Fluid-induced inertia and damping in vibrating offshore structures

doi:10.1016/0141-1187(80)90042-5

Applied Ocean Research

Volume 2, Issue 1, January 1980, Pages 3-12

https://doi.org/10.1016/0141-1187(80)90042-5 Get rights and content

Abstract

The problem addressed in this paper is that of the fluid-structure interaction in offshore structures for which effects due to fluid viscosity are negligible. A method for evaluating the dynamic response of structures is described in which the generalized coordinates for the analysis are associated with the ‘dry’ modes of the structure. All hydrodynamic actions, including those induced by motions of the structure, are retained on the right-hand side of the equations of motion. This formulation requires the determination of generalized added mass and damping matrices associated with motions of the structure in its first few ‘dry’ modes. By these means, free surface and three dimensional fluid flow effects are retained in the analysis. Examples of the resulting frequency dependent matrices, computed using the boundary integral method, are presented for some common structural forms, and the validity of this approach is demonstrated through some experiments on a deforming column structure. Finally, results for the wave-excited dynamic response of a typical offshore structure obtained using (i) conventional strip theory ‘wet’ modes, and (ii) ‘dry’ modes, are compared.

References (12)

C.C. Mei
Numerical methods in water wave diffraction and radiation
A. Rev. Fluid Mech.
(1978)
C.J. Garrison
Hydrodynamic loading of large offshore structures: three dimensional source distribution methods
O.C. Zienkiewicz et al.
Dynamic fluid-structure interaction: numerical modelling of the coupled problem
R. Eatock Taylor et al.
The dynamics of offshore structures evaluated by boundary integral techniques
Int. J. Num. Meth. Eng.
(1978)
P.E. Duncan et al.
A note on the dynamic analysis of non-proportionally damped systems
Earthquake Eng. Struct. Dyn.
(1979)
R. Eatock Taylor
A linear analysis of interaction problems in offshore platforms

There are more references available in the full text version of this article.

Cited by (4)

Simplified methods for efficient seismic design and analysis of water-surrounded composite axisymmetric structures
2015, Ocean Engineering
Citation Excerpt :
When subjected to earthquake loads, the interaction between an axisymmetric structure and the surrounding water induces hydrodynamic loads while affecting the structural dynamic properties such as natural periods. Earlier literature devoted to the analysis of the vibration characteristics and dynamic response of immersed axisymmetric structures can be roughly classified into three categories depending on the type of modeling adopted for hydrodynamic loads: (i) added-mass formulations where the effect of surrounding water is approximated by added masses distributed along the height of the structure (Lamb, 1932; Nagaya and Hai, 1985; Chang and Liu, 1989; Barltrop and Adams, 1991; Spyrakos and Xu, 1997; Uowska and Koodziej, 1998; Öz, 2003; Wu and Chen, 2005), (ii) continuum-based solutions where hydrodynamic loads are obtained as analytical solutions of the wave equation governing hydrodynamic pressure (Liaw and Chopra, 1974; Eatock Taylor and Duncan, 1980; Williams, 1986; Tanaka and Hudspeth, 1988; Goyal and Chopra, 1989; Xing and Price, 1997; Wei et al., 2012), and (iii) finite element, boundary element or scaled boundary finite element approaches based on the discretization of the surrounding water (Everstine, 1981; Olson and Bathe, 1985; Chen, 2000; Czygan and von Estorff, 2002; Sigrist and Garreau, 2007; Millán et al., 2009; Lu and Jeng, 2010; Tao et al., 2007; Meng and Zou, 2012; Li et al., 2013a,b; Liu and Lin, 2013). Although the dynamic response of axisymmetric structures surrounded by water can now be solved using coupled fluid–structure finite or boundary elements, most of these techniques have not yet been fully implemented in day-to-day engineering practice, especially at the early stages of seismic design, as they require specialized software or advanced programming, and may result in extensive modeling and computational efforts, combined with high-level expertise.
Available simplified formulations for the seismic analysis of axisymmetric structures address materially homogeneous solids with uniform cross-sections, while generally neglecting the effects of higher vibration modes and soil flexibility. In this paper, we develop original simplified procedures that remove these restrictions for practical seismic design and safety evaluation of axisymmetric structures vibrating in contact with water. The procedures proposed take account of higher vibration modes, water compressibility and flexibility of underlying foundation of the structure. For practical purposes, the formulations are first derived while neglecting the effects of surface gravity waves, and are then extended to account for these effects when required. Composite axisymmetric structures made of different materials as well as those with non-uniform hollow cross-sections due to geometric irregularity of interior wall are covered. Step-by-step flowcharts are provided so that the calculations can be easily implemented in a daily practical engineering environment. Application of the proposed techniques is illustrated through the examples of homogeneous and composite axisymmetric tower–water systems with rigid and flexible foundations. The obtained results are successfully validated against advanced coupled fluid–structure finite element solutions.
Hydrodynamic coefficients for flexible offshore columns by wave diffraction techniques
1989, Applied Ocean Research
This paper discusses the wave forces on flexible offshore columns by taking into account the vibration mode shapes. Expressions for the wave forces and the hydrodynamic coefficients are derived using linear diffraction theory, for a flexible vertical circular column fixed at the sea bed and extending to the water surface. Ideal fluid theory is used and consequently, hydrodynamic drag and damping forces due to viscous effects of water are not included. It is shown that when the column is slender i.e., when the column diameter/wave length ratio tends to zero, dispersional damping coefficient $C_{r}$ approaches zero for all modes, whereas added mass coefficient $C_{m}$ approaches 1.0 for the first mode and less than unity for higher modes.
The dynamics of a flexible articulated column in waves
1983, Engineering Structures
A theoretical analysis is developed for the dynamic response of a flexible articulated column, excited harmonically by regular waves. Viscous effects in the fluid are neglected, but the hydrodynamic loading is evaluated by means of a complete wave diffraction and radiation analysis. The column is idealized by Euler-Bernoulli beam theory. Theoretical results for a doubly articulated column are successfully compared with experimental data from a model tested in random waves, and confidence in the analysis is thereby acquired. This is then emplyed in a parameter study of a range of column configurations. Important conclusions are that hydrodynamic damping plays a major role in limiting flexural resonances, and that strip theory can grossly overpredict or underpredict responses. The existence of cancellation effects is investigated, by recourse to the theoretical relationship between generalized wave force and radiation damping in any mode of vibration: this can result in zero responses at certain frequencies.
A review of hydrodynamic load analysis for submerged structures excited by earthquakes
1981, Engineering Structures
Analysis of hydrodynamic loads on submerged structures is reviewed in the context of aseismic design of dams, intake towers and offshore platforms. The structures are considered to be flexible, and a linear fluid-structure interaction analysis is developed using the modes of vibration of a structure oscillating in the absence of a surrounding fluid. Particular attention is paid to the significance of fluid compressibility and free surface effects. As an illustration of the influence of these effects, a closed form solution and results are given for a simple rectangular reservoir-dam system. Numerical solutions are also discussed, based on finite element and boundary integral techniques for complex three-dimensional problems.

View full text

Fluid-induced inertia and damping in vibrating offshore structures

Abstract

Numerical methods in water wave diffraction and radiation

A. Rev. Fluid Mech.

Hydrodynamic loading of large offshore structures: three dimensional source distribution methods

Dynamic fluid-structure interaction: numerical modelling of the coupled problem

The dynamics of offshore structures evaluated by boundary integral techniques

Int. J. Num. Meth. Eng.

A note on the dynamic analysis of non-proportionally damped systems

Earthquake Eng. Struct. Dyn.

A linear analysis of interaction problems in offshore platforms