Summary
Nonlinear excitations cause angular vibrations in torsional strings. In long strings, the vibrations are characterized by different dynamic behavior over the length. For a general case of a long torsional string, a simplified mathematical model is introduced and numerically simulated. In order to gain insight into the complex spatio-temporal dynamics, the method of proper orthogonal decomposition is applied. A short description of this powerful technique for continuous as well as discrete systems follows. By proper orthogonal decomposition, the dynamic response is projected on a subset of the state space in which the most dominant dynamic effects take place. The time-invariant eigenfunctions represent the most persistent structures in the system. By this method the eigenfunctions of long torsional strings are investigated. The reduction of the system's dimension as well as the approximation of the system state is presented.
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Kreuzer, E., Kust, O. Analysis of long torsional strings by proper orthogonal decomposition. Arch. Appl. Mech. 67, 68–80 (1996). https://doi.org/10.1007/BF00787141
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DOI: https://doi.org/10.1007/BF00787141