• 소음진동
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• 제8권4호
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• pp.715-722
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• 1998

An investigation into the stochastic bifurcation and response statistics of an autoparameteric system under broad-band random excitation is made. The specific system examined is a spring-pendulum system with internal resonance, which is known to be a good model for a variety of engineering systems, including ship motions with nonlinear coupling between pitching and rolling motions. The Fokker-Planck equations is used to genrage a general first-order differential equation in the dynamic moment of response coordinates. By means of the Gaussian and non-Gaussian closure methods the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinanary differential equations. In view of equilibrium solutions of this system and their stability we examine the stochastic bifurcation and response statistics. The analytical results are compared with results obtained by Monte Carlo simulation.

• Journal of applied mathematics & informatics
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• 제7권2호
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• pp.453-465
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• 2000

In this paper, a new method for finding the approximate solution of a second order nonlinear partial differential equation is introduced. In this method the problem is transformed to an equivalent optimization problem. them , by considering it as a distributed parameter control system the theory of measure is used for obtaining the approximate solution of the original problem.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제16권2호
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• pp.93-105
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• 2012

In this paper, we consider the controllability of a certain class of impulsive neutral evolution differential equations in Banach spaces. Sufficient conditions for controllability are obtained by using the Hausdorff measure of noncompactness and Monch fixed point theorem under the assumption of noncompactness of the evolution system.

• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.65-77
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• 2013

In this paper, we develop the operational Tau method for solving nonlinear Volterra integro-differential equations of the second kind. The existence and uniqueness of the problem is provided. Here, we show that the nonlinear system resulted from the operational Tau method has a semi triangular form, so it can be solved easily by the forward substitution method. Finally, the accuracy of the method is verified by presenting some numerical computations.

• Coupled systems mechanics
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• 제3권3호
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• pp.291-304
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• 2014

Paper discusess a dynamic engineering problem of a mass attached to a pendulum sliding along a cable. In this problem the pendulum mass and the cable are coupled together in a model described by a system of differential algebraic equations (DAE). In the paper we have presented formulation of the system of differential equations that models the problem and determination of the initial conditions. The developed model is general in a sense of free choice of support location, elastic cable properties, pendulum length and inclusion of braking forces. Examples illustrate and validate the model.

• 대한수학회지
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• 제54권4호
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• pp.1209-1229
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• 2017

We coupled the so-called Sumudu transform with the homotopy perturbation method (HPM) and the homotopy analysis method (HAM), which are called homotopy perturbation Sumudu transform method (HPSTM) and homotopy analysis Sumudu transform method (HASTM), respectively. Then we show how HPSTM and HASTM are more convenient than HPM and HAM by conducting a comparative analytical study for a system of time fractional nonlinear differential equations. A Maple package is also used to enhance the clarity of the involved numerical simulations.

• East Asian mathematical journal
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• 제30권5호
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• pp.631-637
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• 2014

In this paper, we construct some results on the existence and regularity for solutions of neutral functional differential equations with unbounded principal operators in Hilbert spaces. In order to establish the existence and regularity for solutions of the neutral system by using fractional power of operators and the local Lipschtiz continuity of nonlinear term without using many of the strong restrictions considering in the previous literature.

• 충청수학회지
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• 제27권3호
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• pp.495-502
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• 2014

In this paper, we show the ${\psi}$-uniform stability for linear impulsive differential equations and their perturbations by using the impulsive Gronwall's inequalities.

• Journal of Applied and Pure Mathematics
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• 제6권1_2호
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• pp.71-96
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• 2024

In this paper we present many interesting results such as completeness and composition theorems in the 𝛼 norm. Moreover, under some conditions, we establish the existence and uniqueness of Cⁿ-(𝜇, 𝜈) pseudo-almost automorphic solutions of class r in the 𝛼-norm for some partial functional differential equations in Banach space when the delay is distributed. An example is given to illustrate our results.

• Structural Engineering and Mechanics
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• 제43권1호
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• pp.105-126
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• 2012

Based on the first-order shear deformation theory (FSDT), and the virtual work principle, an elastic analysis for axisymmetric clamped-clamped Pressurized thick truncated conical shells made of functionally graded materials have been performed. The governing equations are a system of nonhomogeneous ordinary differential equations with variable coefficients. Using the matched asymptotic method (MAM) of the perturbation theory, these equations could be converted into a system of algebraic equations with variable coefficients and two systems of differential equations with constant coefficients. For different FGM conical angles, displacements and stresses along the radius and length have been calculated and plotted.