000013642 001__ 13642
000013642 005__ 20161114170126.0
000013642 04107 $$aeng
000013642 046__ $$k2011-05-25
000013642 100__ $$aSorokin, S.
000013642 24500 $$aA Hierarchy of Timoshenko Beam Theories

000013642 24630 $$n3.$$pComputational Methods in Structural Dynamics and Earhquake Engineering
000013642 260__ $$bNational Technical University of Athens, 2011
000013642 506__ $$arestricted
000013642 520__ $$2eng$$aThis paper shows that conventional Timoshenko theory for bending waves is a member of a two-parameter family (m; n) of approximations to the exact equations of linear elasticity. Higher members of the family are shown to represent the exact dispersion relation with extraordinary accuracy; in particular, an arbitrary number of branches can be captured accurately over their entire length, i.e. up to arbitrarily high frequencies and wavenumbers. The theory admits a rational accuracy analysis, and resolves certain controversies about the validity of higher-branch approximations. The paper demonstrates conclusively that Timoshenko theory is a completely rational theory, thus ending decades of doubt on the matter. The standard Euler-Bernoulli theory is a lower member of the two-parameter family. Especially useful is Timoshenko (1; 2) theory, which extends conventional Timoshenko (0; 1) theory by capturing the first four branches of the exact dispersion relation rather than merely the first two.

000013642 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000013642 653__ $$aBending Wave, Dispersion Relation, Finite Products, Beam, Timoshenko Theory.

000013642 7112_ $$aCOMPDYN 2011 - 3rd International Thematic Conference$$cIsland of Corfu (GR)$$d2011-05-25 / 2011-05-28$$gCOMPDYN2011
000013642 720__ $$aSorokin, S.$$iChapman, J.
000013642 8560_ $$ffischerc@itam.cas.cz
000013642 8564_ $$s90037$$uhttps://invenio.itam.cas.cz/record/13642/files/423.pdf$$yOriginal version of the author's contribution as presented on CD, section: MS 15 Linear Wave Propagation in Advanced Elastic Wave Guides.
000013642 962__ $$r13401
000013642 980__ $$aPAPER