• 제어로봇시스템학회논문지
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• 제6권7호
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• pp.523-528
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• 2000

In this short note the characteristics of a nonlinear system of which the state trajectories are oscillating in the phase plane are overviewed. The physical concept of stuck and sliding patch phenomena are also introduced by adding some switching functions and their stability on the sliding patches are analyzed by using the Lyapunov stability theory and Frobenius theorem.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.15-33
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• 2024

In this article, we considered a class of nonlinear variational hemivariational inequality problems and investigated a gap function and regularized gap function for the problems. We discussed the global error bounds for such inequalities in terms of gap function and regularized gap functions by utilizing the Clarke generalized gradient, relaxed monotonicity, and relaxed Lipschitz continuous mappings. Finally, as applications, we addressed an application to non-stationary non-smooth semi-permeability problems.

• Advances in nano research
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• 제9권1호
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• pp.47-58
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• 2020

The present paper deals with analyzing nonlinear forced vibrational behaviors of nonlocal multi-phase piezo-magnetic beam rested on elastic substrate and subjected to an excitation of elliptic type. The applied elliptic force may be presented as a Fourier series expansion of Jacobi elliptic functions. The considered multi-phase smart material is based on a composition of piezoelectric and magnetic constituents with desirable percentages. Additionally, the equilibrium equations of nanobeam with piezo-magnetic properties are derived utilizing Hamilton's principle and von-Kármán geometric nonlinearity. Then, an exact solution based on Jacobi elliptic functions has been provided to obtain nonlinear vibrational frequencies. It is found that nonlinear vibrational behaviors of the nanobeam are dependent on the magnitudes of induced electrical voltages, magnetic field intensity, elliptic modulus, force magnitude and elastic substrate parameters.

• Nonlinear Functional Analysis and Applications
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• 제26권1호
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• pp.71-81
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• 2021

The main object of this present paper is to study some majorization problems for certain classes of analytic functions defined by means of q-calculus operator associated with exponential function.

• Nonlinear Functional Analysis and Applications
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• 제28권1호
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• pp.81-93
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• 2023

By utilizing a certain Libera integral operator considered on analytic multivalent functions in the unit disk U. Using the hypergeometric function and the Libera integral operator, we included a new convolution operator that expands on some previously specified operators in U, which broadens the scope of certain previously specified operators. We introduced and investigated the properties of new subclasses of functions f (z) ∈ A_p using this operator.

• 한국자동차공학회논문집
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• 제13권4호
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• pp.105-112
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• 2005

Analyses of dynamic models which were one and two degrees of freedom, and had the nonlinear springs and dampings with certain polynomial functions were performed from SIMULINK in MATLAB. Those consisted of 12 programs and were built on the basis of the preceding programs fur the linear dynamic simulations. However the programs for the nonlinear simulations were quite different from those f3r the linear ones, and showed the results of the analyses in real time with animating. It was found that the programs would help us to solve any kind of nonlinear dynamic simulation with one and two degrees of freedom. Especially, the simulations for 1 DOF system with cubic nonlinear spring farce showed the results for Duffing's equation, of which phenomena were jump-up and jump-down. It will be applied to the dynamic simulation of the car seat vibration with a passenger, of which model has the equivalent nonlinear springs and is two degrees of freedom.

• Journal of Mechanical Science and Technology
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• 제17권10호
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• pp.1496-1506
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• 2003

The SIMP (solid isotropic material with penalization) approach is perhaps the most popular density variable relaxation method in topology optimization. This method has been very successful in many applications, but the optimization solution convergence can be improved when new variables, not the direct density variables, are used as the design variables. In this work, we newly propose S-shape functions mapping the original density variables nonlinearly to new design variables. The main role of S-shape function is to push intermediate densities to either lower or upper bounds. In particular, this method works well with nonlinear mathematical programming methods. A method of feasible directions is chosen as a nonlinear mathematical programming method in order to show the effects of the S-shape scaling function on the solution convergence.

• 대한수학회보
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• 제57권4호
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• pp.1061-1073
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• 2020

In this paper, the expressions of meromorphic solutions of the following nonlinear complex differential equation of the form $$f^n+Qd(z,f)=\sum\limits_{i=1}^{3}pi(z)e^{{\alpha}_i(z)}$$ are studied by using Nevanlinna theory, where n ≥ 5 is an integer, Q_d(z, f) is a differential polynomial in f of degree d ≤ n - 4 with rational functions as its coefficients, p₁(z), p₂(z), p₃(z) are non-vanishing rational functions, and α₁(z), α₂(z), α₃(z) are nonconstant polynomials such that α'₁(z), α'₂(z), α'₃(z) are distinct each other. Moreover, examples are given to illustrate the accuracy of the condition.

• 대한전기학회논문지
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• 제43권6호
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• pp.991-1000
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• 1994

To control nonlinear systems adaptively, we improve learning speed of neural networks and present a novel control algorithm characterized by compensation of control inputs. In an error-backpropagation algorithm for tranining multilayer neural networks(MLNN's) the effect of the slope of activation functions on learning performance is investigated and the learning speed of neural networks is improved by auto-adjusting the slope of activation functions. The control system is composed of two MLNN's, one for control and the other for identification, with the weights initialized by off-line training. The control algoritm is modified by a control strategy which compensates the control error induced by the indentification error. Computer simulations show that the proposed control algorithm is efficient in controlling a nonlinear system with abruptly changing parameters.

• Journal of Advanced Research in Ocean Engineering
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• 제2권2호
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• pp.81-85
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• 2016

Nonlinear wave loads can lead to resonant responses of offshore structures in sum or difference frequencies. In this study, the roll motion of an FPSO with a low natural frequency is simulated in the time domain. To generate the time signals of wave loads, the quadratic transfer functions of the second-order excitations are calculated in the frequency domain. The equations of motions based on the time memory functions are used to evaluate the roll responses in irregular waves. The roll damping in empirical form is accounted for in the simulation.