Modelling dynamics of certain class of discrete multi-body systems based on direct method of the dynamics of relative motion

The motions of floating moored structures are affected by first order wave loads which are proportional to the wave amplitude and associated with the wave frequency. On the other hand, second order wave loads are proportional to the square of the wave amplitude and related to the sum or difference of a pair of frequencies of the irregular sea. Although the second order loads are usually smaller compared to the first order loads, these loads can excite resonance motions in frequencies that the system has very low damping. Therefore, second order wave loads have particular importance in the design of mooring systems. The multi-body system composed by Tension Leg Platform (TLP) and Tender Assisted Drilling (TAD) is particularly susceptible to the second order effects, due to the very low natural frequencies of their horizontal modes and the very high natural frequencies of the vertical modes of the TLP. This work presents a numerical study of second order wave loads on the TLP-TAD multi-body system. An extensive hydrodynamic analysis focus on the hydrodynamic interactions between the floaters and how these effects modify the second order loads on the platforms was performed. The second order quadratic transform functions (QTFs) were evaluated using the indirect and the direct method. Moreover, the importance of the free surface integral was checked. Finally, the accuracy of Newman approximation for the low-frequency QTF was evaluated.

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Characterizing Natural Relative Motion of Formations on Invariant Tori in Multi-Body Systems

10.2514/6.2022-2385 ◽

2022 ◽

Author(s):

Ian Elliott ◽

Natasha Bosanac

Keyword(s):

Relative Motion ◽

Invariant Tori ◽

Multi Body

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A Comparison of Approaches to Multi-Body Relative Motion using the Kestrel Solver

AIAA Scitech 2019 Forum ◽

10.2514/6.2019-1346 ◽

2019 ◽

Cited By ~ 1

Author(s):

Haimin Huang ◽

Regina H. Blyth ◽

Matthew A. Prior ◽

Matteo Giacobello ◽

Rafael Perez ◽

...

Keyword(s):

Relative Motion ◽

Multi Body

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Tank Side-Wall Effect Evaluated by Using Multi-Body Interaction Computation

Volume 1: Offshore Technology; Special Symposium on Ocean Measurements and Their Influence on Design ◽

10.1115/omae2007-29540 ◽

2007 ◽

Author(s):

W. Y. Duan ◽

H. Shaheen ◽

X. B. Chen

Keyword(s):

Wave Diffraction ◽

Direct Method ◽

Side Wall ◽

Floating Body ◽

Wall Effects ◽

Usual Model ◽

Body Interaction ◽

Parallel Side ◽

Side Walls ◽

Multi Body

It is well known that hydrodynamic first- and second-order loads measured on ships or offshore structures in wave tanks exhibit large scatter compared to the expected results in open sea, due to wave reflections from the side walls. A number of recent works have given theoretical models for diffraction and radiation solutions including side-wall effects. One way consisting of defining a Green function satisfying the boundary condition on two parallel side walls can yield reliable solutions for a floating body of arbitrary geometry in any position of the tank. Unlike previous studies, we evaluate the side-wall effects by directly using the option of multi-body interaction in usual model of wave diffraction and radiation. The tank side-walls are considered as an independent fixed body. The wave diffraction and radiation around a floating body in tanks is solved by taking into account of interaction between the two bodies. The excellent agreement between numerical results of first-order quantities and experimental measurements validates the present method. It is shown that this direct method is very efficient and can be further applied to the case of two side walls in non-parallel position as well as to take into account of bathymetric variation of sea bottom.

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Reflections on Nonlinear Dynamics of Machines and Structures

Journal of Mechanics ◽

10.1017/s1727719100001647 ◽

2000 ◽

Vol 16 (2) ◽

pp. 79-83

Author(s):

Francis C. Moon

Keyword(s):

Nonlinear Dynamics ◽

Nonlinear Analysis ◽

Relative Motion ◽

Short Note ◽

Structural Systems ◽

Machine Systems ◽

Multi Body

ABSTRACTIn this short note a comparison is made between the methodology of nonlinear analysis in machine systems versus structural systems. Because of strong nonlinearities in machines with parts in relative motion, chaotic-like dynamics are more likely to occur in complex multi-body machines than in structural systems. Furthermore, it is conjectured that well designed machines have evolved to where a small amount of chaos is always present and is sometimes desired.

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Characterization of frozen hydrated biological specimens by low-loss EELS

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100132492 ◽

1992 ◽

Vol 50 (2) ◽

pp. 1572-1573

Author(s):

Songquan Sun ◽

Richard D. Leapman

Keyword(s):

Water Content ◽

Direct Method ◽

Internal Standard ◽

Dry Weight ◽

Dark Field ◽

Protein Solutions ◽

Subcellular Compartment ◽

Differential Shrinkage ◽

Electron Energy Loss

Analyses of ultrathin cryosections are generally performed after freeze-drying because the presence of water renders the specimens highly susceptible to radiation damage. The water content of a subcellular compartment is an important quantity that must be known, for example, to convert the dry weight concentrations of ions to the physiologically more relevant molar concentrations. Water content can be determined indirectly from dark-field mass measurements provided that there is no differential shrinkage between compartments and that there exists a suitable internal standard. The potential advantage of a more direct method for measuring water has led us to explore the use of electron energy loss spectroscopy (EELS) for characterizing biological specimens in their frozen hydrated state.We have obtained preliminary EELS measurements from pure amorphous ice and from cryosectioned frozen protein solutions. The specimens were cryotransfered into a VG-HB501 field-emission STEM equipped with a 666 Gatan parallel-detection spectrometer and analyzed at approximately −160 C.

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The restoration of blurred electron micrographs

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100142529 ◽

1986 ◽

Vol 44 ◽

pp. 180-181

Author(s):

Bridget Carragher ◽

David A. Bluemke ◽

Michael J. Potel ◽

Robert Josephs

Keyword(s):

Cross Section ◽

Electron Micrographs ◽

Relative Motion ◽

Finite Thickness ◽

Image Plane ◽

Helical Axis ◽

Thin Sections ◽

Structural Details

We have investigated the feasibility of restoring blurred electron micrographs. Two related problems have been considered; the restoration of images blurred as a result of relative motion between the specimen and the image plane, and the restoration of images which are rotationally blurred about an axis. Micrographs taken while the specimen is drifting result in images which are blurred in the direction of motion. An example of rotational blurring arises in micrographs of thin sections of helical particles viewed in cross section. The twist of the particle within the finite thickness of the section causes the image to appear rotationally blurred about the helical axis. As a result, structural details, particularly at large distances from the helical axis, will be obscured.

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A Simple Real-Space Channelling Theory for Electron Diffraction and HREM

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100179075 ◽

1990 ◽

Vol 48 (1) ◽

pp. 64-65

Author(s):

D. Van Dyck

Keyword(s):

High Resolution ◽

Electron Diffraction ◽

Direct Method ◽

Real Space ◽

Zone Axis ◽

Phase Object ◽

High Resolution Images ◽

The Many ◽

Analytical Expressions ◽

Electron Wavefunction

The computation of the many beam dynamical electron diffraction amplitudes or high resolution images can only be done numerically by using rather sophisticated computer programs so that the physical insight in the diffraction progress is often lost. Furthermore, it is not likely that in this way the inverse problem can be solved exactly, i.e. to reconstruct the structure of the object from the knowledge of the wavefunction at its exit face, as is needed for a direct method [1]. For this purpose, analytical expressions for the electron wavefunction in real or reciprocal space are much more useful. However, the analytical expressions available at present are relatively poor approximations of the dynamical scattering which are only valid either for thin objects ((weak) phase object approximation, thick phase object approximation, kinematical theory) or when the number of beams is very limited (2 or 3). Both requirements are usually invalid for HREM of crystals. There is a need for an analytical expression of the dynamical electron wavefunction which applies for many beam diffraction in thicker crystals. It is well known that, when a crystal is viewed along a zone axis, i.e. parallel to the atom columns, the high resolution images often show a one-to-one correspondence with the configuration of columns provided the distance between the columns is large enough and the resolution of the instrument is sufficient. This is for instance the case in ordered alloys with a column structure [2,3]. From this, it can be suggested that, for a crystal viewed along a zone axis with sufficient separation between the columns, the wave function at the exit face does mainly depend on the projected structure, i.e. on the type of atom columns. Hence, the classical picture of electrons traversing the crystal as plane-like waves in the directions of the Bragg beams which historically stems from the X-ray diffraction picture, is in fact misleading.

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