Notes on a function minimization approach to structural control

✍ Scribed by N. D. Ebrahimi

• Publisher: John Wiley and Sons
• Year: 1989
• Tongue: English
• Weight: 293 KB
• Volume: 18
• Category: Article
• ISSN: 0098-8847
• DOI: 10.1002/eqe.4290180113

✦ Synopsis

In this issue of this journal Warburton has presented a discussion' on a recent paper by the author., The original paper illustrated a technique for vibration control of continuous mechanical systems. Warburton's suggested method is an ingenious and intriguing concept. As he points out, his approach uses prescribed values of the location of the control forces. For this reason, this brief note provides some further comments on the subject when the problem is viewed as an unconstrained (two-parameter) mathematical programming problem (with locations of control fwces as known quantities).

Let us apply the vibration control strategy to the case of longitudinal vibration of a fixed-fixed elastic bar which is under the action of a harmonically varying force, such a s f = F sinwt. Figure 1 shows a schematic drawing of such a system. In this diagram, 1 is the length of the bar, p l ( 0 < p < 1) is the distance of the point of application of the load from the left end of the bar, x is the horizontal reference coordinate and u is the response of the system to the excitation (f). The steady-state response can be found by solving the partial X X