By Wodek Gawronski
The booklet provides and integrates the equipment 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
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. 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.
Determine the first four natural modes and frequencies of the antenna presented in Fig. 6. We used the finite-element model of the antenna to solve this problem. The modes are shown in Fig. 4. 3 rad/s. 5. The Matlab code for this example is in Appendix B. For the simple system from Fig. 1 determine the natural frequencies and modes, the system transfer function, and transfer functions of each mode. Also determine the system impulse response and the impulse responses of each mode. 01ki , i = 1, 2, 3, 4.
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. In this subsection we introduce three different state-space models using modal coordinates qm . We obtain the first model by defining the following state variables as x1 and x2 qm , that is, x x1 ½ :qm ½ ® ¾ ® ¾. 37) y Cmq : 1 x1 Cmv x2 . 1), with the state triple as follows: : º ª 0 A « », ¬ : 2 =: ¼ B ª 0 º «B » , ¬ m¼ C ªCmq : 1 Cmv º .
Advanced Structural Dynamics & Active Control of Structures by Wodek Gawronski