By Wodek Gawronski
The booklet offers 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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Determine the rigid-body modes of the Deep Space Network antenna. The antenna has actually two rigid-body modes: rigid-body rotation with respect to the azimuth (vertical) axis, and rigid-body rotation with respect to the elevation (horizontal) axis. 2 shows the azimuth rigid-body mode. 2(a) presents the initial position from the side view, Fig. 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.
3280» . 3 Modal Models Although the above representations were derived using modal displacements, qm , they are not considered modal state representations. The modal state-space representation is a triple ( Am , Bm , Cm ) characterized by the block-diagonal state matrix, Am , Am diag( Ami ) ªu u 0 0 " " 0 0º «u u 0 0 " " 0 0» « » «0 0 u u " " 0 0» « » « 0 0 u u " " 0 0 » , i 1, 2,! 48) where Bmi and Cmi are 2 u s and r u 2 blocks, respectively. 49) and each component consists of two states xi xi1 ½ ® ¾.
Consider, for example, T Tº qm the third representation, with the state vector xT ª qm , consisting of modal ¬ 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 ° m 1 ° ° °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 ° ° ®] 2Z 2 qm 2 qm 2 ¾ ° ° # ° ° Z n qmn ° ° ° ° ¯] nZ n qmn qmn ¿ x1 ½ °x ° ° 2° ® ¾.