• Structural Engineering and Mechanics
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• v.64 no.2
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• pp.259-270
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• 2017

The stochastic vibration response of the sandwich beam with the nonlinear adjustable visco-elastomer core and supported mass under stochastic support motion excitations is studied. The nonlinear dynamic properties of the visco-elastomer core are considered. The nonlinear partial differential equations for the horizontal and vertical coupling motions of the sandwich beam are derived. An analytical solution method for the stochastic vibration response of the nonlinear sandwich beam is developed. The nonlinear partial differential equations are converted into the nonlinear ordinary differential equations representing the nonlinear stochastic multi-degree-of-freedom system by using the Galerkin method. The nonlinear stochastic system is converted further into the equivalent quasi-linear system by using the statistic linearization method. The frequency-response function, response spectral density and mean square response expressions of the nonlinear sandwich beam are obtained. Numerical results are given to illustrate new stochastic vibration response characteristics and response reduction capability of the sandwich beam with the nonlinear visco-elastomer core and supported mass under stochastic support motion excitations. The influences of geometric and physical parameters on the stochastic response of the nonlinear sandwich beam are discussed, and the numerical results of the nonlinear sandwich beam are compared with those of the sandwich beam with linear visco-elastomer core.

• Bulletin of the Korean Mathematical Society
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• v.41 no.3
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• pp.559-571
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• 2004

The aim of the present paper is to establish some nonlinear integral inequalities in two independent variables which provide explicit bounds on unknown functions. The inequalities given here can be used as tools in the qualitative theory of certain partial differential equations.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.425-441
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• 2023

This paper is concerned with the value distribution for meromorphic solutions f of a class of nonlinear partial differential-difference equation of first order with small coefficients. We show that such solutions f are uniquely determined by the poles of f and the zeros of f - c, f - d (counting multiplicities) for two distinct small functions c, d.

• Korean Journal of Mathematics
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• v.23 no.1
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• pp.11-27
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• 2015

Nonlinear partial differential equations are more suitable to model many physical phenomena in science and engineering. In this paper, we consider three nonlinear partial differential equations such as Novikov equation, an equation for surface water waves and the Geng-Xue coupled equation which serves as a model for the unidirectional propagation of the shallow water waves over a at bottom. The main objective in this paper is to apply the generalized Riccati equation mapping method for obtaining more exact traveling wave solutions of Novikov equation, an equation for surface water waves and the Geng-Xue coupled equation. More precisely, the obtained solutions are expressed in terms of the hyperbolic, the trigonometric and the rational functional form. Solutions obtained are potentially significant for the explanation of better insight of physical aspects of the considered nonlinear physical models.

• Geomechanics and Engineering
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• v.32 no.2
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• pp.125-135
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• 2023

Nonlinear vibration analysis of composite beam reinforced by carbon nanotubes resting on the nonlinear viscoelastic foundation is investigated in this study. The material properties of the composite beam is considered as a polymeric matrix by reinforced carbon nanotubes according to different distributions. With using Hamilton's principle, the governing nonlinear partial differential equations are derived based on the Euler-Bernoulli beam theory. In the nonlinear kinematic assumption, the Von Kármán nonlinearity is used. The Galerkin's decomposition technique is utilized to discretize the governing nonlinear partial differential equation to nonlinear ordinary differential equation and then is solved by using of multiple time scale method. The nonlinear natural frequency and the nonlinear free response of the system is obtained. In addition, the effects of different patterns of reinforcement, linear and nonlinear damping coefficients of the viscoelastic foundation on the nonlinear vibration responses and phase trajectory of the carbon nanotube reinforced composite beam are investigated.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.35-45
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• 2024

In this paper, we study the existence and multiplicity of nontrivial solutions for a p-Kirchhoff equation involving critical Sobolev-Hardy exponent by using variational methods and we need to estimate the energy levels.

• Structural Engineering and Mechanics
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• v.25 no.5
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• pp.501-518
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• 2007

In this work, a new approach is developed for dynamic analysis of a composite beam with an interply crack, based on finite element solution of partial differential equations with the use of the COMSOL Multiphysics package, allowing for fast and simple change of geometric characteristics of the delaminated area. The use of COMSOL Multiphysics package facilitates automatic mesh generation, which is needed if the problem has to be solved many times with different crack lengths. In the model, a physically impossible interpenetration of the crack faces is prevented by imposing a special constraint, leading to taking account of a force of contact interaction of the crack faces and to nonlinearity of the formulated boundary value problem. The model is based on the first order shear deformation theory, i.e., the longitudinal displacement is assumed to vary linearly through the beam's thickness. The shear deformation and rotary inertia terms are included into the formulation, to achieve better accuracy. Nonlinear partial differential equations of motion with boundary conditions are developed and written in the format acceptable by the COMSOL Multiphysics package. An example problem of a clamped-free beam with a piezoelectric actuator is considered, and its finite element solution is obtained. A noticeable difference of forced vibrations of the delaminated and undelaminated beams due to the contact interaction of the crack's faces is predicted by the developed model.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.1
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• pp.83-102
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• 2015

The present paper analyses the radiation effects of mass transfer on steady nonlinear MHD boundary layer flow of a viscous incompressible fluid over a nonlinear porous stretching surface in a porous medium in presence of heat generation. The liquid metal is assumed to be gray, emitting, and absorbing but non-scattering medium. Governing nonlinear partial differential equations are transformed to nonlinear ordinary differential equations by utilizing suitable similarity transformation. The resulting nonlinear ordinary differential equations are solved numerically using Runge-Kutta fourth order method along with shooting technique. Comparison with previously published work is obtained and good agreement is found. The effects of various governing parameters on the liquid metal fluid dimensionless velocity, dimensionless temperature, dimensionless concentration, skin-friction coefficient, Nusselt number and Sherwood number are discussed with the aid of graphs.

• Nuclear Engineering and Technology
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• v.49 no.8
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• pp.1680-1688
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• 2017

In this study, analysis is performed on entropy generation during cilia transport of water based titanium dioxide nanoparticles in the presence of viscous dissipation. Moreover, thermal heat flux is considered at the surface of a channel with ciliated walls. Mathematical formulation is constructed in the form of nonlinear partial differential equations. Making use of suitable variables, the set of partial differential equations is reduced to coupled nonlinear ordinary differential equations. Closed form exact solutions are obtained for velocity, temperature, and pressure gradient. Graphical illustrations for emerging flow parameters, such as Hartmann number (Ha), Brinkmann number (Br), radiation parameter (Rn), and flow rate, have been prepared in order to capture the physical behavior of these parameters. The main goal (i.e., the minimizing of entropy generation) of the second law of thermodynamics can be achieved by decreasing the magnitude of Br, Ha and ${\Lambda}$ parameters.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.1
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• pp.43-50
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• 2014

In this paper we discussed Euler-Maruyama method for stochastic differential equations with jump diffusion. We give a convergence result for Euler-Maruyama where the coefficients of the stochastic differential equation are locally Lipschitz and the pth moments of the exact and numerical solution are bounded for some p > 2.