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Enhanced nonlinear 3D Euler-Bernoulli beam with flying support
Zohoor, H ; Sharif University of Technology | 2008
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- Type of Document: Article
- DOI: 10.1007/s11071-007-9205-6
- Publisher: 2008
- Abstract:
- Using Hamilton's principle the coupled nonlinear partial differential motion equations of a flying 3D Euler-Bernoulli beam are derived. Stress is treated three dimensionally regardless of in-plane and out-of-plane warpings of cross-section. Tension, compression, twisting, and spatial deflections are nonlinearly coupled to each other. The flying support of the beam has three translational and three rotational degrees of freedom. The beam is made of a linearly elastic isotropic material and is dynamically modeled much more accurately than a nonlinear 3D Euler-Bernoulli beam. The accuracy is caused by two new elastic terms that are lost in the conventional nonlinear 3D Euler-Bernoulli beam theory by differentiation from the approximated strain field regarding negligible elastic orientation of cross-sectional frame. In this paper, the exact strain field concerning considerable elastic orientation of cross-sectional frame is used as a source in differentiations although the orientation of cross-section is negligible. © 2007 Springer Science+Business Media, Inc
- Keywords:
- Degrees of freedom (mechanics) ; Dynamic models ; Nonlinear equations ; Partial differential equations ; Stress analysis ; 3D Euler-Bernoulli beam theory ; Elastic orientation ; Beams and girders
- Source: Nonlinear Dynamics ; Volume 51, Issue 1-2 , 2008 , Pages 217-230 ; 0924090X (ISSN)
- URL: https://link.springer.com/article/10.1007/s11071-007-9205-6