Nonlinear vibration modes of an offshore articulated tower
Nonlinear vibration modes of an offshore articulated tower
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DOI：
10.1016/j.oceaneng.2015.08.028
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发表时间：
2015-11
影响因子：
5
通讯作者：
E. Gavassoni;P. Gonçalves;D. Roehl
中科院分区：
文献类型：
--
作者：
E. Gavassoni;P. Gonçalves;D. Roehl
柔性结构由于其低刚度和恶劣的环境载荷，可能会出现大的位移和转动，导致显着的非线性效应。本文应用非线性模态理论研究了一个两自由度柔性铰接塔的离散概念模型的非线性振动。分析中考虑了浮力、附加质量、海流和波浪的影响。弹性恢复力建模，Augusti的模型的基础上，使用两个正交的旋转弹簧。不变流形的方法，然后施加到运动方程，并通过渐近展开求解得到的方程。导出的非线性正常模式，然后用于减少问题的一个单自由度的非线性振子在每个模式。通过Floquet理论和Mathieu图研究了解的稳定性。稳定和不稳定模式的多重性检测使用庞加莱截面。还识别了相似和不相似模式。降阶模型的结果进行了比较，原来的运动方程的数值解。这两种解决方案之间的有利比较证实，非线性正常模式是一个很好的替代非线性分析的铰接塔和类似的海洋结构物。
Compliant structures, due to their low stiffness and hostile environmental loads, may present large displacements and rotations, leading to significant nonlinear effects. This work applies the theory of nonlinear normal modes to investigate the nonlinear vibrations of a discrete two-degree-of-freedom conceptual model of an offshore compliant articulated tower. The effects of buoyancy, added mass, ocean currents and waves are considered in the analysis. The elastic restoring forces are modeled, based on Augusti's model, using two orthogonal rotational springs. The invariant-manifold approach is then applied to the equations of motion, and the resulting equations are solved through an asymptotic expansion. The derived nonlinear normal modes are then used to reduce the problem to a single degree-of-freedom nonlinear oscillator in each mode. The stability of the solution is investigated through Floquet theory and Mathieu charts. Multiplicity of stable and unstable modes is detected using Poincaré sections. Similar and non-similar modes are also identified. The results of the reduced order model are compared to the numerical solutions of the original equations of motion. The favorable comparisons between both solutions confirm that nonlinear normal modes are a good alternative for the nonlinear analysis of an articulated tower and similar offshore structures.