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Powerful FE approaches for Pochhammer's dispersion modelling
Author(s) -
Mazúch Tibor
Publication year - 2003
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.691
Subject(s) - finite element method , dispersion (optics) , simple (philosophy) , mathematics , phase (matter) , mathematical analysis , geometry , structural engineering , engineering , physics , optics , philosophy , epistemology , quantum mechanics
Simple and very effective finite element approaches for modelling of the dispersion of torsional, longitudinal and flexural waves propagated in infinite and elastic cylindrical bars (Pochhammer's problem) and hollow cylinders are presented. The approaches allow one to model given problems without using infinite elements and their usage is demonstrated by using dispersion curves, shapes of waves and tables of phase velocities. Comparison of finite element solutions (solved in one task from small‐sized models) with exact solutions shows an excellent agreement. The maximum relative differences among the 20 lowest FEM and analytical phase velocities was less than 0.000015%. The approaches and results hold also for cylinders with finite lengths, simply supported on both ends. Copyright © 2003 John Wiley & Sons, Ltd.