• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.4
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• pp.245-275
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• 2017

The present investigation deals, Dufour and heat source effects on radiative MHD slip flow of a viscous fluid in a parallel porous plate channel in presence of chemical reaction. The non-linear coupled partial differential equations are solved by using two term perturbation technique subject to physically appropriate boundary conditions. The numerical values of the fluid velocity, temperature and concentration are displayed graphically whereas those of shear stress, rate of heat transfer and rate of mass transfer at the plate are presented in tabular form for various values of pertinent flow parameters. By increasing the slip parameter at the cold wall the velocity increases whereas the effect is totally reversed in the case of shear stress at the cold wall. It is observed that the effect of Dufour and heat source parameters decreases the velocity and temperature profiles.

• Journal of the Korean Physical Society
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• v.73 no.9
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• pp.1219-1224
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• 2018

We investigate the evolutionary dynamics and the phase transitions of the island model which consists of subdivided populations of individuals confined to two islands. In the island model, the population is subdivided so that migration acts to determine the evolutionary dynamics along with selection and genetic drift. The individuals are assumed to be haploid and to be one of two species, X or Y. They reproduce according to their fitness values, die at random, and migrate between the islands. The evolutionary dynamics of an individual based model is formulated in terms of a master equation and is approximated by using the diffusion method as the multidimensional Fokker-Planck equation (FPE) and the coupled non-linear stochastic differential equations (SDEs) with multiplicative noise. We analyze the infinite population limit to find the phase transitions from the monomorphic state of one type to the polymorphic state to the monomorphic state of the other type as we vary the ratio of the fitness values in two islands and complete the phase diagram of our island model.

• Advances in nano research
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• v.16 no.6
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• pp.579-591
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• 2024

This study explained the effects of radiation, magnetic field, and nanoparticle shape on the peristaltic flow of an Upper-Convected Maxwell nanofluid through a porous medium in an asymmetric channel for a better understanding of cooling and heating mechanisms in the presence of magnetic fields. These phenomena are modeled mathematically as a system of non-linear differential equations, that are solved under long-wavelength approximation and low Reynolds number conditions using the perturbation method. The results for nanofluid and temperature described the behavior of the pumping characteristics during their interaction with (the vertical position, thermal radiation, the shape of the nanoparticle, and the magnetic field) analytically and explained graphically. Also, the combined effects of thermal radiation parameters and some physical parameters on pressure rise, pressure gradient, velocity, and heat distribution are pointed out. Qualitatively, a reverse velocity appears with combined high radiation and Grashof number or combined high radiation and low volume flow rate. At high radiation, the spherical nanoparticle shape has the greatest effect on heat distribution.

• Structural Engineering and Mechanics
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• v.22 no.3
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• pp.371-399
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• 2006

The theoretical background and capabilities of the developed program, SAR-CWF, for stochastic analysis of 3D reinforced-concrete shear wall-frame structures subject to seismic excitations is presented. Incremental stiffness and strength properties of system members are modeled by extended Roufaiel-Meyer hysteretic relation for bending while shear deformations for walls by Origin-Oriented hysteretic model. For the critical height of shear-walls, division to sub-elements is performed. Different yield capacities with respect to positive and negative bending, finite extensions of plastic hinges and P-${\delta}$ effects are considered while strength deterioration is controlled by accumulated hysteretic energy. Simulated strong motions are obtained from a Gaussian white-noise filtered through Kanai-Tajimi filter. Dynamic equations of motion for the system are formed according to constitutive and compatibility relations and then inserted into equivalent It$\hat{o}$-Stratonovich stochastic differential equations. A system reduction scheme based on the series expansion of eigen-modes of the undamaged structure is implemented. Time histories of seismic response statistics are obtained by utilizing the computer programs developed for different types of structures.

• Kyungpook Mathematical Journal
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• v.61 no.4
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• pp.831-843
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• 2021

In this paper we look at the three dimensional stagnation point flow problem over a rough rotating disk. We study the theoretical behaviour of the stagnation point flow, or forced flow, in the presence of a slip factor in which convective instability stationary modes appear. We make a numerical investigation of the effects of slip on the behaviour of the flow components of the stagnation point flow where the disk is rough. We provide, for the first time in the literature, a complete convective instability analysis and an energy analysis. Suitable similarity transformations are used to reduce the Navier-Stokes equations and the continuity equation into a system of highly non-linear coupled ordinary differential equations, and these are solved numerically subject to suitable boundary conditions using the bvp4c function of MATLAB. The convective instability analysis and the energy analysis are performed using the Chebyshev spectral method in order to obtain the neutral curves and the energy bars. We observe that the roughness of the disk has a destabilising effect on both Type-I and Type-II instability modes. The results obtained will be prominently treated as benchmarks for our future studies on stagnation flow.

• Structural Engineering and Mechanics
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• v.49 no.4
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• pp.427-448
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• 2014

At present, the time of easy oil and gas is over. Now, the largest part of fossil fuels is concentrated in the deepest levels of tectonic structures and in the sea shelves. One of the most cumbersome operations of their extraction is the bore-hole drilling. In connection with austere tectonic and climate conditions, their drivage every so often is associated with great and diversified technological difficulties causing emergencies on frequent occasions. As a rule, they are linked with drill string accidents. A key role in prediction of these situations should play methods of theoretical modelling. For this reason, there is a growing need for development and implementation of new numerical methods for computer simulation of critical and post-critical behavior of drill strings (DSs). In this paper, the processes of non-linear deforming of a DS in cylindrical cavity of a deep bore-hole are considered. On the basis of the theory of curvilinear flexible rods, non-linear constitutive differential equations are deduced. The effects of the longitudinal non-uniform preloading, action of torque and interaction between the DS and the bore-hole surface are taken into account. Owing to the use of curvilinear coordinates in the constraining cylindrical surface and a specially chosen concomitant reference frame, it became possible to separate the desired variables and to reduce the total order of the equation system. To solve it, the method of continuation the solution by parameter and the transfer matrix technique are applied. As a result of the completed numerical analysis, the critical states of the DS loading in the cylindrical channels of inclined bore-holes are found. It is shown that the modes of the post-critical deforming of the DS are associated with its irregular spiral curving prevailing in the zone of bottom-hole-assembly. The possibility of invariant state generation during post-critical deforming is established, condition of its bifurcation is formulated. It is shown that infinite variety of loads can correspond to one geometrical configuration of the DS. They differ each from other by contact force functions.

• Structural Engineering and Mechanics
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• v.38 no.1
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• pp.39-63
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• 2011

Referring to the formulation of physical stochastic optimal control of structures and the scheme of optimal polynomial control, a nonlinear stochastic optimal control strategy is developed for a class of structural systems with hysteretic behaviors in the present paper. This control strategy provides an amenable approach to the classical stochastic optimal control strategies, bypasses the dilemma involved in It$\hat{o}$-type stochastic differential equations and is applicable to the dynamical systems driven by practical non-stationary and non-white random excitations, such as earthquake ground motions, strong winds and sea waves. The newly developed generalized optimal control policy is integrated in the nonlinear stochastic optimal control scheme so as to logically distribute the controllers and design their parameters associated with control gains. For illustrative purposes, the stochastic optimal controls of two base-excited multi-degree-of-freedom structural systems with hysteretic behavior in Clough bilinear model and Bouc-Wen differential model, respectively, are investigated. Numerical results reveal that a linear control with the 1st-order controller suffices even for the hysteretic structural systems when a control criterion in exceedance probability performance function for designing the weighting matrices is employed. This is practically meaningful due to the nonlinear controllers which may be associated with dynamical instabilities being saved. It is also noted that using the generalized optimal control policy, the maximum control effectiveness with the few number of control devices can be achieved, allowing for a desirable structural performance. It is remarked, meanwhile, that the response process and energy-dissipation behavior of the hysteretic structures are controlled to a certain extent.

• Wind and Structures
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• v.29 no.6
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• pp.457-469
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• 2019

In this paper, a numerical solution is presented for supersonic flutter analysis of cantilever non-symmetric functionally graded (FG) sandwich plates. The plate is considered to be composed of two different functionally graded face sheets and an isotropic homogeneous core made of ceramic. Based on the first order shear deformation theory (FSDT) and linear piston theory, the set of governing equations and boundary conditions are derived. Dimensionless form of the governing equations and boundary conditions are derived and solved numerically using generalized differential quadrature method (GDQM) and critical velocity and flutter frequencies are calculated. For various values of the yaw angle, effect of different parameters like aspect ratio, thickness of the plate, power law indices and thickness of the core on the flutter boundaries are investigated. Numerical examples show that wings and tail fins with larger length and shorter width are more stable in supersonic flights. It is concluded for FG sandwich plates made of Al-Al₂O₃ that increase in volume fraction of ceramic (Al₂O₃) increases aeroelastic stability of the plate. Presented study confirms that improvement of aeroelastic behavior and weight of wings and tail fins of aircrafts are not consistent items. It is shown that value of the critical yaw angle depends on aspect ratio of the plate and other parameters including thickness and variation of properties have no considerable effect on it. Results of this paper can be used in design and analysis of wing and tail fin of supersonic airplanes.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.22 no.1
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• pp.9-17
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• 2021

Curved beams are increasingly used in buildings, vehicles, ships, and aircraft, which has resulted in considerable effort being directed toward developing an accurate method for analyzing the dynamic behavior of such structures. The stability behavior of elastic circular arches has been the subject of a large number of investigations. One of the efficient procedures for the solution of ordinary differential equations or partial differential equations is the differential quadrature method DQM. This method has been applied to a large number of cases to overcome the difficulties of the complex computer algorithms, as well as excessive use of storage due to conditions of non-linear geometries, loadings, or material properties. This study uses DQM to analyze the in-plane vibration of the circular arches considering the effects of midsurface extension and rotatory inertia. Fundamental frequency parameters are calculated for the member with various parameter ratios, boundary conditions, and opening angles. The solutions from DQM are compared with exact solutions or other numerical solutions for cases in which they are available and given to analyze the effects of midsurface extension and rotatory inertia on the frequency parameters of the circular arches.

• Smart Structures and Systems
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• v.18 no.6
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• pp.1125-1143
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• 2016

Forced vibration analysis of a simple supported viscoelastic nanobeam is studied based on modified couple stress theory (MCST). The nanobeam is excited by a transverse triangular force impulse modulated by a harmonic motion. The elastic medium is considered as Winkler-Pasternak elastic foundation.The damping effect is considered by using the Kelvin-Voigt viscoelastic model. The inclusion of an additional material parameter enables the new beam model to capture the size effect. The new non-classical beam model reduces to the classical beam model when the length scale parameter is set to zero. The considered problem is investigated within the Timoshenko beam theory by using finite element method. The effects of the transverse shear deformation and rotary inertia are included according to the Timoshenko beam theory. The obtained system of differential equations is reduced to a linear algebraic equation system and solved in the time domain by using Newmark average acceleration method. Numerical results are presented to investigate the influences the material length scale parameter, the parameter of the elastic medium and aspect ratio on the dynamic response of the nanobeam. Also, the difference between the classical beam theory (CBT) and modified couple stress theory is investigated for forced vibration responses of nanobeams.