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Contrasting three alternative versions of Timoshenko‐Ehrenfest theory for beam on Winkler elastic foundation – simply supported beam
Author(s) -
Elishakoff Isaac,
Tonzani Giulio Maria,
Zaza Nicolò,
Marzani Alessandro
Publication year - 2018
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/zamm.201700019
Subject(s) - timoshenko beam theory , beam (structure) , foundation (evidence) , context (archaeology) , vibration , inertia , physics , classical mechanics , quantum mechanics , optics , archaeology , biology , history , paleontology
In this paper the free vibration frequencies of beam on one‐parameter (Winkler) elastic foundation are analyzed via original Timoshenko‐Ehrenfest theory as well as two truncated versions of the Timoshenko‐Ehrenfest beam theory. The traditional version of Timoshenko‐Ehrenfest beam theory is contrasted with the truncated version that lacks the fourth‐order time derivative, as well as with the recently developed version that incorporates slope inertia effect. Advantages and disadvantages of each approach are indicated in the context of free vibrations of the beam on Winkler foundation. In addition an intriguing intermingling phenomenon is discussed in detail, and its implications on three theories.