• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.251-269
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• 1994

In this paper we extend Kim and Pollard's cube root asymptotics to other rates of convergence, to establish an asymptotic theory for a multidimensional mode estimator based on uniform kernel with shrinking bandwidths. We obtain rates of convergence depending on shrinking rates of bandwidth and non-normal limit distributions. Optimal decreasing rates of bandwidth are discussed.

• Korean Journal of Mathematics
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• v.14 no.1
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• pp.113-123
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• 2006

The arches may buckle in a symmetrical snap-through mode or in an asymmetry bifurcation mode if the load reaches a certain value. Each bifurcation curve develops as pressure increases. The governing equation is derived according to the bending theory. The balance of forces provides a nonlinear equilibrium equation. Bifurcation theory near trivial solution of the equation is developed, and the buckling pressures are investigated for various spring constants and opening angles.

• Structural Engineering and Mechanics
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• v.74 no.4
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• pp.471-479
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• 2020

This paper aims to study the effect of the elastic nonlocality on the transient waves in a two-dimensional thermoelastic medium influenced by thermal loading due to the laser pulse. The bounding plane surface is heated by a non-Gaussian laser beam. The problem is discussed under the Eringen's nonlocal elasticity model and the Green-Naghdi (G-N) theory with and without energy dissipation. The normal mode analysis method is used to get the exact expressions for the physical quantities which illustrated graphically by comparison and discussion. The effects of nonlocality and different values of time on the displacement, the stresses, and the temperature were made numerically. All the computed results obtained have been depicted graphically and explained.

• Steel and Composite Structures
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• v.38 no.4
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• pp.355-363
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• 2021

The present paper attempts to investigate the propagation of plane waves in an isotropic elastic medium under the effect of initial stress and temperature-dependent properties. The modulus of elasticity is taken as a linear function of the reference temperature. The formulation is applied under the thermoelasticity theory with dual-phase-lag; the normal mode analysis is used to obtain the expressions for the displacement components, the temperature, the stress, and the strain components. Numerical results for the field quantities are given in the physical domain and illustrated graphically. Comparisons are made with the results predicted by different theories (Lord-Shulman theory, the classical coupled theory of thermoelasticity and the dual-phase-lag model) in the absence and presence of the initial stress as well as the case where the modulus of elasticity is independent of temperature.

• Structural Engineering and Mechanics
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• v.56 no.4
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• pp.649-665
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• 2015

The present paper attempts to investigate the propagation of plane waves in generalized piezo-thermoelastic medium under the effect of rotation. The normal mode analysis is used to obtain the expressions for the displacement components, the temperature, the stress and the strain components. Comparisons are made with the results predicted by different theories (Coupled theory, Lord-Schulman, Green-Lindsay) in the absence and presence of rotation.

• Geomechanics and Engineering
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• v.16 no.2
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• pp.141-150
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• 2018

In this current work a quasi 3D "trigonometric shear deformation theory" is proposed and discussed for the dynamic of thick orthotropic plates. Contrary to the classical "higher order shear deformation theories" (HSDT) and the "first shear deformation theory" (FSDT), the constructed theory utilizes a new displacement field which includes "undetermined integral terms" and presents only three "variables". In this model the axial displacement utilizes sinusoidal mathematical function in terms of z coordinate to introduce the shear strain impact. The cosine mathematical function in terms of z coordinate is employed in vertical displacement to introduce the impact of transverse "normal deformation". The motion equations of the model are found via the concept of virtual work. Numerical results found for frequency of "flexural mode", mode of shear and mode of thickness stretch impact of dynamic of simply supported "orthotropic" structures are compared and verified with those of other HSDTs and method of elasticity wherever considered.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.6
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• pp.993-1000
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• 2002

The objective of this work is to develop the capability to analyze accurately the mixed-mode propagation of a crack in composite structures with elastic orthotropic material stiffness properties and anisotropic material strength characteristics. In order to develop the capability to fully analyze fracture growth and failure in anisotropic structures, we examined the fundamental problem of mixed mode fracture by carrying out the analysis on orthotropic materials with an inclined crack subject to biaxial loading. Our goal here is to include an additional term in the asymptotic expansion of the crack tip stress field and to show that the direction of crack initiation can be significantly affected by that term. We employ the normal stress ratio theory to predict the direction of crack extension. It is shown that the angle of crack extension can be altered by horizontal loads and the use of second order term in the series expansion is important f3r the accurate determination of crack growth direction.

• Smart Structures and Systems
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• v.20 no.5
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• pp.525-537
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• 2017

This paper explores different vibration control strategies for the cancellation of human-induced vibration on a structure with time-varying modal parameters. The main motivation of this study is a lively urban stress-ribbon footbridge (Pedro $G\acute{o}mez$ Bosque, Valladolid, Spain) that, after a whole-year monitoring, several natural frequencies within the band of interest (normal paring frequency range) have been tracked. The most perceptible vibration mode of the structure at approximately 1.8 Hz changes up to 20%. In order to find a solution for this real case, this paper takes the annual modal parameter estimates (approx. 14000 estimations) of this mode and designs three control strategies: a) a tuned mass damper (TMD) tuned to the most-repeated modal properties of the aforementioned mode, b) two semi-active TMD strategies, one with an on-off control law for the TMD damping, and other with frequency and damping tuned by updating the damper force. All strategies have been carefully compared considering two structure models: a) only the aforementioned mode and b) all the other tracked modes. The results have been compared considering human-induced vibrations and have helped the authors on making a decision of the most advisable strategy to be practically implemented.

• Journal of the Korean Chemical Society
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• v.64 no.6
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• pp.350-353
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• 2020

The validity of the calculation method based on the local mode in hydrogen-bonded water molecules was investigated by comparing the frequencies of the local and normal modes of OH stretching vibration in water molecules. By calculating a monomer, dimer, and trimer of water molecules using a quantum chemical ab initio theory, we examined how the frequencies of the local and normal modes and the anharmonicity of local modes vary with molecular cluster size. It was shown that, as the number of molecules increases from monomer to trimer, the anharmonicity of OH bonds increases and the difference between local and normal mode frequencies decreases. This confirms that local-mode-based calculations that can easily handle the anharmonicity can be appropriate for the calculation of the OH stretching frequency of water molecules in the condensed phase.

• Journal of Mechanical Science and Technology
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• v.14 no.8
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• pp.845-850
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• 2000

We consider the problem of determining the singular stresses and electric fields in a piezoelectric ceramic strip containing a Griffith crack under in-plane normal loading within the framework of linear piezoelectricity. The potential theory method and Fourier transforms are used to reduce the problem to the solution of dual integral equations, which are then expressed to a Fredholm integral equation of the second kind. Numerical values on the field intensity factors are obtained, and the influences of the electric fields for PZT-6B piezoelectric ceramic are discussed.