Original Paper

Nonlinear Dynamics

, Volume 51, Issue 1, pp 217-230

First online:

Enhanced nonlinear 3D Euler–Bernoulli beam with flying support

  • Hassan ZohoorAffiliated withCenter of Excellence in Design, Robotics, and Automation, School of Mechanical Engineering, Sharif University of Technology Email author 
  • , S. Mahdi KhorsandijouAffiliated withSchool of Mechanical Engineering, Sharif University of Technology

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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.


3D Euler–Bernoulli beam theory