By S O Reza Moheimani, Dunant Halim, Andrew J Fleming

ISBN-10: 9812383379

ISBN-13: 9789812383372

Vibration is a traditional phenomenon that happens in numerous engineering platforms. in lots of conditions, vibration significantly impacts the character of engineering layout because it frequently dictates proscribing components within the functionality of the approach. the normal remedy is to revamp the procedure or to exploit passive damping. the previous can be a high priced workout, whereas the latter is barely potent at better frequencies. lively regulate suggestions have emerged as potential applied sciences to fill this low-frequency hole. This publication is anxious with the examine of suggestions controllers for vibration keep an eye on of versatile buildings, so as to minimizing vibration over the total physique of the constitution.

The e-book introduces quite a few versatile buildings equivalent to beams, strings, and plates with particular boundary stipulations, and explains intimately how a spatially dispensed version of such structures may be got. It addresses the issues of version aid and version correction for spatially allotted platforms of excessive orders, and is going directly to expand strong regulate ideas akin to H-infinity and H2 keep watch over layout methodologies to spatially dispensed platforms bobbing up in lively vibration keep watch over difficulties. It additionally addresses different vital issues, similar to actuator and sensor placement for versatile platforms, and approach identity for versatile constructions with abnormal boundary stipulations. The textual content comprises a number of examples, and experimental effects received from laboratory-level equipment, with info of ways related try out beds can be outfitted.

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Example text

48). /(*,£) = 0 , 2 EI EI d y(t,r) dr2 r=0 d2y(t,r) dr2 r=L 0 and = 0. 53) and TZ — [0,L]. 57) The eigenfunction, 4>i(r), has to satisfy the corresponding boundary conditions: i(L) = 0, 41 (0) = 0 and 4>'i(L) = 0. 58) 24 Spatial Control of Vibration The general solution to the eigenvalue problem is of the form [67, 16]: 4>i{r) = Ai sin Xir + Bi cos Xir + d sinh Xir + Di cosh Xir. 59) The coefficients Ai, Bi, Ci and Di are to be determined from the boundary conditions. 58) imply Bi = Di = 0.

Therefore, this section is devoted to modeling of flexural vibration of a piezoelectric laminate beam, which is our main experimental test-bed. Modeling sensor V,s2 Ki J, £ ^ ^ ^ P = ^ ^ fc^^i l ^ ^ ^ t val P^^^i • • • fe^^l Vajn vn. actuator Fig. 16. Suppose there are J collocated actuator-sensor pairs distributed over the structure. Piezoelectric patches on one side of the beam act as sensors, while those on the other side serve as actuators. 17). ,VaJ(t)}'. 102) where all parameters are defined in previous sections.

41 Modeling Further, 4"^ can be obtained from rL *ij = / Jo Mr) \d6{r - Tij) dr dd(r - r2j) dr. 113), assuming zero initial conditions, the MHO (Multiple-Input, Infinite-Output) transfer function from the applied actuator-voltages, Va(s) = [ V a l ( s ) , . . , + % r ,ff +u? ,Kj*iJ]. 116) sensor th Consider the k piezoelectric sensor patch attached to the beam. 18. When the beam vibrates due to some external disturbance or non-zero initial conditions, strain is generated inside the beam. Consequently, an electric charge is generated inside the piezoelectric sensor due to the piezoelectric effect.

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Spatial Control of Vibration: Theory and Experiments by S O Reza Moheimani, Dunant Halim, Andrew J Fleming

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