• Steel and Composite Structures
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• v.50 no.2
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• pp.123-133
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• 2024

The paper deals with the propagation of Rayleigh waves in a nonlocal thermoelastic isotropic layer which is lying over a nonlocal thermoelastic isotropic half-space under the purview of Green-Lindsay model and Eringen's nonlocal elasticity in the presence of voids. The normal mode analysis is employed to the considered equations to obtain vector matrix differential equation which is then solved by eigenvalue approach. The frequency equation of Rayleigh waves is derived and different particular cases are also deduced. The effects of voids and nonlocality on different characteristics of Rayleigh waves are presented graphically.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.723-738
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• 2015

In this paper, the prescribed mean curvature Rayleigh p-Laplacian equation with a deviating argument

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.3
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• pp.502-509
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• 2001

In this paper, when stress waves are propagated along the reinforced direction of the composite, the characteristic equation of Rayleigh wave is derived. The relationships between velocities of stress waves and Rayleigh wave are studied for anisotropic ratios(E(sub)11/E(sub)12 or E(sub)22/E(sub)11). The increments of anisotropic ratios is made by using known material properties and being constant of basic properties. When the anisotropic ratios are increased, Rayleigh wave velocities to the shear wave velocities are almost equal to 1 with any anisotropic ratios. Rayleigh wave velocities to the longitudinal wave velocities and Shear wave velocities ratio to the longitudinal wave velocities are almost identical each other, they are between 0.12 and 0.21. When the anisotropic ration is very high, that is, E(sub)11/E(sub)22=46.88, Rayleigh wave velocities and the shear wave velocities are almost constant with Poissons ratio, longitudinal wave velocities are very slowly increased with the increments of Poissons ratios. When E(sub)11(elastic modulus of the reinforced direction)and ν(sub)12 are constant, Rayleigh wave velocities and the shear wave velocities are steeply decreased with the increments of anisotropic ratios and the velocities of longitudinal wave are almost constant with them. When E(sub)22(elastic modulus of the normal direction to the fiber) and ν(sub)12 are constant, Rayeigh wave velocities is slowly increased with the increments of anisotropic ratios, the shear wave velocities are almost constant with them, the longitudinal wave velocities are steeply increased with them.

• Journal of the Korean Society for Nondestructive Testing
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• v.27 no.6
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• pp.582-590
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• 2007

Imperfectly jointed interface serves as mechanical waveguide for elastic waves and gives rise to two distinct kinds of guided wave propagating along the interface. Contact acoustic nonlinearity (CAN) is known to plays major role in the generation of these interface waves called generalized Rayleigh waves in non-welded interface. Closed crack is modeled as non-welded interface that has nonlinear discontinuity condition in displacement across its boundary. Mathematical analysis of boundary conditions and wave equation is conducted to investigate the dispersive characteristics of the interface waves. Existence of the generalized Rayleigh wave(interface wave) in nonlinear contact interface is verified in theory where the dispersion equation for the interface wave is formulated and analyzed. It reveals that the interface waves have two distinct modes and that the phase velocity of anti-symmetric wave mode is highly dependent on contact conditions represented by linear and nonlinear dimensionless specific stiffness.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.29 no.6
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• pp.583-590
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• 2016

This paper presents a dynamic crack propagation algorithm with Rayleigh damping effect based on the MLS(Moving Least Squares) Difference Method. Dynamic equilibrium equation and constitutive equation are derived by considering Rayliegh damping and governing equations are discretized by the MLS derivative approximation; the proportional damping, which has not been properly treated in the conventional strong formulations, was implemented in both the equilibrium equation and constitutive equation. Dynamic equilibrium equation including time relevant terms is integrated by the Central Difference Method and the discrete equations are simplified by lagging the velocity one step behind. A geometrical feature of crack is modeled by imposing the traction-free condition onto the nodes placed at crack surfaces and the effect of movement and addition of the nodes at every time step due to crack growth is appropriately reflected on the construction of total system. The robustness of the proposed numerical algorithm was proved by simulating single and multiple crack growth problems and the effect of proportional damping on the dynamic crack propagation analysis was effectively demonstrated.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.10
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• pp.751-759
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• 2003

The theoretical method is developed to investigate the vibration characteristics of the sloshing and bulging mode for the circular cylindrical storage tank with an annular plate on free surface. The cylindrical tank is filled with an inviscid and incompressible liquid. The liquid domain is limited by a rigid cylindrical surface and a rigid flat bottom. As the effect of free surface waves Is taken into account in the analysis, the bulging and sloshing modes are studied. The solution for the velocity potential of liquid movement is assumed as a suitable harmonic function that satisfies Laplace equation and the relevant boundary conditions. The Rayleigh-Ritz method is used to derive the frequency equation of the cylindrical tank. The effect of Inner-to-outer radius ratio and thickness of annular plate and liquid volume on vibration characteristics of storage tank is studied. The finite element analysis is performed to demonstrate the validity of present theoretical method.

• Coupled systems mechanics
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• v.12 no.4
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• pp.337-364
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• 2023

The Rayleigh wave propagation is considered in the structure of the functionally graded piezoelectric material (FGPM) layer over the elastic substrate. The elastic substrate loosely bonds the layer through a corrugated interface, whereas its upper boundary is also corrugated but stress-free. Additionally, the solutions for the FGPM layer and substrate are derived using the fundamental variable separable approach to convert the partial differential equation to an ordinary differential equation. The results with boundary conditions lead to dispersion relations for the electrically open and electrically short cases in the determinant form. The outcomes have been numerically analyzed using a specific model. The findings were presented in the form of graphs, which were created using Mathematica 7. Graphs are plotted for variations in wavenumber and phase velocity. The outcomes may help measure interface defects and design Surface Acoustic Wave (SAW) devices.

• Structural Engineering and Mechanics
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• v.56 no.3
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• pp.491-506
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• 2015

Propagation of the generalized Rayleigh waves in an initially stressed elastic half-space covered by an elastic layer is investigated. It is assumed that the initial stresses are caused by the uniformly distributed normal compressional forces acting on the face surface of the covering layer. Two different cases where the compressional forces are "dead" and "follower" forces are considered. Three-dimensional linearized theory of elastic waves in initially stressed bodies in plane-strain state is employed and the elasticity relations of the materials of the constituents are described through the Murnaghan potential where the influence of the third order elastic constants is taken into consideration. The dispersion equation is derived and an algorithm is developed for numerical solution to this equation. Numerical results for the dispersion of the generalized Rayleigh waves on the influence of the initial stresses and on the influence of the character of the external compressional forces are presented and discussed. These investigations provide some theoretical foundations for study of the near-surface waves propagating in layered mechanical systems with a liquid upper layer, study of the structure of the soil of the bottom of the oceans or of the seas and study of the behavior of seismic surface waves propagating under the bottom of the oceans.

• Journal of the Korean Society of Visualization
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• v.12 no.1
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• pp.13-17
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• 2014

The growth of micro bubble has been simulated under the variation of ambient pressure. The Rayleigh-Plesset equation governs the dynamic growth and collapse of a bubble according to pressure and temperature conditions. The Rayleigh-Plesset equation was solved by 4th-order Runge-Kutta method for wide range of pressure variations. As numerical parameters, the pressure difference between initial and final pressures, and the temporal pressure gradient are changed. The results show that the pressure difference has little effect on the growth rate of the micro bubble in the inertia controlled growth region. On the other hand, the growth rate increases linearly with the increase of the pressure gradient.

• Structural Engineering and Mechanics
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• v.60 no.3
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• pp.455-470
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• 2016

In this paper, we investigate the free vibration of axially loaded non-uniform Rayleigh cantilever beams. The Rayleigh beams account for the rotary inertia effect which is ignored in Euler-Bernoulli beam theory. Using an inverse problem approach we show, that for certain polynomial variations of the mass per unit length and the flexural stiffness, there exists a fundamental closed form solution to the fourth order governing differential equation for Rayleigh beams. The derived property variation can serve as test functions for numerical methods. For the rotating beam case, the results have been compared with those derived using the Euler-Bernoulli beam theory.