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