• Journal of the Korean Mathematical Society
• /
• v.57 no.3
• /
• pp.721-745
• /
• 2020

In this paper we study fractional Sobolev spaces characterized by a norm based on eigenfunction expansions. The goal of this paper is twofold. The first one is to define fractional Sobolev spaces of order -1 ≤ s ≤ 2 equipped with a norm defined in terms of Neumann eigenfunction expansions. Due to the zero Neumann trace of Neumann eigenfunctions on a boundary, fractional Sobolev spaces of order 3/2 ≤ s ≤ 2 characterized by the norm are the spaces of functions with zero Neumann trace on a boundary. The spaces equipped with the norm are useful for studying cross-sectional traces of solutions to the Helmholtz equation in waveguides with a homogeneous Neumann boundary condition. The second one is to define fractional Sobolev spaces of order -1 ≤ s ≤ 1 for vector-valued functions in a simply-connected, bounded and smooth domain in ℝ². These spaces are defined by a norm based on series expansions in terms of eigenfunctions of the vector Laplacian with boundary conditions of zero tangential component or zero normal component. The spaces defined by the norm are important for analyzing cross-sectional traces of time-harmonic electromagnetic fields in perfectly conducting waveguides.

• Structural Engineering and Mechanics
• /
• v.54 no.5
• /
• pp.955-971
• /
• 2015

In this paper, the influence of the polled direction of piezoelectric materials on the stress distribution is studied under time-harmonic dynamical load (time-harmonic Lamb's problem). The system considered in this study consists of piezoelectric covering layer and piezoelectric half-plane, and the harmonic dynamical load acts on the free face of the covering layer. The investigations are carried out by utilizing the exact equations of motion and relations of the linear theory of electro-elasticity. The plane-strain state is considered. It is assumed that the perfect contact conditions between the covering layer and half-plane are satisfied. The boundary value problems under consideration are solved by employing Fourier exponential transformation techniques with respect to coordinates directed along the interface line. Numerical results on the influence of the polled direction of the piezoelectric materials such as PZT-5A, PZT-5H, PZT-4 and PZT-7A on the normal stresses, shear stresses and electric potential acting on the interface plane are presented and discussed. As a result of the analyses, it is established that the polled directions of the piezoelectric materials play an important role on the values of the studied stresses and electric potential.

• Proceedings of the KIEE Conference
• /
• 2001.07b
• /
• pp.1052-1054
• /
• 2001

This paper describes a boost converter to be operated at the boundary of continuous current mode(CCM) and discontinuous current mode(DCM) for power factor correction and low cost. A control method to be utilized in simulation is a average-current mode method in case of operating in CCM. The simulation results show that Better is the CCM converter then the DCM converter in harmonic content and input current waveform. And A Double-boost converter is superior to single-boost converter for input-current harmonic.

• Structural Engineering and Mechanics
• /
• v.22 no.4
• /
• pp.483-510
• /
• 2006

The dynamic instability characteristics of laminated composite stiffened shell panels subjected to in-plane harmonic edge loading are investigated in this paper. The eight-noded isoparametric degenerated shell element and a compatible three-noded curved beam element are used to model the shell panels and the stiffeners respectively. As the usual formulation of degenerated beam element is found to overestimate the torsional rigidity, an attempt has been made to reformulate it in an efficient manner. Moreover the new formulation for the beam element requires five degrees of freedom per node as that of shell element. The method of Hill's infinite determinant is applied to analyze the dynamic instability regions. Numerical results are presented to demonstrate the effects of various parameters like shell geometry, lamination scheme, stiffening scheme, static and dynamic load factors and boundary conditions, on the dynamic instability behaviour of laminated composite stiffened panels subjected to in-plane harmonic loads along the boundaries. The results of free vibration and buckling of the laminated composite stiffened curved panels are also presented.

• Steel and Composite Structures
• /
• v.35 no.3
• /
• pp.449-462
• /
• 2020

This work aims to study effects of the crack and the surface energy on the free longitudinal vibration of axially functionally graded nanorods. The surface energy parameters considered are the surface stress, the surface density, and the surface Lamé constants. The cracked nanorod is modelled by dividing it into two parts connected by a linear spring in which its stiffness is related to the crack severity. The surface and bulk material properties are considered to vary in the length direction according to the power law distribution. Hamilton's principle is implemented to derive the governing equation of motion and boundary conditions. Considering the surface stress causes that the derived governing equation of motion becomes non-homogeneous while this was not the case in works that only the surface density and the surface Lamé constants were considered. To extract the frequencies of nanorod, firstly the non-homogeneous governing equation is converted to a homogeneous one using an appropriate change of variable, and then for clamped-clamped and clamped-free boundary conditions the governing equation is solved using the harmonic differential quadrature method. Since the present work considers effects of all the surface energy parameters, it can be claimed that this is a comprehensive work in this regard.

• Advances in aircraft and spacecraft science
• /
• v.3 no.4
• /
• pp.379-397
• /
• 2016

In this manuscript, free vibrations of a unidirectional composite orthotropic Timoshenko beam based on finite strain have been studied. Using Green-Lagrange strain tensor and comprising all of the nonlinear terms of the tensor and also applying Hamilton's principle, equations of motion and boundary conditions of the beam are obtained. Using separation method in single-harmonic state, time and locative variables are separated from each other and finally, the equations of motion and boundary conditions are gained according to locative variable. To solve the equations, generalized differential quadrature method (GDQM) is applied and then, deflection and cross-section rotation of the beam in linear and nonlinear states are drawn and compared with each other. Also, frequencies of carbon/epoxy and glass/epoxy composite beams for different boundary conditions on the basis of the finite strain are calculated. The calculated frequencies of the nonlinear free vibration of the beam utilizing finite strain assumption for various geometries have been compared to von Karman one.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.20 no.5
• /
• pp.629-640
• /
• 2007

In this paper an analytical study is carried out to improve the capacity of absorbing boundary using dashpot, one of the most widely used absorbing boundaries in FEM. Using 2-D harmonic plane wave equation, absorbing boundary condition is modified to maximize its capacity according to the incident angle. Validity of the absorbing boundary conditions which is modified is investigated by adopting the solution of Miller and Pursey. The Miller and Pursey's problem is then numerically simulated using the finite element method. The absorption ratios are calculated by comparing the displacements at the absorbing boundary to those at the free field without the absorbing boundary. The numerical study is carried out through comparison of displacement at the interior region and the boundary of the numerical model.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.20 no.9
• /
• pp.2953-2964
• /
• 1996

Heat Transfer with periodic fluctuation of fluid temperature caused by oscillatory flow or compression expansion can be out of phase with balk fluid-wall temperature difference. Newton's law of convection is inadequate to describe this phenomenon. In order to solve this problem the concept of the complex Nusselt number has been introduced by severla researchers. The complex Nusselt number expresses out of phase excellently while the first harmonic is dominant in the variations of both fluid-wall temperature difference and heat flux. However, in the case of oscillatory flow with non-linear wall temperature distribution, the complex Nusselt number is not appropriate to predict the heat transfer phenomena since the higher order harmonic components appear in periodic temperature variation. Analytic solutions to the heat transfer with an sinusoidal well temperature distribution were obtained to investagate the effect of non-linear wall temperature distribution. A new formula considering the thermal boundary layer was suggested based on the solutions. A comparison was also made with the complex Nusselt number. It was verified that the new formula describes well the heat transfer of oscillating flow even if the first harmonic component is not dominant in the fluid-wall temperature difference.

• Journal of the Korean Geotechnical Society
• /
• v.24 no.8
• /
• pp.13-23
• /
• 2008

The evaluation of soundness of pile is very important for the safety of super structure. In this paper, the HWAW(Harmonic Wavelet Analysis of Wave) method which is developed to determine phase and group velocities of waves is applied to evaluate integrity of pile non-destructivly. The proposed method can evaluate a soundness of pile and pile end condition which is very important factor for pile behaviour. To verity the applicability of HWAW method in non-destructive test for pile, the numerical simulation test using ABAQUS was performed. And the model pile was made and the proposed non-destructive pile tests were applied to evaluate soundness and end boundary condition of model pile in the air and soil box. Through a numerical simulation and model tests, it is shown that the HWAW method has good potential of applying to the evaluation of pile integrity.

• Proceedings of the KIEE Conference
• /
• 2004.07e
• /
• pp.14-16
• /
• 2004

This paper describes a boost converter to be operated at the boundary of continuous current mode(CCM) and discontinuous current mode(DCM) for power factor correction and low cost. A control method to be utilized in simulation is a average Current mode method in case of operating in CCM. The simulation results show that Better is the CCM converter then the DCM converter in harmonic content and input current waveform. And A Double-boost converter is superior to single-boost converter for input-current harmonic.