Benaroya Haym, Gabbai Rene D
Department of Mechanical and Aerospace Engineering, Rutgers University, New Brunswick, NJ 08854-8058, USA.
Philos Trans A Math Phys Eng Sci. 2008 Apr 13;366(1868):1231-74. doi: 10.1098/rsta.2007.2130.
The principal goal of this research is developing physics-based, reduced-order, analytical models of nonlinear fluid-structure interactions associated with offshore structures. Our primary focus is to generalize the Hamilton's variational framework so that systems of flow-oscillator equations can be derived from first principles. This is an extension of earlier work that led to a single energy equation describing the fluid-structure interaction. It is demonstrated here that flow-oscillator models are a subclass of the general, physical-based framework. A flow-oscillator model is a reduced-order mechanical model, generally comprising two mechanical oscillators, one modelling the structural oscillation and the other a nonlinear oscillator representing the fluid behaviour coupled to the structural motion.Reduced-order analytical model development continues to be carried out using a Hamilton's principle-based variational approach. This provides flexibility in the long run for generalizing the modelling paradigm to complex, three-dimensional problems with multiple degrees of freedom, although such extension is very difficult. As both experimental and analytical capabilities advance, the critical research path to developing and implementing fluid-structure interaction models entails-formulating generalized equations of motion, as a superset of the flow-oscillator models; and-developing experimentally derived, semi-analytical functions to describe key terms in the governing equations of motion. The developed variational approach yields a system of governing equations. This will allow modelling of multiple d.f. systems. The extensions derived generalize the Hamilton's variational formulation for such problems. The Navier-Stokes equations are derived and coupled to the structural oscillator. This general model has been shown to be a superset of the flow-oscillator model. Based on different assumptions, one can derive a variety of flow-oscillator models.
本研究的主要目标是开发基于物理的、降阶的、分析性的与海上结构物相关的非线性流固相互作用模型。我们的主要重点是推广哈密顿变分框架，以便从第一原理推导流 - 振荡器方程组。这是早期工作的扩展，早期工作得出了一个描述流固相互作用的单一能量方程。这里证明了流 - 振荡器模型是基于物理的一般框架的一个子类。流 - 振荡器模型是一种降阶力学模型，通常由两个力学振荡器组成，一个模拟结构振动，另一个是非线性振荡器，代表与结构运动耦合的流体行为。降阶分析模型的开发继续使用基于哈密顿原理的变分方法进行。从长远来看，这为将建模范式推广到具有多个自由度的复杂三维问题提供了灵活性，尽管这种扩展非常困难。随着实验和分析能力的提高，开发和实施流固相互作用模型的关键研究路径需要——制定广义运动方程，作为流 - 振荡器模型的超集；以及——开发通过实验得出的半解析函数来描述运动控制方程中的关键项。所开发的变分方法产生了一个控制方程组。这将允许对多自由度系统进行建模。推导的扩展推广了此类问题的哈密顿变分公式。推导并将纳维 - 斯托克斯方程与结构振荡器耦合。这个通用模型已被证明是流 - 振荡器模型的超集。基于不同的假设，可以推导出各种流 - 振荡器模型。
