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On Wave Equations for Elastic Rods
Author(s) -
Boström A.
Publication year - 2000
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/(sici)1521-4001(200004)80:4<245::aid-zamm245>3.0.co;2-p
Subject(s) - wave equation , mathematical analysis , axial symmetry , dispersion relation , mathematics , rod , series (stratigraphy) , classical mechanics , physics , geometry , quantum mechanics , medicine , paleontology , alternative medicine , pathology , biology
The derivation of one‐dimensional wave equations for axially symmetric waves in elastic rods is discussed. By series expansions in the radial coordinate a hierarchy of wave equations is derived. As the lowest reasonable approximation the usual simple wave equation for the rod is recovered. At the next level a fourth order wave equation is obtained. The dispersion relation and the displacements for these approximations and for Love's equation are compared with the lowest branch of the exact Pochhammer‐Chree equation. An excitation problem with a shear force is also solved and compared among the theories.