• Smart Structures and Systems
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• 제23권6호
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• pp.641-651
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• 2019

The stochastic stability control of the parameter-excited vibration of an inclined stay cable with multiple modes coupling under random and periodic combined support disturbances is studied by using the direct eigenvalue analysis approach based on the response moment stability, Floquet theorem, Fourier series and matrix eigenvalue analysis. The differential equation with time-varying parameters for the transverse vibration of the inclined cable with control under random and deterministic support disturbances is derived and converted into the randomly and deterministically parameter-excited multi-degree-of-freedom vibration equations. As the stochastic stability of the parameter-excited vibration is mainly determined by the characteristics of perturbation moment, the differential equation with only deterministic parameters for the perturbation second moment is derived based on the $It{\hat{o}}$ stochastic differential rule. The stochastically and deterministically parameter-excited vibration stability is then determined by the deterministic parameter-varying response moment stability. Based on the Floquet theorem, expanding the periodic parameters of the perturbation moment equation and the periodic component of the characteristic perturbation moment expression into the Fourier series yields the eigenvalue equation which determines the perturbation moment behavior. Thus the stochastic stability of the parameter-excited cable vibration under the random and periodic combined support disturbances is determined directly by the matrix eigenvalues. The direct eigenvalue analysis approach is applicable to the stochastic stability of the control cable with multiple modes coupling under various periodic and/or random support disturbances. Numerical results illustrate that the multiple cable modes need to be considered for the stochastic stability of the parameter-excited cable vibration under the random and periodic support disturbances, and the increase of the control damping rather than control stiffness can greatly enhance the stochastic stability of the parameter-excited cable vibration including the frequency width increase of the periodic disturbance and the critical value increase of the random disturbance amplitude.

• Korean Journal of Mathematics
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• 제28권2호
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• pp.223-240
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• 2020

The paper is concerned with periodic linear evolution equations of the form x"(t) = A(t)x(t)+f(t), where A(t) is a family of (unbounded) linear operators in a Banach space X, strongly and periodically depending on t, f is an almost (or asymptotic) almost periodic function. We study conditions for this equation to have almost periodic solutions on ℝ as well as to have asymptotic almost periodic solutions on ℝ⁺. We convert the second order equation under consideration into a first order equation to use the spectral theory of functions as well as recent methods of study. We obtain new conditions that are stated in terms of the spectrum of the monodromy operator associated with the first order equation and the frequencies of the forcing term f.

• 대한수학회지
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• 제47권3호
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• pp.573-583
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• 2010

In this paper, the existence of anti-periodic solutions for higher-order nonlinear ordinary differential equations is studied by using degree theory and some known results are improved to some extent.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.243-256
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• 2010

This paper is concerned with the neutral impulsive functional differential equations $$\{{x'(t)\;+\;a(t)x(t)\;=\;f(t,\;x(t\;-\;\tau(t),\;x'(t\;-\;\delta(t))),\;a.e.\;t\;{\in}\;R, \atop {\Delta}x(t_k)\;=\;b_kx(t_k),\;k\;{\in}\;Z.$$ Sufficient conditions for the existence of at least three positive T-periodic solution are established. Our results generalize and improve the known ones. Some examples are presented to illustrate the main results.

• 충청수학회지
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• 제34권3호
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• pp.221-234
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• 2021

We introduce high-order Hopfield neural networks with Leakage delays. Furthermore, we study the uniqueness and existence of Hopfield artificial neural networks having the weighted pseudo almost periodic forcing terms on finite delay. Our analysis is based on the differential inequality techniques and the Banach contraction mapping principle.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제5권2호
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• pp.1-6
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• 2001

Multiplicity of nonlinear second order nonlinear ordinary differential equations will be discussed.

• 대한수학회보
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• 제50권5호
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• pp.1415-1432
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• 2013

We consider the value distribution of a class of the functions analytic in the exterior of a disc and their applications to complex oscillation theory of differential equations with periodic coefficients in the complex plane.

• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.217-222
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• 2003

In this paper, we consider the fuzzy differential equations (equation omitted) where F(t, x(t)) is a continuous fuzzy mapping on [0, $\infty$) ${\times}$ E$\^$n/. The purpose of this paper is to prove that the solution ${\Phi}$(t) of the fuzzy differential equations is equiasymptotically stable in the large and uniformly asymptotically stable in the large.

• 대한수학회논문집
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• 제32권2호
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• pp.457-466
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• 2017

We study the existence and uniqueness of S-asymptotically ${\omega}-periodic$ mild solutions for some partial functional integrodifferential equations with infinite delay and nonlocal conditions.

• 대한수학회보
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• 제43권2호
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• pp.253-263
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• 2006

In this paper we introduce a new concept, a 'periodicizing' function for the linear differential equation with the periodic forcing function. Moreover, we construct this function, which is closely related with the solution of a difference equation and an indefinite sum. Using this function, we can obtain a representation of solutions from which we see immediately the asymptotic behavior of the solutions.