• Journal of the Korean Statistical Society
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• 제23권2호
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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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• 제14권1호
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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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• 제74권4호
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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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• 제38권4호
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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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• 제56권4호
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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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• 제16권2호
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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.

• 대한기계학회논문집A
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• 제26권6호
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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.

• Steel and Composite Structures
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• 제50권5호
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• pp.489-497
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• 2024

A temperature-dependent generalized thermoelasticity is constructed in the context of a new consideration of the multi-phase-lags model. The theory is then adopted to study wave propagation in anisotropic homogenous generalized magneto-thermoelastic medium under the influence of gravity whose boundary is subjected to thermal and mechanical loading. The basic equations of the problem are solved by using normal mode analysis. The numerical quantities of physical interest are obtained and depicted graphically. Some comparisons of the results are shown in figures to study the effects of the magnetic field, temperature discrepancy, and the gravity field.

• Smart Structures and Systems
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• 제20권5호
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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.

• 대한화학회지
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• 제64권6호
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• pp.350-353
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• 2020

물 분자내의 OH 신축진동(stretching vibration) 운동을 나타내는 정규모드(normal mode)와 국소모드(local mode) 진동수들을 비교하여 수소결합한 물 분자에 대한 국소모드에 기반한 계산의 타당성을 조사하였다. 물 분자의 단량체, 이합체, 삼량체에 대한 계산을 수행하여 분자 클러스터 크기가 커짐에 따라 국소모드 진동수, 국소모드의 비조화성, 그리고 국소모드와 정규모드 진동수들의 유사성이 어떤 경향성을 보이는지 순이론적 양자화학 계산 방법으로 연구하였다. 단량체에서 삼량체로 분자의 갯수가 증가할수록 OH 결합의 비조화성은 증가하며 국소모드와 정규모드 진동수 간의 차이는 줄어드는 것으로 나타났다. 따라서, 응축상에 존재하는 물 분자들의 OH 신축 진동수의 이론적 계산은 비조화성을 쉽게 다룰 수 있는 국소모드에 기반한 방식이 적절할 수 있음을 확인하였다.