{"title":"Implementation of State-Space and Super-Element Techniques for the Modeling and Control of Smart Structures with Damping Characteristics","authors":"Nader Ghareeb, R\u00a8udiger Schmidt","volume":136,"journal":"International Journal of Aerospace and Mechanical Engineering","pagesStart":399,"pagesEnd":409,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10008838","abstract":"Minimizing the weight in flexible structures means
\r\nreducing material and costs as well. However, these structures could
\r\nbecome prone to vibrations. Attenuating these vibrations has become
\r\na pivotal engineering problem that shifted the focus of many research
\r\nendeavors. One technique to do that is to design and implement
\r\nan active control system. This system is mainly composed of a
\r\nvibrating structure, a sensor to perceive the vibrations, an actuator
\r\nto counteract the influence of disturbances, and finally a controller to
\r\ngenerate the appropriate control signals. In this work, two different
\r\ntechniques are explored to create two different mathematical models
\r\nof an active control system. The first model is a finite element model
\r\nwith a reduced number of nodes and it is called a super-element.
\r\nThe second model is in the form of state-space representation, i.e.
\r\na set of partial differential equations. The damping coefficients are
\r\ncalculated and incorporated into both models. The effectiveness of
\r\nthese models is demonstrated when the system is excited by its first
\r\nnatural frequency and an active control strategy is developed and
\r\nimplemented to attenuate the resulting vibrations. Results from both
\r\nmodeling techniques are presented and compared.","references":"[1] N. Ghareeb and Y. Radovcic, \u201dFatigue Analysis of a Wind Turbine\r\nPower Train\u201d, DEWI magazin, Germany, August 2009, pp 12-16.\r\n[2] R. Vepa, \u201dDynamics of Smart Structures\u201d, John Wiley & Sons, 2010.\r\n[3] S. Narayanan and V. Balamurugan, \u201d Finite Element Modeling of\r\nPiezolaminated Smart Structures for Active Vibration Control with\r\nDistributed Sensors and Actuators\u201d, Journal of Sound and Vibration,\r\n2003, vol. 262, pp 529-562.\r\n[4] A. Mallock, \u201dA Method of Preventing Vibration in Certain Classes of\r\nSteamships\u201d, Trans. Inst. Naval Architects, 1905, 47, pp 227-230.\r\n[5] H. Hort, \u201dBeschreibung und Versuchsergebnisse ausgef\u00a8uhrter\r\nSchiffsstabilisierungsanlagen\u201d, Jahrb. Schiffbautechnik Ges., 1934,\r\n35, pp 292-312.\r\n[6] A. Vang, \u201dVibration Dampening\u201d, U.S. Patent US 2,361,071, Oct. 24,\r\n1944.\r\n[7] M. 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