• Advances in nano research
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• v.8 no.2
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• pp.103-114
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• 2020

In this research, buckling and free vibration of rectangular polymeric laminate reinforced by graphene sheets are investigated. Various patterns are considered for augmentation of each laminate. Critical buckling load is evaluated for different parameters, including boundary conditions, reinforcement pattern, loading regime, and laminate geometric states. Furthermore, vibration analysis is investigated for square laminate. Elastic properties of the composite are calculated using a combination of both molecular dynamics (MD) and the rule of mixture (MR). Kinematics of the plate is approximated based on the first shear deformation theory (FSDT). The current analysis is performed based on the energy method. For the numerical investigation, Ritz method is applied, and for shape functions, Chebyshev polynomials are utilized. It is found that the number of layers is effective on the buckling load and natural frequency of laminates which made from non-uniform layers.

• International Journal of Ocean Engineering and Technology Speciallssue:Selected Papers
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• v.3 no.1
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• pp.14-22
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• 2000

The improved Green integral equation for the calculation of time-harmonic potentials in the radiation diffraction problem about a freely floating body in the presence of moderate or weak current is presented. The forward-speed Green function presented by Brard is used. The correct free surface boundary conditions on the physical free surface are employed as well as an appropriate boundary conditions on the non-physical inner free surface. The default in the existing Green integral equation as well as in the source integral equation is discussed in detail.

• Structural Engineering and Mechanics
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• v.73 no.1
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• pp.37-52
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• 2020

This paper investigates the free and forced longitudinal vibration of a double nanorod system using doublet mechanics theory. The doublet mechanics theory is a multiscale theory spanning between lattice dynamics and continuum mechanics. Equations of motion and boundary conditions for the double nanorod system are obtained using Hamilton's principle. Clamped-clamped and clamped-free boundary conditions are considered. Frequencies and dynamic displacements are determined to demonstrate the effects of length scale parameter of considered material and geometry of the nanorods. It is shown that frequencies obtained by the doublet mechanics theory are bounded from above (van Hove singularity) and unlike classical elasticity theory doublet mechanics theory predicts finite number of modes depending on the length of the nanotube. The present doublet mechanics results have been compared to molecular dynamics, experimental and nonlocal theory results and good agreement is observed between the present and other mentioned results. The difference between wave frequencies of graphite is less than 10% between doublet mechanics and experimental results near to the end of the first Brillouin zone.

• Coupled systems mechanics
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• v.12 no.2
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• pp.127-149
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• 2023

A theoretical method is developed to analyze the free vibration of an elastic annular plate in contact with an ideal liquid. The displacement potential functions of the contained liquid are expressed as a combination of the Bessel functions that satisfy the Laplace equation and the liquid boundary conditions. The compatibility condition along the interface between the annular plate and the contained liquid is taken into account to consider the fluid-structure coupling. The dynamic displacement of the wet annular plate is assumed to be a combination of dry eigenfunctions, allowing for prediction of the natural frequencies using the Rayleigh-Ritz method. The study investigates the effect of radial liquid boundary conditions on the natural frequencies of the wet annular plate, considering four types of liquid bounding: outer container bounded, outer and inner bounded, inner bounded, and radially unbounded. The proposed theoretical method is validated by comparing the predicted wet natural frequencies with those obtained from finite element analysis, showing excellent accuracy. The results indicate that the radial liquid bounding effect on the natural frequencies is negligible for the axisymmetric vibrational mode, but relatively significant for the mode with one nodal diameter (n =1) and no nodal circle (m' = 0). Furthermore, the study reveals that the wet natural frequencies are the largest for the plate with an inner bounded cylinder among the radial liquid boundary cases, regardless of the vibration mode.

• 한국전산유체공학회:학술대회논문집
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• 2004.03a
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• pp.119-125
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• 2004

Unsteady nonlinear wave motions on the free surface over a plane beach of constant slope are numerically simulated using a finite difference method in rectangular grid system. Two-dimensional Navier-Stokes equations and the continuity equation are used for the computations. Irregular leg lengths and stars are employed near the boundaries of body and free surface to satisfy the boundary conditions. Also, the free surface which consists of markers or segments is determined every time step with the satisfaction of kinematic and dynamic free surface conditions. Moreover, marker-density method is also adopted to allow plunging jets impinging on the free surface. The second-order Stokes wave theory and solitary wave theory are employed for the generation of waves on the inflow boundary. For the simulation of wave breaking phenomena, the computations are carried out with the plane beach of constant slope in surf zone. The results are compared with each other. The marker-density method is better then the hybrid method. Also they are compared with other existing experimental results. The Agreement between the experimental data and the computation results is good.

• Journal of Ship and Ocean Technology
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• v.8 no.2
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• pp.61-69
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• 2004

Unsteady nonlinear wave motions on the free surface over a plane beach of constant slope are numerically simulated using a finite difference method in rectangular grid system. Two-dimensional Navier-Stokes equations and the continuity equation are used for the computations. Irregular leg lengths and stars are employed near the boundaries of body and free surface to satisfy the boundary conditions. Also, the free surface which consists of markers or segments is determined every time step with the satisfaction of kinematic and dynamic free surface conditions. Moreover, marker-density method is also adopted to allow plunging jets impinging on the free surface. The second-order Stokes wave theory is employed for the generation of waves on the inflow boundary. For the simulation of wave breaking phenomena, the computations are carried out with the plane beach of constant slope in surf zone. The results are compared with other existing experimental results. Agreement between the experimental data and the computation results is good.

• Journal of the Society of Naval Architects of Korea
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• v.29 no.3
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• pp.80-89
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• 1992

This paper deals with the open boundary problems, and two numerical schemes are used for the implementation of open boundary condition. One is to add the artificial damping term to dynamic free-surface boundary condition. Determination of suitable damping coefficient and the damping cone is the most important in this scheme. The other scheme is a modified Orlanski's method. This will be useful for the problems with unidirectional waves. A few typical free-surface wave problems are modeled for the numerical test. Method of solution is fundamental source-distribution method and the fully nonlinear boundary conditions are applied. The computed results are compared with those of others for the proof of practicality of these schemes.

• Advances in nano research
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• v.13 no.3
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• pp.207-216
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• 2022

In this paper, a novel model is developed for frequency behavior of single walled carbon nanotubes. The governing equation of motion is constructed method based on the Sander theory using Rayleigh-Ritz's method The frequencies enhances on increasing the power law index using simply supported, clamped and clamped free end conditions. The frequency curve for C-F is less than other conditions. It is due to the physical constraints which are applied on the edge of the CNT. It is observed that the C-F boundary condition have less frequencies from the other two conditions. The frequency phenomena for zigzag are insignificant throughout the aspect ratio. Moreover when index of power law is increased then frequencies increases for all boundary conditions. The natural frequency mechanism for the armchair (10, 10) for various values of power law index with different boundary conditions is investigated. Here frequencies decrease on increases the aspect ratio for all boundary conditions. The frequency curves of SS-SS edge condition is composed between the C-C and C-F conditions. The curves of frequency are less significant from small aspect ratio (L/d = 4.86 ~ 8.47) and decreases fast for greater ratios. It is found that the frequencies via aspect ratios, armchair (10, 10) have higher values from zigzag (10, 0). It is due to the material structure which is made by the carbon nanotubes. The power law index have momentous effect on the vibration of single walled carbon nanotubes. The present frequency result is also compared numerically experimentally with Raman Spectroscopy.

• 한국전산유체공학회:학술대회논문집
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• 1998.05a
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• pp.145-155
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• 1998

A computer code has been developed for the computation of the viscous flow around a ship model with the free surface. In this code, the incompressible Reynolds-averaged Navier-Stokes equations are solved numerically by a finite difference method which employes second-order finite differences for the spatial discretization and a four-stage Runge-Kutta scheme for the temporal integration of the governing equations. For the turbulence closure, a modified version of the Baldwin-Lomax model is exploited. The location of the free surface is determined by solving the equation of the kinematic free-surface condition using the Lax-Wendroff scheme and the boundary-fitted grid is generated at each time step so that one of the grid surfaces always coincides with the free surface. An inviscid approximation of the dynamic free-surface boundary condition is applied as the boundary conditions for the velocity and pressure on the free surface. To validate the computational method and the computer code developed in the present study, the numerical computations are carried out for both Wigley parabolic hull and Series 60 $C_B=0.6$ ship model and the computational results are compared with the experimental data.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2007.11a
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• pp.113-114
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• 2007