• Proceedings of the Korean Society of Precision Engineering Conference
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• 1993.04b
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• pp.175-180
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• 1993

The nonlinear integro-differential equations of motion of a two-link structurally flexible planar manipulator executing contact tasks are presented. The equations of motion are derived using the extended Hamilton's principle and the Galerkin criterion. Also, Models for the wrist-force sensor and impact that occurs when the manipulator's end point makes contact withthe environment are presented. The dynamic models presented can be used to studythe dynamics of the system and to design controllers.

• Communications of the Korean Mathematical Society
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• v.28 no.3
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• pp.559-569
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• 2013

The purpose of this paper is to establish existence, uniqueness and a variation of constant formula of solutions for semilinear partial functional differential equations with unbounded delays and nonlinear part involving integro differetial terms.

• Journal of Applied and Pure Mathematics
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• v.4 no.5_6
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• pp.299-315
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• 2022

This manuscript deals with the exact (complete) controllability of semilinear stochastic differential equations with infinite delay and Poisson jumps utilizing some basic and readily verified conditions. The results are obtained by using fixed-point approach and by using advance phase space definition for infinite delay part. We have used the axiomatic definition of the phase space in terms of stochastic process to consider the time delay of the system. An infinite delay along with the Poisson jump is the new investigation for the given stochastic system. An example is given to illustrate the effectiveness of the results.

• Journal of the Society of Disaster Information
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• v.10 no.1
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• pp.123-140
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• 2014

This paper proposes a simple and effective method for determining the dynamic characteristics of revolution shells. This is a weighted residual method in which the collocation points are taken at the roots of orthogonal polynomial. In this paper the collocation method is employed to replace a partical differential eqations by a system of ordinary differential equations in time, and the resulting equations are solved by two different numerical methods of time integration : an implicit method and an explicit method. The proposed approach is formulated in some detail. The versatility and accuracy are illustrated through several numerical examples. The method appears to be relatively easy to set up and gives satisfactory results.

• Steel and Composite Structures
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• v.50 no.1
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• pp.25-43
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• 2024

In this article, a mathematical model is developed to predict the dynamic behavior of bio-inspired composite beam with helicoidal orientation scheme under variable axial load using a unified higher order shear deformation beam theory. The geometrical kinematic relations of displacements are portrayed with higher parabolic shear deformation beam theory. Constitutive equation of composite beam is proposed based on plane stress problem. The variable axial load is distributed through the axial direction by constant, linear, and parabolic functions. The equations of motion and associated boundary conditions are derived in detail by Hamilton's principle. Using the differential quadrature method (DQM), the governing equations, which are integro-differential equations are discretized in spatial direction, then they are transformed into linear eigenvalue problems. The proposed model is verified with previous works available in literatures. Parametric analyses are developed to present the influence of axial load type, orthotropic ratio, slenderness ratio, lamination scheme, and boundary conditions on the natural frequencies of composite beam structures. The present enhanced model can be used especially in designing spacecrafts, naval, automotive, helicopter, the wind turbine, musical instruments, and civil structures subjected to the variable axial loads.

• ETRI Journal
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• v.23 no.2
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• pp.71-76
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• 2001

In this paper, the electromagnetic characteristics of a grounded slab and a parallel-plate structure are analyzed by the Spline-type Divided-Difference Interpolation (SDDI) technique. The technique efficiently evaluates the MoM impedance matrix elements of the multifold spectral or spatial domain integrals or summation in integro differential equations. The numerical results of the proposed method agree well with those of the corresponding literatures.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.681-696
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• 2011

In this paper, we consider the existence of mild solutions for a certain class of nonlinear impulsive functional evolution integrodifferential equation with nonlocal conditions in Banach spaces. A sufficient condition is established by using Schaefer's fixed point theorem combined with an evolution system. An example is also given to illustrate our result.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.113-130
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• 2024

In this work, we explore the existence and uniqueness results for a class of boundary value issues for implicit Volterra-Fredholm nonlinear integro-differential equations (IDEs) with Atangana-Baleanu-Riemann fractional (ABR-fractional) that have non-instantaneous multi-point fractional boundary conditions. The findings are supported by Krasnoselskii's fixed point theorem, Gronwall-Bellman inequality, and the Banach contraction principle. Finally, a demonstrative example is provided to support our key findings.

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.545-558
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• 2024

In this study, a class of nonlinear boundary fractional Caputo Volterra-Fredholm integro-differential equations (CV-FIDEs) is taken into account. Under specific assumptions about the available data, we firstly demonstrate the existence and uniqueness features of the solution. The Gronwall's inequality, a adequate singular Hölder's inequality, and the fixed point theorem using an a priori estimate procedure. Finally, a case study is provided to highlight the findings.

• 한국전산유체공학회:학술대회논문집
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• 1998.05a
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• pp.15-28
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• 1998

As an alternative for solving the incompressible Navier-Stokes equations, we present a vorticity-based integro-differential formulation for vorticity, velocity and pressure variables. One of the most difficult problems encountered in the vorticity-based methods is the introduction of the proper value-value of vorticity or vorticity flux at the solid surface. A practical computational technique toward solving this problem is presented in connection with the coupling between the vorticity and the pressure boundary conditions. Numerical schemes based on an iterative procedure are employed to solve the governing equations with the boundary conditions for the three variables. A finite volume method is implemented to integrate the vorticity transport equation with the dynamic vorticity boundary condition . The velocity field is obtained by using the Biot-Savart integral derived from the mathematical vector identity. Green's scalar identity is used to solve the total pressure in an integral approach similar to the surface panel methods which have been well-established for potential flow analysis. The calculated results with the present mettled for two test problems are compared with data from the literature in order for its validation. The first test problem is one for the two-dimensional square cavity flow driven by shear on the top lid. Two cases are considered here: (i) one driven both by the specified non-uniform shear on the top lid and by the specified body forces acting through the cavity region, for which we find the exact solution, and (ii) one of the classical type (i.e., driven only by uniform shear). Secondly, the present mettled is applied to deal with the early development of the flow around an impulsively started circular cylinder.