• Steel and Composite Structures
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• 제18권4호
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• pp.889-907
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• 2015

This paper aims to present an alternative analytical method for transient vibration analysis of doubly-curved laminated shells subjected to dynamic loads. In the method proposed, the governing differential equations of laminated shell are derived using the dynamic version of the principle of virtual displacements. The governing equations of first order shear deformation laminated shell are obtained by Navier solution procedure. Time-dependent equations are transformed to the Laplace domain and then Laplace parameter dependent equations are solved numerically. The results obtained in the Laplace domain are transformed to the time domain with the help of modified Durbin's numerical inverse Laplace transform method. Verification of the presented method is carried out by comparing the results with those obtained by Newmark method and ANSYS finite element software. Also effects of number of laminates, different material properties and shell geometries are discussed. The numerical results have proved that the presented procedure is a highly accurate and efficient solution method.

• 대한수학회지
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• 제46권4호
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• pp.747-758
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• 2009

In this paper, we investigate the growth and fixed points of meromorphic solutions of higher order linear differential equations with meromorphic coefficients and their derivatives. Because of the restriction of differential equations, we obtain that the properties of fixed points of meromorphic solutions of higher order linear differential equations with meromorphic coefficients and their derivatives are more interesting than that of general transcendental meromorphic functions. Our results extend the previous results due to M. Frei, M. Ozawa, G. Gundersen, and J. K. Langley and Z. Chen and K. Shon.

• Structural Engineering and Mechanics
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• 제63권4호
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• pp.481-495
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• 2017

The present article examines the static response of multilayered magneto-electro-elastic (MEE) beam in thermal environment through finite element (FE) methods. On the basis of the minimum total potential energy principle and the coupled constitutive equations of MEE material, the FE equilibrium equations of cantilever MEE beam is derived. Maxwell's equations are considered to establish the relation between electric field and electric potential; magnetic field and magnetic potential. A simple condensation approach is employed to solve the global FE equilibrium equations. Further, numerical evaluations are made to examine the influence of different in-plane and through-thickness temperature distributions on the multiphysics response of MEE beam. A parametric study is performed to evaluate the effect of stacking sequence and different temperature profiles on the direct and derived quantities of MEE beam. It is believed that the results presented in this article serve as a benchmark for accurate design and analysis of the MEE smart structures in thermal applications.

• Ocean Systems Engineering
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• 제4권2호
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• pp.151-167
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• 2014

It is common that analyses of offshore platforms being carried out with the assumption of rigid tubular joints. However, many researches have concluded that it is necessary that local joint flexibility (LJF) of tubular joints should be taken into account. Meanwhile, advanced analysis of old offshore platforms considering local joint flexibility leads to more accurate results. This paper presents an extensive finite-element (FE) based study on the flexibility of uni-planner multi-brace tubular Y-T and K-joints commonly found in offshore platforms. A wide range of geometric parameters of Y-T and K-joints in offshore practice is covered to generate reliable parametric equations for flexibility matrices. The formulas are obtained by non-linear regression analyses on the database. The proposed equations are verified against existing analytical and experimental formulations. The equations can be used reliably in global analyses of offshore structures to account for the LJF effects on overall behavior of the structure.

• Journal of Forest and Environmental Science
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• 제34권4호
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• pp.313-320
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• 2018

Tectona grandis (teak) is one of the most important timber species worldwide and India is one of the major teak growing countries. Though some volume equations were developed for teak in India but the models developed were neither evaluated using robust statistical criteria nor validated. Hence, the objective of this study was to develop statistically tested appropriate volume equation to predict total wood volume (over- and under-bark) for teak trees in Gujarat. A total of 41 trees with age varying from 15 to 33 years and diameter at breast height (dbh) from 7.3 to 30.8 cm were felled for the purpose. Linear and non-linear equations were used to model the relationship of the total wood volume with respect to dbh and total height. The equations tested mostly fitted well to the data. Model evaluation and validation indicated that models should be calibrated with local data for greater accuracy in the prediction.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.763-779
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• 2011

In this paper we apply the Exp-function method to obtain traveling wave solutions of three nonlinear partial differential equations, namely, generalized sinh-Gordon equation, generalized form of the famous sinh-Gordon equation, and double combined sinh-cosh-Gordon equation. These equations play a very important role in mathematical physics and engineering sciences. The Exp-Function method changes the problem from solving nonlinear partial differential equations to solving a ordinary differential equation. Mainly we try to present an application of Exp-function method taking to consideration rectifying a commonly occurring errors during some of recent works.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2010년도 학술발표회
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• pp.213-217
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• 2010

댐붕괴파 (dam-break flow)나 지진해일에 의해 발생하는 undular bore와 충격파 (shock) 현상을 동수압 및 분산효과를 고려하여 수치모의를 수행하였다. 완전비선형 Boussinesq-type equations 모형을 이용하여, 동수압 및 분산 효과를 고려하였다. 방정식은 4차 정확도의 유한체적법을 이용하여 해석하였고, 시간적으로도 4차정확도의 기법을 이용하여 고차미분항에 대한 수치분산을 억제하였다. 다양한 경우의 1차원과 2차원 공간에서의 수치모의를 수행하고 검증을 수행하였다. 그 결과, 완전비선형 Boussinesq-type equations 모형은 천수방정식 (shallow water equations) 기반의 모형에서 재현이 불가능한 undular bore 등을 재현 하는 등, 전반적으로 천수방정식 기반의 모형 보다 물리적으로도 타당하고 정량적으로도 실험결과와 잘 일치하는 경향을 보였다. 즉, 댐붕괴파나 지진해일 등에 의한 범람 모의에 있어 동수압과 분산 효과의 중요성이 공학적으로도 매우 중요한 고려사항 임이 나타났다.

• Journal of Electrical Engineering and Technology
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• 제11권4호
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• pp.1027-1034
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• 2016

This paper proposes a sum of squares (SOS) method for anti-swing control of overhead crane system using HOSM (High-Order Sliding-Mode) observer. By representing the dynamic equations of overhead crane as the polynomial dynamic equations via Taylor series expansion, the control input is obtained from the converted polynomial dynamic equations by numerical tool SOSTOOL. Since the actual crane systems include disturbance such as wind and friction, we propose a method to compensate for the disturbance by estimating the disturbance using HOSM observer. Numerical simulations show the effectiveness and the applicability of the proposed method.

• 대한수학회논문집
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• 제30권4호
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• pp.447-456
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• 2015

In this paper, we investigate the differential-difference equation $(f(z+c)-f(z))^2+P(z)^2(f^{(k)}(z))^2=Q(z)$, where P(z), Q(z) are nonzero polynomials. In addition, we also investigate Fermat type q-difference differential equations $f(qz)^2+(f^{(k)}(z))^2=1$ and $(f(qz)-f(z))^2+(f^{(k)}(z))^2=1$. If the above equations admit a transcendental entire solution of finite order, then we can obtain the precise expression of the solution.

• Kyungpook Mathematical Journal
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• 제60권4호
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• pp.767-779
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• 2020

This paper primarily discusses and proves the Hyers-Ulam stability of three types of polynomial equations: xn+a1x+a0 = 0, anxn+⋯+a1x+a0 = 0, and the infinite series equation: ${\sum\limits_{i=0}^{\infty}}\;a_ix^i=0$, in dislocated quasi-metric spaces under certain conditions by constructing contraction mappings and using fixed-point methods. We present an example to illustrate that the Hyers-Ulam stability of polynomial equations in dislocated quasi-metric spaces do not work when the constant term is not equal to zero.