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Analysis of the Dynamics of Slender Continua Using Karhunen‐Loève‐Transformation
Author(s) -
Göbel M.,
Kreuzer E.
Publication year - 2008
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200810887
Subject(s) - drill string , transformation (genetics) , string (physics) , dynamics (music) , slip (aerodynamics) , sensitivity (control systems) , control theory (sociology) , computer science , mathematics , mechanics , mathematical analysis , physics , drill , engineering , mechanical engineering , theoretical physics , acoustics , artificial intelligence , electronic engineering , chemistry , biochemistry , control (management) , gene , thermodynamics
Abstract The dynamics of continua with very small diameter–to–length ratio, like bridges or drill–strings, has been object of mechanical analysis for a long time. While it is often possible to create a well–suited mechanical model, it is difficult to determine the exact current loads and the exact operational state. For drill–strings, the load of the drill–bit depends on the material of the rock, but also on other unknown disturbances like differential sticking which can occur along the drill–string without being noticed directly. Karhunen–Loève–Transformation (KLT) provides a possibility to describe the dynamics of a continuous system with few Characteristic Functions (CF), as long as the motion of the system is stationary. On the other hand, the resulting CFs of the KLT are sensitive to changes in the dynamic system behavior. These changes can result e. g. from the occurrence of stick–slip of the bit or differential sticking of the string. On the basis of a simple model, we show that this sensitivity can be used to detect and characterize such changes. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)