• Structural Engineering and Mechanics
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• v.37 no.1
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• pp.61-77
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• 2011

Static and dynamic responses of a completely free elastic beam resting on a two-parameter tensionless Pasternak foundation are investigated by assuming that the beam is symmetrically subjected to a uniformly distributed load and concentrated load at its middle. Governing equations of the problem are obtained and solved by paying attention on the boundary conditions of the problem including the concentrated edge foundation reaction in the case of complete contact and lift-off condition of the beam ina two-parameter foundation. The nonlinear governing equation of the problem is evaluated numerically by adopting an iterative procedure. Numerical results are presented in figures to demonstrate the non-linear behavior of the beam-foundation system for various values of the parameters of the problem comparatively by considering the static and dynamic loading cases.

• Proceedings of the Optical Society of Korea Conference
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• 1989.02a
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• pp.20-25
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• 1989

The nonlinear, time dependent photon transport equations of Frantz and Nodvik, which describe the amplification of an optical pulse in an active medium, are modified to a simpler equation which describes only the amplification of energy. with this equation, the output energy of the high power YLF(Nd3+)-Phosphate Glass(Nd3+) Laser System is calculated. When the stored energy density Est is 0.10J/㎤, 0.16J/㎤, 0.228J/㎤, and 0.50J/㎤, and with the assumption of uniform population inversion density, the final output energy of this laser system is 5.38J, 176J, 317J, and 283J, respectively. The gain saturation causes distortion of the output beam. This phenomenon is described in detail at the first three rod amplifier systems in the case of E=0.228J/㎤. The peak current and decay time constant of the flashlamps, which are used to obtain population inversion in the active medium, are investigated. The flashlamp driving circuit which has optimum operational performance should have {{{{ SQRT { LC} }} time about 100$\mu$sec.

• Wind and Structures
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• v.28 no.3
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• pp.171-180
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• 2019

This paper presents a restart iterative approach for time-domain flutter analysis of long-span bridges using the commercial FE package ANSYS. This approach utilizes the recursive formats of impulse-response-function expressions for bridge's aeroelastic forces. Nonlinear dynamic equilibrium equations are iteratively solved by using the restart technique in ANSYS, which enable the equilibrium state of system to get back to last moment absolutely during iterations. The condition for the onset of flutter instability becomes that, at a certain wind velocity, the amplitude of vibration is invariant with time. A long-span suspension bridge was taken as a numerical example to verify the applicability and accuracy of the proposed method by comparing calculated results with wind tunnel tests. The proposed method enables the bridge designers and engineering practitioners to carry out time-domain flutter analysis of bridges in commercial FE package ANSYS.

• Steel and Composite Structures
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• v.32 no.4
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• pp.509-519
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• 2019

In this paper, an analytical approach for the free vibration analysis of spiral stiffened functionally graded (SSFG) cylindrical shells is investigated. The SSFG shell is resting on linear and non-linear elastic foundation with damping force. The elastic foundation for the linear model is according to Winkler and Pasternak parameters and for the non-linear model, one cubic term is added. The material constitutive of the stiffeners is continuously changed through the thickness. Using the Galerkin method based on the von $K\acute{a}rm\acute{a}n$ equations and the smeared stiffeners technique, the non-linear vibration problem has been solved. The effects of different geometrical and material parameters on the free vibration response of SSFG cylindrical shells are adopted. The results show that the angles of stiffeners and elastic foundation parameters strongly effect on the natural frequencies of the SSFG cylindrical shell.

• Journal of the Korea Institute of Military Science and Technology
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• v.21 no.6
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• pp.850-856
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• 2018

In this paper, a controller based on repetitive learning control is designed to control an unmanned surface vessel with nonlinear characteristics and unknown parameters. First, we define the equations of motion and error system of the unmanned vessel, and then design an repetitive learning controller composed of system error and estimated unknown parameters based on repetitive learning control and adaptive control. The stability of the unmanned vessel model controlled by the designed controller is verified through the analysis of the Lyapunov stability. Simulation shows that the error converges asymptotically to zero with semi-global result, confirming that the unmanned vessel is moving toward a given ideal path, and verifies that the controller is also feasible.

• Coupled systems mechanics
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• v.7 no.6
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• pp.755-774
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• 2018

The Ritz method is known as very successful strategy for discretizing continuous problems, but it has never been used for solving systems of algebraic equations. The Iterated Ritz Method (IRM) is a novel iterative solver based on the discretized Ritz procedure applied at each iteration step. With an appropriate choice of coordinate vectors, the method may be efficient in linear, nonlinear and optimization problems. Additionally, some iterative methods can be explained as special cases of this approach, which helps to understand advantages and limitations of these methods and gives motivation for their improvement in sense of IRM. In this paper, some ideas for generation of efficient coordinate vectors are presented. The algorithm was developed and tested independently and then implemented into the open source program FEAP. Method has been successfully applied to displacement based (even ill-conditioned) models of structural engineering practice. With this original approach, a new iterative solution strategy has been opened.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1297-1314
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• 2019

In this work, we investigate the following fractional boundary value problems $$\{_tD^{\alpha}_T({\mid}_0D^{\alpha}_t(u(t)){\mid}^{p-2}_0D^{\alpha}_tu(t))\\={\nabla}W(t,u(t))+{\lambda}g(t){\mid}u(t){\mid}^{q-2}u(t),\;t{\in}(0,T),\\u(0)=u(T)=0,$$ where ${\nabla}W(t,u)$ is the gradient of W(t, u) at u and $W{\in}C([0,T]{\times}{\mathbb{R}}^n,{\mathbb{R}})$ is homogeneous of degree r, ${\lambda}$ is a positive parameter, $g{\in}C([0,T])$, 1 < r < p < q and ${\frac{1}{p}}<{\alpha}<1$. Using the Fibering map and Nehari manifold, for some positive constant ${\lambda}_0$ such that $0<{\lambda}<{\lambda}_0$, we prove the existence of at least two non-trivial solutions

• Geomechanics and Engineering
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• v.23 no.6
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• pp.547-560
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• 2020

This paper studies the dynamic foundation-soil-foundation interaction for two square rigid foundations embedded in a viscoelastic soil layer. The vibrations come from only one rigid foundation placed in the soil layer and subjected to harmonic loads of translation, rocking, and torsion. The required dynamic response of rigid surface foundations constitutes the solution of the wave equations obtained by taking account of the conditions of interaction. The solution is formulated using the frequency domain Boundary Element Method (BEM) in conjunction with the Kausel-Peek Green's function for a layered stratum, with the aid of the Thin Layer Method (TLM), to study the dynamic interaction between adjacent foundations. This approach allows the establishment of a mathematical model that enables us to determine the dynamic displacements amplitude of adjacent foundations according to their different separations, the depth of the substratum, foundations masss, foundations embedded, and the frequencies of excitation. This paper attempts to introduce an approach based on a polynomial mathematical tool conducted from several results of numerical methods (BEM-TLM) so that practicing civil engineers can evaluation the dynamic foundations displacements more easy.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.273-288
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• 2021

We proposed to give some new 𝜓-coupled fixed point theorems using simulation function coupled with other control functions in a complete partially ordered metric space which includes many related results. Further we prove the existence of solution of a fractional integral equation by using this fixed point theorem and explain it with the help of an example.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.303-322
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• 2021

The concepts of new classes of mappings are introduced in the spaces which are more general space than the usual metric spaces. The existence and uniqueness of common fixed points and fixed point results are established in the setting of complete complex valued b-metric spaces. An illustration is given by establishing the existence of solution of periodic differential equations in the framework of a complete complex valued b-metric spaces.