• Advances in aircraft and spacecraft science
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• v.7 no.3
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• pp.215-228
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• 2020

As is shown in the paper, the Koltunov-Rzhanitsyn singular kernel of heredity (when constructing mathematical models of the dynamics problem of the hereditary theory of viscoelasticity) adequately describes real mechanical processes, best approximates experimental data for a long period of time. A mathematical model of the problem of the flutter of viscoelastic plates moving in a gas with a high supersonic velocity is given. Using the Bubnov-Galerkin method, discrete models of the problem of the flatter of viscoelastic plates flowed over by supersonic gas flow are obtained. A numerical method is developed to solve nonlinear integro-differential equations (IDE) for the problem of the hereditary theory of viscoelasticity with weakly singular kernels. A general computational algorithm and a system of application programs have been developed, which allow one to investigate the nonlinear dynamic problems of the hereditary theory of viscoelasticity with weakly singular kernels. On the basis of the proposed numerical method and algorithm, nonlinear problems of the flutter of viscoelastic plates flowed over in a gas flow at an arbitrary angle are investigated. In a wide range of changes in various parameters of the plate, the critical velocity of the flutter is determined. It is shown that the singularity parameter α affects not only the oscillations of viscoelastic systems, but the critical velocity of the flutter as well.

• The Korean Journal of Rheology
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• v.9 no.3
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• pp.97-102
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• 1997

내피로성은 기계적 구조물로 사용되는 고분자재료에는 반드시 필요한 성질이며, 피 로거동은 재료특유의 비선형 동적 점탄특성과 아주 밀접한 관계가 있다. 본 연구에서는 피 로과정에서의 비선형 동적 점탄특성을 정량적, 연속적으로 측정할수 있는 시험 기기와 가해 준 변형에 대한 응답 응력파의 기본 응력파(선형적 응답)로부터의 차이를 직접 측정하여 이 를 규격화한 비선형 점탄성파라미터, NVP(Nonlinear Viscoelastic Parameter)라 명명한 새 로운 평가방법을 개발하였다. 그리고 고밀도 폴리에틸렌(HDPE) 배향물을 사용하여 그 평가 방법의 타당성을 조사한 결과 피로과정에서의 비선형동적 점탄특성을 나타내는 NVP가 증 가함에 따라 재료의 피로수명은 감소하였다. 따라서 NVP가 고분자재료의 내피로성을 평가 하는 척도로서 사용가능하다는 사실이 증명되었다. 또한 각 고조파 성분에대해 조사한 결과 인장형 피로시험양식에서는 고체입자 분산계의 전단변형에서 나타난 비선형 점탄성의 결과 와는 달리 2차 성분의 크기가 가장컸으며 NVP에의 기여도도 가장 크게 나타났다. 이는 변 형양식의 차이에 따른 결과를 볼수 있다.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.311-326
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• 2011

In this paper, we adopt discontinuous Galerkin methods with penalty terms namely symmetric interior penalty Galerkin methods, to solve nonlinear viscoelasticity type equations. We construct finite element spaces and define an appropriate projection of u and prove its optimal convergence. We construct extrapolated fully discrete discontinuous Galerkin approximations for the viscoelasticity type equation and prove ${\ell}^{\infty}(L^2)$ optimal error estimates in both spatial direction and temporal direction.

• Korea-Australia Rheology Journal
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• v.17 no.3
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• pp.141-143
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• 2005

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.829-850
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• 2012

In this paper, we adopt symmetric interior penalty discontinuous Galerkin (SIPG) methods to approximate the solution of nonlinear viscoelasticity-type equations. We construct finite element space which consists of piecewise continuous polynomials. We introduce an appropriate elliptic-type projection and prove its approximation properties. We construct semidiscrete discontinuous Galerkin approximations and prove the optimal convergence in $L^2$ normed space.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.15 no.6
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• pp.3435-3441
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• 2014

A dynamic modeling and prediction of polyurethane foam material, which is used as the seat in vehicles is very important for improving the ride quality of vehicle occupants. In this study, parameters to define the nonlinear stiffness and time-variant characteristics of the viscoelasticity of polyurethane foam were obtained using a static compression test. Polynomial functions and convolution integral were used to model the nonlinear and viscoelastic characteristics of polyurethane foam mathematically. The dynamic behaviors excited by the seat floor displacement were analyzed using a numerical integration method for the nonlinear vibration model. As a result, the viscoelastic characteristics of polyurethane foam was found to be an important parameter for improving the ride quality.

• Korea-Australia Rheology Journal
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• v.13 no.4
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• pp.179-187
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• 2001

As part of continuing efforts to investigate nonlinear dynamics and stability of film casting process, our earlier results obtained by Lee et al. (2001b) have been extended in the present study to cover the film casting of both extension thickening and extension thinning fluids. The same instability mechanism and draw resonance criterion previously derived have been found valid here, and a rather complex dynamic behavior of film width in contrast to that of film thickness has also been confirmed. The effect of fluid viscoelasticity on draw resonance, however, exhibits opposite results depending on whether the fluid is extension thickening or thinning, i.e., it stabilizes film casting in the former while destabilizing in the latter. The encapsulation extrusion method which recently has been successfully employed to stabilize industrially important paper coating process, has been theoretically explained in the present study as to why such stabilization is possible.

• Polymer Science and Technology
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• v.8 no.1
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• pp.32-40
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• 1997

• Journal of Mechanical Science and Technology
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• v.17 no.9
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• pp.1324-1331
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• 2003

A bushing is a device used in automotive suspension systems to cushion the force transmitted from the wheel to the frame of the vehicle. A bushing is essentially a hollow cylinder which is bonded to a solid metal shaft at its inner surface and a metal sleeve at its outer surface. The shaft is connected to the suspension and the sleeve is connected to the frame. The cylinder provides the cushion when it deforms due to relative motion between the shaft and sleeve. The relation between the force applied to the shaft or sleeve and its deformation is nonlinear and exhibits features of viscoelasticity. An explicit force-displacement relation has been introduced for multi-body dynamics simulations. The relation is expressed in terms of a force relaxation function and a method of determination by experiments on bushings has been developed. Solutions allow for comparison between the force-displacement behavior by experiments and that predicted by the proposed method. It is shown that the predictions by the proposed force-displacement relation are in very good agreement with the experimental results.

• Transactions of Materials Processing
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• v.18 no.6
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• pp.494-499
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• 2009

The time-dependent constitutive law was utilized based on viscoelastic-plasticity to predict the time-dependent spring-back behavior of aluminum alloy 6022-T4 sheets. Besides nonlinear viscoelasticity, non-quadratic anisotropic yield function, Yld2000-2d, was used to account for the anisotropic yield behavior, while the combined isotropic-kinematic hardening law was used to represent the Bauschinger effect and transient hardening. For verification purposes, finite element simulations were performed for the draw-bending and the results were compared with experimental results.