×

Active vibration suppression of moderately thick rectangular plates. (English) Zbl 1271.74335

Summary: In the present work, active vibration suppression of moderately thick rectangular plates by means of piezoelectric actuators is investigated. Based on Lagrange energy method, a finite element formulation is presented for mathematical modeling of the system. Using modal controllability criterion, a simple method is offered for optimal placement of the piezoelectric actuator. For a cantilevered plate with specific characteristics, the optimal position of a piezoelectric patch is investigated. Then, for suppression of plate vibrations, an active damping controller is designed using modal velocity feedbacks. Numerical simulations are then performed for studying the performance of the designed controller. Presented simulations indicate the feasibility of vibration control of moderately thick plates by means of high voltage piezoelectric actuators. These simulations also show that, for a specific excitation force, the maximum required voltage for vibration suppression approaches to an asymptotic value as the values of modal feedback gains increase. This conclusion is of high importance in practical controller design.

MSC:

74M05 Control, switches and devices (“smart materials”) in solid mechanics
74H45 Vibrations in dynamical problems in solid mechanics
74K20 Plates
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Abdel-Motagaly K, AIAA Journal 43 (3) pp 671– (2005)
[2] DOI: 10.1016/j.jsv.2004.03.042
[3] Carra S, Journal of Intelligent Material Systems and Structures 18 pp 637– (2007)
[4] Chang M-Y, Journal of Sound and Vibration 228 pp 731– (1999)
[5] Chen T, Journal of Sound and Vibration 320 pp 221– (2009)
[6] Dimitridis EK, Journal of Vibration and Acoustics 113 pp 100– (1991)
[7] DOI: 10.1016/j.jsv.2004.01.009
[8] Ebrahimi F, European Journal of Mechanics A/Solids 28 pp 962– (2009) · Zbl 1176.74107
[9] Fares ME, Composite Structures 56 pp 1– (2002)
[10] Hashemi SH, International Journal of Solids and Structures 42 pp 819– (2005) · Zbl 1125.74338
[11] Kim TW, Smart Materials and Structures 14 pp 904– (2005)
[12] Lee Y, Smart Materials and Structures 12 pp 541– (2003)
[13] DOI: 10.1016/S0020-7683(02)00081-1 · Zbl 1033.74019
[14] Mindlin RD, ASME Journal of Applied Mechanics 18 pp 31– (1951)
[15] Sadri AM, Smart Materials and Structures 8 pp 490– (1999)
[16] Tang J, Smart Materials and Structures 10 pp 794– (2001)
[17] Zhang W, Journal of Intelligent Material Systems and Structures 15 pp 923– (2004)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.