The lateral vibration of non-uniform bars, with application to ships

1928 ◽  
Vol 24 (4) ◽  
pp. 531-556 ◽  
Author(s):  
E. B. Moullin
Keyword(s):  
Large Amplitude ◽  
Elastic Structure ◽  
Lateral Vibration ◽  
Natural Period ◽  
Disturbing Force ◽  
Hull Structure ◽  
Set Up

The heavy elastic structure of a ship possesses many natural periods of lateral vibration, and if any periodic disturbing force within the hull happens to synchronise approximately with any of these natural periods, considerable vibration may result. Experience has shown that the damping of the hull structure is small, and when the rate of revolution of the propeller coincides with a natural period of the ship, a vibration of large amplitude is set up. No doubt reciprocating machinery is competent to produce more violent vibration than turbine machinery, but the inevitable lack of balance of the propeller itself is sufficient to vibrate seriously a turbine-driven ship.

Development and Verification of Modeling Practice for CFD Decay Calculations to Obtain Roll Damping of FPSO

2021 ◽  
Author(s):  
Arjen Koop ◽  
Pierre Crepier ◽  
Sebastien Loubeyre ◽  
Corentin Dobral ◽  
Kai Yu ◽  
...  
Keyword(s):  
Model Test ◽  
Test Results ◽  
Cfd Modelling ◽  
Roll Damping ◽  
Natural Period ◽  
Computational Mesh ◽  
Safety Studies ◽  
Offshore Industry ◽  
Decay Tests ◽  
Set Up

Abstract Estimates for roll damping are important input parameters for simulation studies on vessels operating at sea, e.g. FPSO mooring in waves, wind and current, workability and operability investigations, Dynamic Position studies, ship-to-ship operations and safety studies of vessels. To accurately predict the motions of vessels this quantity should be determined with confidence in the values. Traditionally, model experiments in water basins using so-called decay tests are carried out to determine the roll damping. With recent advancements in CFD modelling, the offshore industry has started using CFD as an alternative tool to compute the roll damping of FPSO’s. In order to help adopt CFD as a widely accepted tool, there is a need to develop confidence in CFD predictions. Therefore, a practical CFD modelling practice is developed within the Reproducible CFD JIP for roll decay CFD simulations. The Modelling Practice describes the geometry modelling, computational mesh, model set-up and post-processing for these type of CFD calculations. This modelling practice is verified and validated by three independent verifiers against available model test data. This paper provides an overview of the developed modelling practice and the calculated CFD results from the verifiers. The CFD modelling practice is benchmarked against available model test results for a tanker-shaped FPSO. By following this modelling practice, the CFD predictions for the equivalent linear damping coefficient and natural period of the roll motions are within 10% for all verifiers and within 10% from the model test results. Therefore, we conclude that when following the developed modelling practice for roll decay simulations, reliable, accurate and reproducible results can be obtained for the roll damping of tanker-shaped FPSOs.

Statistics of TLP Tendon Tension Behaviour During Hurricane Lili

2004 ◽  
Author(s):  
Alberto Morandi ◽  
Diego Martinez ◽  
Charles Smith
Keyword(s):  
Frequency Domain ◽  
Lessons Learned ◽  
Management Service ◽  
Natural Period ◽  
Environmental Event ◽  
Hull Structure ◽  
The Us ◽  
Global Performance ◽  
Design Values ◽  
Tendon Tension

Hurricane Lili permitted an assessment of the global performance of several deepwater structures under a major environmental event. The US Minerals Management Service (MMS) commissioned American Global Maritime Inc. (AGMI) to collect and assess information on the performance of the deepwater production facilities that were impacted by Lili. The Shell Brutus Tension Leg Platform (TLP) provided comprehensive measurements of winds, motions and tendon tensions during Lili. The tendon tension data recorded was analyzed in both the time and frequency domain and tendon tension statistics were comparable to the relevant design values. Other relevant comparisons included natural period and damping estimates. Overall the design ‘recipe’ adopted for Brutus was sufficient to prevent exceedance of design capacities and damage to the hull structure and tendons during Hurricane Lili. The lessons learned from the analyses and recommendations for further work are also summarized in this paper.

The Study on Vibration of Marine Riser under Deep Water

2010 ◽  
Vol 97-101 ◽  
pp. 2816-2819
Author(s):  
Chun Jie Han ◽  
Tie Yan
Keyword(s):  
Water Depth ◽  
Deep Water ◽  
Wave Loads ◽  
Lateral Vibration ◽  
Actual Situation ◽  
Marine Riser ◽  
Drilling Engineering ◽  
Set Up

With the development of deep water drilling engineering, marine riser has become the important equipment. With the increase in water depth, the failure of marine riser is very serious, the vibration is the main reason. According to the actual situation, the model of marine is set up, the rule of lateral vibration is obtained. The result is helpful to avoid the phenomena of resonance of marine riser under wave loads.

Anharmonic potential constants and the large amplitude bending vibration in nitrogen dioxide

1976 ◽  
Vol 54 (1) ◽  
pp. 80-91 ◽  
Author(s):  
J. L. Hardwick ◽  
J. C. D. Brand
Keyword(s):  
Nitrogen Dioxide ◽  
Potential Function ◽  
Large Amplitude ◽  
Perturbation Expansion ◽  
Hamiltonian Operator ◽  
Wave Functions ◽  
Bending Vibration ◽  
Equilibrium Bond Length ◽  
Anharmonic Potential ◽  
Set Up

The anharmonic potential function of the ground electronic state of nitrogen dioxide has been determined within the framework of three different vibrational Hamiltonians. The first of these, which involves a perturbation expansion of the vibrational wave functions in terms of normal coordinate harmonic oscillator wave functions, is the most widely used and generally applicable of the three. It suffers, however, from demonstrably large systematic errors. The other two are vibration–rotation Hamiltonians which allow explicitly for a large amplitude vibration in the bending vibration of a triatomic molecule; they set up the Hamiltonian operator as an explicit function of the bond angle and solve the Schrödinger equation numerically. The more sophisticated of these, the so-called nonrigid bender Hamiltonian, reproduces the spin-free virtual term values to the (0, ν2, 0) manifold of 14NO2 to a standard deviation of 0.026 cm−1 for states with N ≤ 10 and ν2 ≤ 3. It is, moreover, observed to be a more useful tool for extrapolation than is the ordinary parametrized Hamiltonian.The potential function for the bending coordinate is defined by αe = 133.888 ± 0.002°, fαα = 1.61022 ± 0.00005 mdyn Å/rad2, fααα = −2.1172 ± 0.0003 mdyn Å/rad3, and fαααα = 6.0228 ± 0.0020 mdyn Å/rad4. The equilibrium bond length, re, is found to be 1.19464 ± 0.00015 Å.

Experimental Method Using the Inertial Loading Equipment by the Large Scale Shaking Table

2002 ◽  
Author(s):  
Satoshi Yamada ◽  
Yuka Matsumoto ◽  
Michio Yamaguchi ◽  
Nobuyuki Ogawa ◽  
Akira Wada ◽  
...  
Keyword(s):  
Experimental Method ◽  
Real Time ◽  
Large Scale ◽  
Full Scale ◽  
Shaking Table ◽  
Building Structures ◽  
Natural Period ◽  
Test Set ◽  
Inertial Loading ◽  
Set Up

In this paper, a new experimental method of full scale real time shaking table test of structural element is introduced. The main feature of this experimental method is characterized by the use of the inertial loading equipment. The inertial loading equipment consists of a loading frame, a counter weight and isolators. The loading frame supported by the isolators was set on the shaking table. Specimens used in this experimental method were partial frames taken out from full scale building structures. The test set-up was composed of a specimen, the inertial loading equipment and loading beam which transmits the horizontal force to the specimen from the inertial loading equipment. This test set-up, regarded as a single degree of freedom system, makes it easy to understand the dynamic behavior of the test set-up including a specimen. Furthermore, the natural period of the experimental system corresponds to the fundamental natural period of existing building structures. So, full scale and real time dynamic loading test of partial frame can be realized. This method was developed for the existing large scale shaking table and the effectiveness has been already verified through many experiments. Further development of the experimental method adjusted to the 3-D largest shaking table under construction at present is also described.

scholarly journals Application of the Electronic Differential Analyzer to the Oscillation of Beams, Including Shear and Rotary Inertia

1955 ◽  
Vol 22 (1) ◽  
pp. 13-19
Author(s):  
C. E. Howe ◽  
R. M. Howe
Keyword(s):  
Transverse Shear ◽  
Normal Modes ◽  
Bending Moment ◽  
Accurate Method ◽  
Rotary Inertia ◽  
Lateral Vibration ◽  
Wide Range ◽  
Modes Of Vibration ◽  
Set Up ◽  
Differential Analyzer

Abstract The equations for normal modes of lateral vibration of beams are set up on the electronic differential analyzer. Beam deflections due to transverse shear and rotary-inertia forces are included. The differential analyzer is shown to be a fast and accurate method for solving the problem. Analyzer outputs include mode shape, slope, bending moment, and shear force along the beam. Curves showing the normal-mode frequencies for the first three modes of vibration of a uniform free-free beam are presented for a wide range of transverse shear and rotary-inertia parameters. The electronic differential analyzer also is utilized to solve the problem of lateral vibration of nonuniform beams.

East/west directional measurements of the cosmic-ray solar daily variation at an equatorial station

1968 ◽  
Vol 46 (10) ◽  
pp. S801-S804 ◽  
Author(s):  
A. Hashim ◽  
T. Thambyahpillai ◽  
D. M. Thomson ◽  
T. Mathews
Keyword(s):  
Diurnal Variation ◽  
Large Amplitude ◽  
Solar Minimum ◽  
Daily Variation ◽  
Cosmic Ray ◽  
Local Source ◽  
Equatorial Station ◽  
East And West ◽  
Set Up ◽  
East West

Two large scintillator telescopes of cubical geometry, tilted at an angle of 45° to the vertical, were set up pointing in the east and west directions at the equatorial station Makerere. Data from these telescopes are available from July 1964 onwards. During the initial year of observation the solar diurnal variation in both telescopes, after pressure correction, had an amplitude of about 0.2%, but the absence of any appreciable phase difference between the east and west directions suggests that in the intermediate range of rigidities (say 50–150 GV) there was no appreciable primary anisotropy during the last solar minimum. This conclusion is in agreement with that drawn from similar measurements made at Chacaltaya. The large amplitude of the Makerere diurnal variation, however, suggests that there is a substantial "local" source of the diurnal variation which is significantly different from that observed at Chacaltaya. The possible origin of this "local" source is briefly discussed.

scholarly journals A new method for the measurement of the natural periods of buildings

1964 ◽  
Vol 54 (1) ◽  
pp. 233-241
Author(s):  
D. E. Hudson ◽  
W. O. Keightley ◽  
N. N. Nielsen
Keyword(s):  
Fundamental Mode ◽  
New Method ◽  
Inertia Force ◽  
Large Structure ◽  
Structural Vibrations ◽  
Natural Period ◽  
The Past ◽  
Modes Of Vibration ◽  
Set Up

abstract It is shown that the inertia force obtained by a man moving his body back and forth in synchronism with the natural period of vibration of a large structure is sufficient to build up a measurable amplitude of motion. By recording such structural vibrations versus time, the natural period and damping of several of the lower modes of vibration can be determined. The amplitudes of motion set up in this way are for many structures significantly larger than can be obtained from wind excitation, which has been used in the past for the measurement of the period of the fundamental mode.

Research on Nonlinear Dynamic Characteristics of Fluid-Conveying Pipes System

2011 ◽  
Vol 228-229 ◽  
pp. 574-579 ◽  
Author(s):  
Yu Hou ◽  
Guo Hua Zeng
Keyword(s):  
Finite Element ◽  
Flow Rate ◽  
Fluid Pressure ◽  
Lateral Vibration ◽  
Vibration System ◽  
Boundary Constraints ◽  
Mode Decomposition ◽  
Set Up ◽  
The Impact ◽  
Fluid Conveying Pipes

Lateral vibration equations of fluid-conveying pipes system are high order partial differential equations, and the analytic solution is difficult to obtain, so in this paper the numerical solution is obtained by the finite element method. Firstly, the finite element equations of lateral vibration of fluid-conveying pipes were set up, and four kinds of boundary constraints were proposed. The modal analysis of vibration system was carried out by using mode decomposition method, and the system responses were solved by using Newmark method. The impact of pipe span, flow rate, fluid pressure, flow rate disturbance and fluid pressure disturbance on the modes and responses of vibration system were studied. The research results provided theoretical support for the vibration reduction research of fluid-conveying pipes.

scholarly journals Wind structure and evaporation in a turbulent atmosphere

1934 ◽  
Vol 146 (858) ◽  
pp. 701-722 ◽  
Keyword(s):  
Kinetic Theory ◽  
Plane Surface ◽  
Turbulent Medium ◽  
Lower Atmosphere ◽  
Collision Dynamics ◽  
Disturbing Force ◽  
Wind Structure ◽  
Diffusion Phenomena ◽  
Set Up ◽  
Preliminary Consideration

1-It is now generally recognized that in a turbulent medium, such as the lower atmosphere, the processes of the diffusion of mass, heat, and momentum are dominated by the action of eddies in the wind. The exact mechanism by which the typical frictional and diffusion effects are set up by the turbulence is still obscure, and at the present time there appears to ire little hope of the presentation of a comprehensive theory of turbulent motion. The object of the present paper is to set forth a theory which, while admittedly non-exact and based partly upon an empirical assumption, appears to afford a satisfactory basis for the preliminary consideration of the allied problems of wind structure and the natural evaporation from a freely exposed plane surface in the lower atmosphere. 2-It is noticeable that most of the theories of turbulence which have been advanced treat the diffusion phenomena by means of a model which is suggested by the kinetic theory of gases. The eddies are regarded as distinct masses of fluid which behave like the molecules of the kinetic theory in that they are assumed to move along a hind of "free path," and thereby to transfer mass, heat momentum from one layer of the fluid to another by a process which is regarded as being substantially identical with that described by the collision dynamics of the kinetic theory. Briefly, it is assumed that a certain mass of fluid, of dimensions small compared with those of the total volume of fluid under consideration, breaks away from its surroundings under the influence of some mechanical or thermal disturbing force, and moves to another region of the medium, carrying with it a content of mass, heat, and momentum topical of the layer from which it originated. Having moved a certain distance (the Mischungsweg of Prandtl) the eddy is then conceived to mix instantaneously with the surrounding fluid, much in the same manner as a molecule transfers a portion of its energy when it comes into collision with another molecule.

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