Zeitschrift für angewandte Mathematik und Physik

, Volume 66, Issue 1, pp 239–252 | Cite as

Vibration analysis and robust control of highly deformable beams in a heavy pinched loop configuration



A heavy pinched loop is formed by bringing and clamping the two ends of a highly deformable slender beam, elastica. A collocation solution technique is implemented for studying the formation statically and dynamically, i.e. small vibrations around the large deformed static solutions, and the earlier work using a shooting method is validated. A new and clear Galerkin formulation capable of modelling damping is established for finding transients, and a new theoretical multi-point boundary value problem approach is used for numerically obtaining the frequency response function. Lastly, the obtained dynamic model is used for active vibration control, wherein a controller is designed using H algorithm for active damping in a heavy pinched loop for two simplified cases, and the simulated results are shown.

Mathematics Subject Classification

74B20 74H45 93C05 65L15 


Elastica Pinched loop Collocation Frequency response function Robust control 


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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Mechanical EngineeringTampere University of TechnologyTampereFinland
  2. 2.Mechanical EngineeringChemnitz University of TechnologyChemnitzGermany
  3. 3.Mechanical EngineeringKarlsruhe Institute of TechnologyKarlsruheGermany

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