• 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.26 no.4
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• pp.453-461
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• 2018

In this paper, nonlinear vibrations of the unsymmetrical laminated composite beam (LCB) on a nonlinear elastic foundation are studied. The governing equation of the problem is derived by using Galerkin method. Two different end conditions are considered: the simple-simple and the clamped-clamped one. The Hamiltonian Approach (HA) method is adopted and applied for solving of the equation of motion. The advantage of the suggested method is that it does not need any linearization of the problem and the obtained approximate solution has a high accuracy. The method is used for frequency calculation. The frequency of the nonlinear system is compared with the frequency of the linear system. The influence of the parameters of the foundation nonlinearity on the frequency of vibration is considered. The differential equation of vibration is solved also numerically. The analytical and numerical results are compared and is concluded that the difference is negligible. In the paper the new method for error estimation of the analytical solution in comparison to the exact one is developed. The method is based on comparison of the calculation energy and the exact energy of the system. For certain numerical data the accuracy of the approximate frequency of vibration is determined by applying of the suggested method of error estimation. Finally, it has been indicated that the proposed Hamiltonian Approach gives enough accurate result.

• Structural Engineering and Mechanics
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• v.42 no.6
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• pp.761-781
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• 2012

The collapse of structures due to snow loads on roofs occurs frequently for steel structures and rarely for reinforced concrete structures. Since the most significant difference between these structures is related to their ability to handle dead loads, dead loads are believed to play an important part in the collapse of structures by snow loads. As such, the effect of dead loads on displacements and stress couples produced by live loads is presented for plates with different edge conditions. The governing equation of plates that takes into account the effect of dead loads is formulated by means of Hamilton's principle. The existence and effect of dead loads are proven by numerical calculations based on the Galerkin method. In addition, a closed-form solution for simply supported plates is proposed by solving, in approximate terms, the governing equation that includes the effect of dead loads, and this solution is then examined. The effect of dead loads on static live loads can be explained explicitly by means of this closed-form solution. A method that reflects the effects of dead loads on live loads is presented as an example. The present study investigates an additional factor in lightweight roof structural elements, which should be considered due to their recent development.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.1 s.173
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• pp.103-109
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• 2000

A method to measure the crack length in rubbery materials is described. Through dimensional analysis and experiments, an equation is derived to give the crack length as a function of the change of strain energy density in a region remote from the crack. The function is provided in a form of separated terms of loading and material, the validity of which is experimentally proved using separation parameters.

• Management Science and Financial Engineering
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• v.10 no.2
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• pp.53-71
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• 2004

In this study, a mathematical model that shows the optimal payout policy is developed. The model is new and unique in the sense that not only continuous-time framework is used, but also both partial differential equation (PDE) and real-option approach are utilized in the derivation of optimal payouts for the first time. In the model building, non-linear demand curve for dividend payouts in the competitive capital markets is assumed. From the sensitivity analysis using traditional comparative static analysis, some useful managerial implications which are consistent with famous previous studies are derived under realistic conditions. All results in this study, however, are valid under the assumption that the opportunity costs follow geometric Brownian motion, which is widely used in economic science and finance literature.

• Journal of the Korean Data and Information Science Society
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• v.18 no.1
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• pp.73-80
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• 2007

Cointegration(together with VARMA(vector ARMA)) has been proven to be useful for analyzing multivariate non-stationary data in the field of financial time series. It provides a linear combination (which turns out to be stationary series) of non-stationary component series. This linear combination equation is referred to as long term equilibrium between the component series. We consider two sets of Korean bivariate financial time series and then illustrate cointegration analysis. Specifically estimated VAR(vector AR) and VECM(vector error correction model) are obtained and CV(cointegrating vector) is found for each data sets.

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.109-116
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• 1997

In the present paper we consider an abstract partial dif-ferential equation of the form $\frac{\partial^2u}{{\partial}t^2}-\frac{\partial^2u}{{\partial}x^2}+A(x.t)u=f(x, t)$, where ${A(x, t):(x, t){\epsilon}\bar{G} }$ is a family of linear closed operators and $G=GU{\partial}G$, G is a suitable bounded region in the (x, t)-plane with bound-are ${\partial}G$. It is assumed that u is given on the boundary ${\partial}G$. The objective of this paper is to study the considered Dirichlet problem for a wide class of operators $A(x, t)$. A Dirichlet problem for non-elliptic partial differential equations of higher orders is also considerde.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.04a
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• pp.53-60
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• 2003

This paper explores the governing differential equations for the non-linear behavior of shear deformable simple beam with a concentrated load. In order to apply the Bernoulli-Euler beam theory to simple beam, the bending moment equation on any point of the elastica is obtained by concentrated load. The Runge-Kutta and Regula-Felsi methods, respectively, are used to integrate the governing differential equations and to compute the beam's rotation at the left end of the beams. The characteristic values of deflection curves for various load parameters are calculated and discussed

• Journal of the Korean Applied Science and Technology
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• v.32 no.4
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• pp.661-668
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• 2015

The surface rheological properties of polymer monolayer show complicated non-linear viscoelastic flow phenomena when they are subjected to spreading flow. These spreading flow properties are controlled by the characteristics of flow units. The kinetics of the formation of an interfacial film obtained after spreading poly(diisobutylene maleic acid) at air-water interface were studied by measuring of the surface pressure with time. The experimental data were analyzed theoretically according to a nonlinear surface viscoelastic model. The values of dynamic modulus, static modulus, surface viscosities and rheological parameters in various area/ monomer were obtained by appling experimental data to the equation of nonlinear surface viscoelastic model.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.629-634
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• 2000

Dynamic behavior of an automatic dynamic balancer is analyzed by a theoretical approach. Using Lagrange's equation, we derive the non-linear equations of motion for an automatic dynamic balancer equipped in a rotor with the bending flexibility with respect to the rectangular coordinate. Considering the rotor bending flexibility we analyze out-of-plane vibrations as well as in-plane vibrations of the automatic dynamic balaner. The time responses are computed from the non-linear equations by using a time integration method. We also investigate the effect of rotor flexibility on the behavior of the automatic dynamic balancer