scholarly journals Discussion: “The Usefulness of Elementary Theory for the Linear Vibrations of Layered, Orthotropic Elastic Beams and Corrections to Two-Dimensional End Effects” (Duva, J. M., and Simmonds, J. G., 1991, ASME J. Appl Mech., 58, pp. 175–180)

1992 ◽  
Vol 59 (1) ◽  
pp. 240-241 ◽  
Author(s):  
Yi-Yuan Yu
Keyword(s):  
Elementary Theory ◽  
Two Dimensional ◽  
End Effects ◽  
Elastic Beams ◽  
Linear Vibrations

The Usefulness of Elementary Theory for the Linear Vibrations of Layered, Orthotropic Elastic Beams and Corrections Due to Two-Dimensional End Effects

1991 ◽  
Vol 58 (1) ◽  
pp. 175-180 ◽  
Author(s):  
J. M. Duva ◽  
J. G. Simmonds
Keyword(s):  
Natural Frequencies ◽  
Elementary Theory ◽  
Beam Theory ◽  
Relative Order ◽  
Bernoulli Beam ◽  
End Effects ◽  
Cantilevered Beam ◽  
Linear Vibrations ◽  
Order Of Magnitude ◽  
Euler Bernoulli Beam

With the aid of formal asymptotic expansions, we conclude not only that elementary (Euler-Bernoulli) beam theory can be applied successfully to layered, orthotropic beams, possibly weak in shear, but also that, in computing the lower natural frequencies of a cantilevered beam, the most important correction to the elementary theory—of the relative order of magnitude of the ratio of depth to length—comes from effects in a neighborhood of the built-in end. We compute this correction using the fundamental work on semi-infinite elastic strips of Gregory and Gladwell (1982) and Gregory and Wan (1984). We also show that, except in unusual cases (e.g., a zero Poisson’s ratio in a homogeneous, elastically isotropic beam), Timoshenko beam theory produces an erroneous correction to the frequencies of elementary theory of the relative order of magnitude of the square of the ratio of depth to length.

Bending of an Infinite Beam on an Elastic Foundation

1937 ◽  
Vol 4 (1) ◽  
pp. A1-A7 ◽  
Author(s):  
M. A. Biot
Keyword(s):  
Elastic Foundation ◽  
Poisson Ratio ◽  
Elementary Theory ◽  
Three Dimensional ◽  
Bending Moment ◽  
Two Dimensional ◽  
Concentrated Load ◽  
Elastic Continuum ◽  
Infinite Beam ◽  
A Value

Abstract The elementary theory of the bending of a beam on an elastic foundation is based on the assumption that the beam is resting on a continuously distributed set of springs the stiffness of which is defined by a “modulus of the foundation” k. Very seldom, however, does it happen that the foundation is actually constituted this way. Generally, the foundation is an elastic continuum characterized by two elastic constants, a modulus of elasticity E, and a Poisson ratio ν. The problem of the bending of a beam resting on such a foundation has been approached already by various authors. The author attempts to give in this paper a more exact solution of one aspect of this problem, i.e., the case of an infinite beam under a concentrated load. A notable difference exists between the results obtained from the assumptions of a two-dimensional foundation and of a three-dimensional foundation. Bending-moment and deflection curves for the two-dimensional case are shown in Figs. 4 and 5. A value of the modulus k is given for both cases by which the elementary theory can be used and leads to results which are fairly acceptable. These values depend on the stiffness of the beam and on the elasticity of the foundation.

Application of Contourlet in Research of Rough Surface Topography

2012 ◽  
Vol 542-543 ◽  
pp. 115-118
Author(s):  
Chao Zhou ◽  
Cheng Hui Gao
Keyword(s):  
Surface Topography ◽  
Rough Surface ◽  
Surface Analysis ◽  
Signal Analysis ◽  
Elementary Theory ◽  
Rough Surfaces ◽  
Good Method ◽  
Two Dimensional ◽  
Multi Scale

Since the tribology properties of rough surfaces are closely related to its topography, one of the most important ingredients in tribology research is to find an appropriate tool to analyze and characterize rough surfaces. The elementary theory of contourlet which is a good method for multi-scale and multi-direction signal analysis was introduced and an application of contourlet in rough surface analysis was demonstrated. It was found that contourlet is more sensitive to curved features than general two dimensional wavelets; it is possible to become a new powerful tool for rough surface analysis and characterization.

A Comparative Study Between Two-Dimensional and Three-Dimensional Simulation Results of Melting Inside a Container

2020 ◽  
Author(s):  
Nan Hu ◽  
Li-Wu Fan
Keyword(s):  
Velocity Profile ◽  
Heating Temperature ◽  
Three Dimensional ◽  
Detailed Comparison ◽  
Melting Rate ◽  
Two Dimensional ◽  
End Effects ◽  
Wall Superheat ◽  
Simulation Results ◽  
Dimensional Simulation

Abstract Bother two-dimensional (2D) and three-dimensional (3D) simulations on two example melting problems, i.e., melting in a differentially-heated rectangular cavity and constrained melting in a horizontal cylindrical capsule, were carried out to investigate the rationality of 2D simplification. The effects of thermophysical properties of the phase change material, size of the container along the direction perpendicular to the 2D cross-section, as well as wall superheat were taken into consideration for a systematic and detailed comparison. It was shown that a small length of the container perpendicular to 2D plane will result in a confine space to limit the development of velocity distribution (i.e., parabolic velocity profile) due to the end effects, leading to to an almost identical melting rate to that obtained by the 2D simplified case. A larger size indicates stronger thermal convection (bulk uniform velocity profile) and faster melting rate. When fixing a large size of the container perpendicular to the 2D plane, decreasing the heating temperature and increasing the viscosity of liquid PCM (e.g., by adding nanoparticles) reduce the discrepancy between 2D and 3D simulation results.

Predicting Roll Damping for Barge-Type FPSO Using CFD

2019 ◽  
Author(s):  
Arjen Koop ◽  
Frédérick Jaouën ◽  
Xavier Wadbled ◽  
Erwan Corbineau
Keyword(s):  
Turbulence Model ◽  
Three Dimensional ◽  
Model Tests ◽  
Vortical Flow ◽  
Damping Coefficient ◽  
Physical Parameters ◽  
Two Dimensional ◽  
Roll Damping ◽  
End Effects ◽  
Hydrodynamic Damping

Abstract An accurate prediction of the non-linear roll damping is required in order to calculate the resonant roll motion of moored FPSO’s. Traditionally, the roll damping is obtained with model tests using decays or forced roll oscillation tests. Calculation methods based on potential flow are not capable of predicting this hydrodynamic damping accurately as it originates from the viscous nature of the fluid and the complex vortical flow structures around a rolling vessel. In recent years Computational Fluid Dynamics (CFD) has advanced such that accurate predictions for the roll damping can be obtained. In this paper CFD is employed to predict the roll damping for a barge-type FPSO. The objectives of the paper are to investigate the capability and accuracy of CFD to determine roll damping of an FPSO and to investigate whether two-dimensional calculations can be used to estimate the roll damping of a three-dimensional FPSO geometry. To meet these objectives, extensive numerical sensitivity studies are carried out for a 2D hull section mimicking the midsection of the FPSO. The numerical uncertainty for the added mass and damping coefficients were found to be 0.5% and 2%, respectively. The influence of the turbulence model was found to be significant for the damping coefficient with differences up to 14%. The 2D CFD results are compared to results from two-dimensional model tests. The calculated roll damping using the k-ω SST 2003 turbulence model matches the value from the experiments within 2%. The influence of various physical parameters on the damping was investigated through additional 2D calculations by changing the scale ratio, the roll amplitude, the roll period, the water depth, the origin of rotation and the bilge keel height. Lastly, three-dimensional calculations are carried out with the complete FPSO geometry. The 3D results agree with the 2D results except for the largest roll amplitude calculated, i.e. for 15 degrees, where the damping coefficient was found to be 7% smaller. For this amplitude end-effects from the ends of the bilge keels seem to have a small influence on the flow field around the bilge keels. This indicates that the 2D approach is a cost-effective method to determine the roll damping of a barge-type FPSO, but for large roll amplitudes or for different vessel geometries the 2D approach may not be valid due to 3D effects.

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