Download Active Structural Control: Theory and Practice (Longman by T. T. Soong PDF

By T. T. Soong

Energetic structural keep watch over capacity making buildings aware of exterior forces like earthquakes and hurricanes. Large-scale experimentation is now occurring during this box and this e-book brings jointly a wealth of knowledge at the perform and idea of lively structural keep an eye on. in addition to documenting the newest advances within the box, the e-book additionally appears on the swift improvement in allied applied sciences similar to electronics, fabrics and size options, that have fuelled the expansion of this quarter.

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Example text

2 (a) variance of X 1 (t); (b) variance of X 2 {t) 5 response variance is achieved by the use of active control. It is further observed that, the smaller the i' value is, the more reduction in response is ach'ieved. However, as }' decreases, mqre control forces are required. The standard deviations au,(t) and "u,(t) of the optimal control forces are computed from Eq. 30) and plotted in Fig. 10 to give an indication of required magnitudes of the control forces. From a safety standpoint, the relative displacement between the first floor and the second floor is important, since a},(t) is much greater than a},(t).

38) For the ith eigenvalue 1];, Eq. 38) is satisfied if a column or a row of A(l];) consists entirely of zeros. Thus, suppose thejth column is selected and let ei and 1/1)•1;) denote the jth columns of I, and 1/1(11;), respectively, then defines m linear equations. The procedure described above is then repeated for each eigenvalue 1f 1, i = 1, 2, ... , 211. 39) where E is made up, column by column, of the vectors ei and

If the system experiences a forced vibration, its response after pulse application can be regarded as the resultant of the response due to the pulse alone and the system response to the forcing function alone. t = T,/10, 1~ is the natural period) is illustrated in Fig. 24, Suppose the frequency of the forcing function is lower than the natural frequency of the system. A pure pulse applied in the proper direction can reduce the response of the system during a time period of one half of the natural period, where maximum reduction is achieved after one fourth the natural period and no reduction at half the natural period.

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