• Smart Structures and Systems
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• v.29 no.2
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• pp.279-286
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• 2022

In this article, a novel propagation formulation of Rayleigh waves in a compressible isotropic half-space with impedance boundary condition is proposed by embedding the normal stress. In a two-dimensional case, it is assumed that a design boundary is free of normal traction and a shear traction depends on linearly a normal component of displacements multiplied by frequencies. Therefore, impedance boundary conditions affect the normal stress, where the impedance parameters correspond to dimensions of stresses over velocity. On the other hand, vanished impedance values are traction-free boundary conditions. The main purpose of this article is to present theoretically the existence and uniqueness of a Rayleigh wave formulation relying on secular equation's mathematical analyses. Its velocity varies along with the impedance parameters. Moreover, numerical experiments with different values for the velocity of Rayleigh waves are carried out. The present Rayleigh waves study is a fundamental step in analyzing the cause and effect of physical states such as building or structure damages resulting from natural dynamics. The results of the study generate a basic design formulation theory to test the effects of Rayleigh waves affecting structures when an earthquake occurs. The presence and uniqueness of the proposed formulation is verified by mutual comparisons of several numerical examples.

• Structural Engineering and Mechanics
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• v.25 no.5
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• pp.597-611
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• 2007

Many works have been done in classical theory of thermoelasticity in materials with memory by researchers like Nunziato, Chen and Gurtine and many others. No work is located in generalized thermoelasticity regarding materials with memory till date. The present paper deals with the wave propagation in materials with memory in generalized thermoelasticity. Plane progressive waves and Rayleigh waves have been discussed in details. In the classical theory of heat conduction it was observed that heat propagates with infinite speed. This paradox has been removed in the present discussion. The set of governing equations has been developed in the present analysis. The results of wave velocity and attenuation coefficient corresponding to low and high frequency have been obtained. For thermal wave the results show appreciable differences with those in the usual thermoelasticity theory.

• Proceedings of the KSME Conference
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• 2000.04a
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• pp.242-247
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• 2000

In this study, the Rayleigh's energy method and the Rayleigh-Ritz method on the basis of Flugge's shell theory was used to analyze the dynamic characteristics of the scroll compressor housing with clamped boundary condition. The frequencies and mode shapes from theoretical calculation were compared with those of commercial finite element code, ANSYS. In order to validate the theory, modal test was also performed by impact test and FFT analysis.

• Structural Engineering and Mechanics
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• v.32 no.6
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• pp.811-833
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• 2009

In the present article bending, buckling and vibration analyses of tapered beams using Eringen non-local elasticity theory are being carried out. The associated governing differential equations are solved employing Rayleigh-Ritz method. Both Euler-Bernoulli and Timoshenko beam theories are considered in the analyses. Present results are in good agreement with those reported in literature. Beam material is considered to be made up of functionally graded materials (fgms). Non-local analyses for tapered beam with simply supported - simply supported, clamped - simply supported and clamped - free boundary conditions are carried out and discussed. Further, effect of length to height ratio on maximum deflections, vibration frequencies and critical buckling loads are studied.

• Communications of Mathematical Education
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• v.22 no.4
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• pp.445-457
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• 2008

Although both theory and experiment are very important parts in sciences, especially in mathematics, theory only seems to be very important. But the subject of numerical analysis needs both theory and practice in computer. In this paper, I provide some Matlab program codes and matrices which are used in good understanding OR methods in class.

• Earthquakes and Structures
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• v.9 no.1
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• pp.111-126
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• 2015

In this study, the coupled effects of magnetic field, stress and thermal field on gravity waves propagating in a liquid layer over a solid surface are discussed. Due to change in temperature, initial hydrostatic stress and magnetic field, the gravity-sound Rayleigh waves can propagate in the liquid-solid interface. Dispersion properties of waves are derived by using classical dynamical theory of thermoelasticity. The phase velocity of gravity waves influenced quite remarkably in the presence of initial stress parameter, magneto-thermoelastic coupling parameter in the half space. Numerical solutions are also discussed for gravity-Rayleigh waves. In the absence of temperature, stress and magnetic field, the obtained results are in agreement with classical results.

• 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.

• Steel and Composite Structures
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• v.42 no.6
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• pp.723-732
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• 2022

The present research is concerned to study the effect of fractional parameter and rotation on the propagation of Rayleigh waves in an orthotropic magneto-thermoelastic media with three-phase-lags in the context of fractional order theory of generalized thermoelasticity with combined effect of rotation and hall current. The secular equations of Rayleigh waves are derived by using the appropriate boundary conditions. The wave properties such as phase velocity, attenuation coefficient are computed numerically and the numerical simulated results are presented through graphs to show the effect on all the components. Some special cases are also discussed in the present investigation.

• Structural Engineering and Mechanics
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• v.81 no.5
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• pp.607-616
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• 2022

In this work, the free vibration problem of a rotating Rayleigh beam is solved using the meshless Petrov-Galerkin method which is a truly meshless method. The Rayleigh beam includes rotatory inertia in addition to Euler-Bernoulli beam theory. The radial basis functions, which satisfy the Kronecker delta property, are used for the interpolation. The essential boundary conditions can be easily applied with radial basis functions. The results are obtained using six nodes within a subdomain. The results accurately match with the published literature. Also, the results with Euler-Bernoulli are obtained to compare the change in higher natural frequencies with change in the slenderness ratio (${\sqrt{A_0R^2/I_0}}$). The mass and stiffness matrices are derived where we get two stiffness matrices for the node and boundary respectively. The non-dimensional form is discussed as well.

• Advances in nano research
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• v.9 no.3
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• pp.157-172
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• 2020

The aim of this present research is the effect of the higher-order terms of the governing equation on the forced longitudinal vibration of a nanorod model and making comparisons of the results with classical nonlocal elasticity theory. For this purpose, the free axial vibration along with forced one under the two various linear and harmonic axial concentrated forces in zigzag Single-Walled Carbon Nanotube (SWCNT) are analyzed dynamically. Three various theories containing the classical theory, which is called Eringen's nonlocal elasticity, along with Rayleigh and Bishop theories (higher-order theories) are established to justify the nonlocal behavior of constitutive relations. The governing equation and the related boundary conditions are derived from Hamilton's principle. The assumed modes method is adopted to solve the equation of motion. For the free axial vibration, the natural frequencies are calculated for the various values of the nonlocal parameter only based on Eringen's theory. The effects of the nonlocal parameter, thickness, length, and ratio of the excitation frequency to the natural frequency over time in dimensional and non-dimensional axial displacements are investigated for the first time.