Wodek Gawronski's Advanced Structural Dynamics and Active Control of PDF

By Wodek Gawronski

The e-book offers and integrates the equipment of structural dynamics, id and keep an eye on right into a universal framework. It goals to create a typical language among structural and keep watch over method engineers.

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Additional info for Advanced Structural Dynamics and Active Control of Structures

Example text

A structure without external excitation (u { 0) and with the damping matrix D = 0. 7) in this case turns into the following equation: Mq + Kq = 0. 8) 18 Chapter 2 The solution of the above equation is q I e jZ t . Hence, the second derivative of the solution is q Z 2I e jZ t . 8) gives ( K  Z 2 M )I e jZ t 0. 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.

Nodal coordinates are defined through displacements and velocities of selected structural locations, called nodes; and modal coordinates are defined through the displacements and velocities of structural (or natural) modes. In this book we use both coordinate systems; however, we put more weight on the modal coordinate system. At the beginning of this chapter we present a generic state-space system model and its transfer function; next, structural state-space models follow the second-order models of flexible structures.

03¼» B ª0 º «0 » « » «0 » « », «0 » «0 » « » ¬«1 ¼» Standard Models 31 ª1 0 0 0 0 0 º «0 0 0 1 0 0 » . 2 Models in Modal Coordinates Frequently the order of the nodal representation is unacceptably high. For example, it is not uncommon that the number of degrees of freedom of the finite-element model exceeds 1000. Therefore, the nodal state representation is rarely used in structural dynamics. 19), where the number of equations is significantly lower, while the accuracy of the analysis has not suffered.

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