• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.497-512
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• 2021

In this paper, we study the analytical and approximate solutions for a fractional quadratic integral equation involving Katugampola fractional integral operator. The existence and uniqueness results obtained in the given arrangement are not only new but also yield some new particular results corresponding to special values of the parameters 𝜌 and ϑ. The main results are obtained by using Banach fixed point theorem, Picard Method, and Adomian decomposition method. An illustrative example is given to justify the main results.

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.163-170
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• 2021

We present a concise proof of the conjecture of Mazur-Rubin-Stein on the distribution of modular symbols.

• 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.

• Geophysics and Geophysical Exploration
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• v.8 no.3
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• pp.207-217
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• 2005

We present a new approximate formulation of the integral equation (IE) method for models with variable background conductivity. This method overcomes the standard limitation of the conventional If method related to the use of a horizontally layered background only. The new approximate IE method still employs the Green's functions for a horizontally layered 1-D model. However, the new method allows us to use an inhomogeneous background with the IE method. The method was carefully tested for modeling the EM field for complex structures with a known variable background conductivity. It can find wide application in modeling EM data for multiple geological models with some common geoelectrical features, like a known inhomogeneous overburden, or salt dome structures.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.5
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• pp.789-797
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• 2003

In the procedure of the hydraulic control system design, a linearized approximate equation described by the first order terms of Taylor series has been widely used. Such a linearized equation is effective just near the operating point, However, pressure and flowrate in actual hydraulic systems are usually not confined near an operating point. This study suggests a new linearized flow equation for a servovalve as a modified form of the conventional linearized flow equation. Subsequently, a procedure to determine effective operating point for the new linearized equation is proposed. From the evaluations of time responses and frequency responses obtained from simulations for a hydraulic control system, the effectiveness of the new linearized equation and the procedure to determine effective operating point is confirmed.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.1
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• pp.32-38
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• 2001

This paper presents an approximate synthesis of 5-SS multi link suspension for 2 D.O.F motions. In the proposed synthesis method, alteration curves of camber, toe, kingpin and caster angles are optimized during the bump rebound and the steering motions. And joint positions can be located within desired boundari es. Especially, steering motions are considered for control of kingpin offset and caster trail. Prescribed motions contain both wheel center positions and imaginary kingpin axes in the multi link type suspension. Constraint equations are formulated with di splacement matrix and velocity matrix using instantaneous screw axis.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.11
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• pp.2665-2671
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• 2000

Dimensional Synthesis, which is apart of kinematic synthesis, is to determine the dimensions of a mechanism of preconceived typer for a specified task and prescribed performance. In this paper, in an effort to provide designers with flexibility, a dimensional approximate synthesis method is presented for utilizing prescribed tolerance both the displacement and joint positions of a mechanism to be synthesized. For this, a constrained optimization problem is formulated with displacement parameters and joint positions as variables. The proposed method is applied to the synthesis of a 5-SS multi link suspension mechanism. The method discussed here, however, can be easily applied to any mechanism of which the kinematic constraint equations can be derived.

• Journal of Institute of Control, Robotics and Systems
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• v.7 no.12
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• pp.993-1000
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• 2001

Configuration-dependent nonlinear coefficient matrices in the dynamic equation of robot manipulator impose computa- tional burden in real-time implementation of tracking control based on the inverse dynamics controller. However, parallel manipulators such as Stewart platform have relatively small workspace compared to serial manipulators. Based on the characteristics of small motion range. nonlinear coefficient matrices can be approxiamted to constant ones. The modeling errors caused by such approximation are compensated for by H-infinity controller that treats the modeling errors disturbance. The proposed inverse dynamics controller with approximate dynamics combined with H-infinity control shows good tracking performance even for fast tracking control in which computation of full inverse dynamics is not easy to implement.

• Structural Engineering and Mechanics
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• v.56 no.3
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• pp.461-472
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• 2015

In this paper, the nonlinear static response of curled cantilever beam actuators subjected to the one-sided electrostatic field is focused on. By assuming the deflection function of electrostatically actuated beam, analytical approximate solutions are established via using Galerkin method to solve the equilibrium equation. The Pull-In voltages which determine the stability of the curled beam actuators are also obtained. These approximate solutions show excellent agreements with numerical solutions obtained by the shooting method and the experimental data for a wide range of beam length. Expressions of these analytical approximate solutions are brief and could easily be used to derive the effects of various physical parameters on MEMS structures.

• Tribology and Lubricants
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• v.13 no.2
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• pp.60-67
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• 1997

ER(electro-rheological) fluids, which are represented as Bingham fluids, have large and reversible changes in yield shear stresses by application of an electric field. In this paper, ER fluids are employed in a short squeeze film damper. The modified Reynolds equation for an ER short squeeze film damper is theoretically solved to get the approximate solutions of pressure profiles and damping coefficients. The theoretical approximate solutions are compared with numerical ones and both results are coincided very well. Both the direct and cross coupled damping coefficients substantially increase with increasing the yield shear stress of ER fluids. Furthermore, the synchronous response analysis of a rigid rotor supported on ER short squeeze film dampers is performed to show the improved damping capability of an ER short squeeze film damper.