Comparison of Formulas Obtained for Analytical and LQ Idea Approaches to Determine the Optimal Actuator Location in Active Multimodal Beam Vibration Reduction

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In this paper an active multimodal beam vibration reduction via one actuator is considered. The optimal actuator distribution is analyzed with two methods: an exact mathematical principles and the LQ problem idea. It turned out that the same mathematical expressions are derived. Thus, these methods are equivalent.

[1] AUGUSTYN E., KOZIEŃ M.S., PR4CIK M. (2014), Reduction of torsional vibration of free-clamped beam by piezoelectric elements, E-book Forum Acusticum, SS22_8,

[2] BRAŃSKI A., BORKOWSKI M., SZELA S. (2010), The idea of the selection of PZT-beam interaction forces in active vibration protection problem, Acta Physica Polonica, 118, 17-22.

[3] BRAŃSKI A. (2011), An optimal distribution of actuators in active beam vibration-some aspects, theoretical considerations, Acoustic Waves, Chapter 18, InTech, Rijeka, Chorwacja, 397-418.

[4] BRAŃSKI A., LIPINSKI G. (2011), Analytical determination of the PZT's distribution in active beam vibration protection problem, Acta Physica Polonica 119, 936-941.

[5] BRAŃSKI A. (2013), Effectiveness analysis of the beam modes active vibration protection with different number of actuators, Acta Physica Polonica, 123, 1123-1127.

[6] BRUANT I., PROSLIER L. (2005), Optimal location of actuators and sensors in active vibration control, J. In-telligent Material System Structures, 16, 197-206.

[7] BRUANT I., GALLIMARD L., NIKOUKAR S. (2010), Optimal piezoelectric actuator and sensor location for active vibration control, using genetic algorithm, J.S.V., 329, 1615-1635.

[8] FULLER C.R., ELLIOT S.J., NIELSEN P.A. (1997), Active control of vibration, Academic Press, London.

[9] GUNEY M., ESKINAT E. (2007), Optimal actuator and sensor placement inflexible structures using closed-loop criteria, J.S.V., 312, 210-233.

[10] GUPTA V., SHARMA M., THAKUR N. (2010), Op-timization Criteria for Optimal Placement of Piezo-electric Sensors and Actuators on Smart Structure: A Technical Review, Journal of Intelligent Material Systems and Structures, 21.

[11] HANSEN C.H., SNYDER S.D. (1997), Active control of noise and vibration, E&FN SPON, London.

[12] KALISKI S. (1986), Vibrations and waves [in Polish], PWN, Warszawa.

[13] KASPRZYK S., WICIAK M. (2007), Differential equation of transverse vibrations of a beam with a local stroke change of stiffness, Opuscula Mathematica, 27, 245-252.

[14] KOZIEŃ M.S., WICIAK J. (2008), Reduction of struc-tural noise inside crane cage by piezoelectric actuators -FEM simulation, Arch. Acoust., 33, 4, 643-652.

[15] KOZIEŃ M.S. (2013), Analytical Solutions of Excited, Vibrations of a Beam with Application of Distribution, Acta Physica Polonica, 123, 1029-1033.i

[16] QIU Z., ZHANG X., WU H., ZHANG H. (2007), Optimal placement and active vibration control for piezoelectric smart flexible cantilever plate, J.S.V., 301, 521-543.

[17] DE SILVA C.W. (2000), Vibration, Fundamentals and practice, CRC Press.

[18] WICIAK J. (2007), Modeling of vibration and noise con-trol of a submerged circular plate, Arch. Acoust., 32, 4 (Suppl.), 265-270.

[19] WICIAK J. (2008), Vibration and Structural Acoustic Control-Selected, Aspects, AGH, Krakow.

[20] ŻOLOPA E., BRAŃSKI A. (2014a), Analytical Determi-nation of Optimal Actuators Position for Single Mode Active Reduction of Fixed-free Beam Vibration Using the LQ Problem Idea, Acta Physica Polonica, 125, 155-158.

[21] ŻOLOPA E., BRAŃSKI A. (2014b), An active reduction of general beam vibration via actuator, E-book Forum Acusticum, SS22_11,

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The Journal of Institute of Fundamental Technological of Polish Academy of Sciences

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