• Nonlinear Functional Analysis and Applications
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• 제26권4호
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• pp.839-853
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• 2021

Let 𝕽ⁿ be an Euclidean space and g : 𝕽ⁿ → 𝕽ⁿ be a monotone and continuous mapping. Suppose the convex constrained nonlinear monotone equation problem x ∈ 𝕮 s.t g(x) = 0 has a solution. In this paper, we construct an inertial-type algorithm based on the three-term derivative-free projection method (TTMDY) for convex constrained monotone nonlinear equations. Under some standard assumptions, we establish its global convergence to a solution of the convex constrained nonlinear monotone equation. Furthermore, the proposed algorithm converges much faster than the existing non-inertial algorithm (TTMDY) for convex constrained monotone equations.

• Steel and Composite Structures
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• 제11권5호
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• pp.403-421
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• 2011

In the present manuscript, geometrically nonlinear free vibration analysis of thin laminated plates resting on non-linear elastic foundations is investigated. Winkler-Pasternak type foundation model is used. Governing equations of motions are obtained using the von Karman type nonlinear theory. The method of discrete singular convolution is used to obtain the discretised equations of motion of plates. The effects of plate geometry, boundary conditions, material properties and foundation parameters on nonlinear vibration behavior of plates are presented.

• Steel and Composite Structures
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• 제32권2호
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• pp.225-237
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• 2019

In this research, the dynamic stability and nonlinear vibration behavior of a smart rotating sandwich cylindrical shell is studied. The core of the structure is a functionally graded material (FGM) which is integrated by functionally graded piezoelectric material (FGPM) layers subjected to electric field. The piezoelectric layers at the inner and outer surfaces used as actuator and sensor, respectively. By applying the energy method and Hamilton's principle, the governing equations of sandwich cylindrical shell derived based on first-order shear deformation theory (FSDT). The Galerkin method is used to discriminate the motion equations and the equations are converted to the form of the ordinary differential equations in terms of time. The perturbation method is employed to find the relation between nonlinear frequency and the amplitude of vibration. The main objective of this research is to determine the nonlinear frequencies and nonlinear vibration control by using sensor and actuator layers. The effects of geometrical parameters, power law index of core, sensor and actuator layers, angular velocity and scale transformation parameter on nonlinear frequency-amplitude response diagram and dynamic stability of sandwich cylindrical shell are investigated. The results of this research can be used to design and vibration control of rotating systems in various industries such as aircraft, biomechanics and automobile manufacturing.

• Structural Engineering and Mechanics
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• 제37권4호
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• pp.367-383
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• 2011

In this paper, nonlinear partial differential equations of motion for a hybrid composite plate subjected to initial stresses on elastic foundations are established to investigate its nonlinear vibration behavior. Pasternak foundation and Winkler foundations are used to represent the plate-foundation interaction. The initial stress is taken to be a combination of pure bending stress plus an extensional stress in the example problems. The governing equations of motion are reduced to the time-dependent ordinary differential equations by the Galerkin's method. Then, the Runge-Kutta method is used to evaluate the nonlinear vibration frequency and frequency ratio of hybrid composite plates. The nonlinear vibration behavior is affected by foundation stiffness, initial stress, vibration amplitude and the thickness ratio of layer. The effects of various parameters on the nonlinear vibration of hybrid laminated plate are investigated and discussed.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1991년도 한국자동제어학술회의논문집(국내학술편); KOEX, Seoul; 22-24 Oct. 1991
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• pp.105-107
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• 1991

A chemical process model represented by partial differential equations was studied as one of nonlinear distributed parameter control problems. Using an optimal control theory in the form of maximum principles based on nonlinear integral equations, an algorithm to solve the problem was developed and coded into a computer program.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.445-453
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• 2007

This paper deals with the approximate controllability for the nonlinear functional differential equations with time delay and studies a variation of constant formula for solutions of the given equations.

• Kyungpook Mathematical Journal
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• 제56권1호
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• pp.29-40
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• 2016

In this paper, we consider the nonlinear hyperbolic equations with forcing term. Some suffcient conditions for the oscillation are derived by using integral averaging method and a generalized Riccati technique.

• 대한수학회보
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• 제52권2호
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• pp.685-697
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• 2015

We investigate the stability of nonlinear differential equations of the form $y^{(n)}(x)=F(x,y(x),y^{\prime}(x),{\cdots},y^{(n-1)}(x))$ with a Lipschitz condition by using a fixed point method. Moreover, a Hyers-Ulam constant of this differential equation is obtained.

• 대한수학회지
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• 제45권3호
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• pp.757-769
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• 2008

This paper deals with the existence of optimal controls and maximal principles for semilinear evolution equations with the nonlinear term satisfying Lipschitz continuity. We also present the necessary conditions of optimality which are described by the adjoint state corresponding to the linear equations without a condition of differentiability for nonlinear term.

• 대한수학회보
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• 제51권6호
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• pp.1697-1710
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• 2014

The initial-boundary value problem for a class of nonlinear higher-order wave equations system with a damping and source terms in bounded domain is studied. We prove the existence of global solutions. Meanwhile, under the condition of the positive initial energy, it is showed that the solutions blow up in the finite time and the lifespan estimate of solutions is also given.