there are no springs k1 and k4 that attach the structure to the base). For this system, the nodal model consists of the mass matrix M diag(m1 , m2 , m3 ) I 3 , and the stiffness matrix: M, Special Models 43 K ª k2 « k « 2 «¬ 0 k2 k2 k3 k3 ª 3 3 0 º « 3 6 3» . 8165» . 4083»¼ The modes are shown in Fig. 1. Note that the first mode does not have flexible deformations (springs are neither expanded nor compressed).
The proportionality of damping is commonly assumed for analytical convenience. This approach is justified by the fact that the nature of damping is not known exactly, that its values are rather roughly approximated, and that the off-diagonal terms in most cases—as will be shown later—have negligible impact on the structural dynamics. 17) where D1 and D 2 are nonnegative scalars. Modal models of structures are the models expressed in modal coordinates. In order to do so we use a modal matrix to introduce a new variable, qm , called modal displacement.
4. 87 Hz). For each mode the nodal displacements are sinusoidal, have the same frequency, and the displacements are shown at their extreme values. Gray color denotes undeformed state. 28), and their magnitudes and phases are shown in Fig. 6. 1, the transfer function of the entire structure is a sum of the modal transfer functions, and this is shown in Fig. 6, where the transfer function of the structure was constructed as a sum of transfer functions of individual modes. The impulse response of the structure is shown in Fig.