Abstract
This paper presents a study on the nonlinear steady state response of a slender beam partially immersed in a fluid and carrying an intermediate mass. The model is developed based on the large deformation theory with the constraint of inextensible beam, which is valid for most engineering structures. The Lagrangian dynamics in conjunction with the assumed mode method is utilized in deriving the non-linear unimodal temporal equation of motion. The distributed and concentrated sinusoidal loads are accounted for in a consistent manner using the assumed mode method. The non-linear equation of motion is, analytically, solved using the single term harmonic balance (SHB) and the two terms harmonic balance (2HB) methods. The stability of the system, under various loading conditions, is investigated. The results are presented, discussed and some conclusions on the partially immersed beam nonlinear dynamics are extracted.
Highlights
Offshore structures such as piles, oil plat-forms supports, oil-loading terminals and towers surrounded by water is usually modeled as a beam or a column when studying its static or dynamic behavior
Westergard [1] investigated the hydrodynamic pressure on a rigid dam under earthquake excitation
His investigation resulted in the finding that the magnitude of the hydrodynamic pressure is dependent on the frequency of excitation
Summary
Offshore structures such as piles, oil plat-forms supports, oil-loading terminals and towers surrounded by water is usually modeled as a beam or a column when studying its static or dynamic behavior. Xing et al [6] reported the results of their investigation on the natural frequencies of beam water interaction system They developed a coupled fluid-beam dynamic model in which the fluid domain was modeled by a pressure differential equation and the structure was modeled using twosegments Euler- Bernoulli beam differential equations, with the small deformations assumption. In the previously cited investigations where the immersed beam dynamics was the concern, only the natural frequencies of a structure that undergoes small deformation were calculated and no attention was given to system nonlinearities that develop as a result of large deformations due to beam slenderness. In the presnt work the first order stability are presented and discussed
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