By Wodek Gawronski
The publication offers and integrates the tools of structural dynamics, indentification and keep watch over right into a universal framework. It goals to create a typical language among structural and keep watch over approach engineers.
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Extra resources for Advanced structural dynamics and active control of structures
Consider, for example, T Tº the third representation, with the state vector xT ª qm , consisting of modal qm ¬ ¼ 38 Chapter 2 displacements followed by modal rates. 58) where the modal displacement for each mode stays next to its rate. 57). 59) while ei is an n row vector with all elements equal to zero except the ith which is equal to one, and 0 denotes an n row vector of zeros (actually, we simply rearrange the coordinates). 40). The new state vectors for these representations are as follows: x Z1qm1 ½ ° q ° ° m1 ° °Z 2 qm 2 ° ° ° ® qm 2 ¾ ° # ° ° ° °Z n qmn ° ° ° ¯ qmn ¿ x1 ½ °x ° ° 2° ® ¾, °#° °¯ xn °¿ x Z1qm1 ½ ° ] Z q q ° ° 1 1 m1 m1 ° ° ° Z 2 qm 2 ° ° q q ] Z ® 2 2 m2 m2 ¾ ° ° # ° ° Z n qmn ° ° ° ° ¯] nZ n qmn qmn ¿ x1 ½ °x ° ° 2° ® ¾.
Properties of a typical flexible structure: (a) Poles are complex with small real parts; (b) magnitude of a transfer function shows resonant peaks; (c) impulse response is composed of harmonic components; and (d) phase of a transfer function displays 180 deg shifts at resonant frequencies. 11. Structure response depends strongly on damping: (a) Poles of a structure with small (x) and larger (u) damping – damping impacts the real parts; (b) impulse response for small (solid line) and larger (dashed line) damping – damping impacts the transient time; (c) magnitude of the transfer function for small (solid line) and larger (dashed line) damping – damping impacts the resonance peaks; and (d) response to the white noise input for small (solid line) and larger damping (dashed line) – damping impacts the rms of the response.
There is a single input force at mass 3 and a single output: velocity of mass 1. 2. The magnitude and phase of the transfer function are plotted in Fig. 5. 1210 rad/s. The phase plot shows a 180-degree phase change at each resonant frequency. 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.
Advanced structural dynamics and active control of structures by Wodek Gawronski