Zeitschrift für angewandte Mathematik und Physik

, Volume 66, Issue 1, pp 239–252

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


DOI: 10.1007/s00033-014-0407-8

Cite this article as:
Sharma, N., Kern, D. & Seemann, W. Z. Angew. Math. Phys. (2015) 66: 239. doi:10.1007/s00033-014-0407-8


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 

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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