Sliding beams, Part II: time integration
โ Scribed by K. Behdinan; M. C. Stylianou; B. Tabarrok
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 487 KB
- Volume
- 43
- Category
- Article
- ISSN
- 0029-5981
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โฆ Synopsis
In this paper we obtain solutions for the discretized incremental system equations, as obtained in Part I, under certain initial and boundary conditions and/or specified applied loads, using the variable domain beam element. As a check on the validity of implementation, we first limit ourselves to linear analysis and obtain results for the axially inextensible sliding beams which we compare with the results reported in the literature. Second we set the axial velocity to zero and solve some special cases when the length of the beam is constant. In this case, we check the formulation and its implementation for non-linearities in the system due to large displacements. Finally, we solve the sliding beam problem for small amplitude oscillations, with a non-linear solver and compare the results with those obtained by the linear solver used for inextensible sliding beams. With these preliminary tests completed, we obtain the transient response of the free and forced large amplitude vibrations of the flexible sliding beam and demonstrate the need for using a nonlinear analysis for this complex system. Finally, we consider the stability of the motion of periodically time varying flexible sliding beams and show that in the case of parametric resonance, the unstable regions obtained in the linear analysis, which imply unbounded amplitudes, are indeed stable and bounded when non-linear terms are taken into account.
๐ SIMILAR VOLUMES
We use the updated Lagrangian and the co-rotational finite element methods to obtain solutions for geometrically non-linear flexible sliding beams. Finite element formulations are normally carried out for fixed domains. Since the sliding beam is a system of changing mass, first we discretize the sys
Equations of motion for the geometrically non-linear analysis of flexible sliding beams, deployed or retrieved through a rigid channel, are derived through an extension of Hamilton's principle. Based on the assumptions of Euler-Bernoulli beam theory, the equations of motion account for small strains