• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1583-1602
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• 2011

A special system of partial differential equations (PDEs) occur in a natural way while studying a class of irrotational inviscid fluid flow problems involving infinite channels. Certain aspects of solutions of such PDEs are analyzed in the context of flow problems involving multiple layers of fluids of different constant densities in a channel associated with arbitrary bottom topography. The whole analysis is divided into two parts-part A and part B. In part A the linearized theory is employed along with the standard Fourier analysis to understand such flow problems and physical quantities of interest are derived analytically. In part B, the same set of problems handled in part A are examined in the light of a weakly non-linear theory involving perturbation in terms of a small parameter and it is shown that the original problems can be cast into KdV type of nonlinear PDEs involving the bottom topography occurring in one of the coefficients of these equations. Special cases of bottom topography are worked out in detail and expressions for quantities of physical importance are derived.

• Proceedings of the KIEE Conference
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• 1987.11a
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• pp.82-85
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• 1987

The objective of this paper is to develop computer programs to aid in the design and analysis of control systems in which nonlinear characteristics exist. Control systems are dynamic systems, which can be described using various mathematical models. A convenient model for digital computer simulation is the state model in which described using a set of linear and non linear first order differential equations. The digital simulation was performed on a IBM PC/XT personal computer, and the computer language was BASIC. There are four possible configurations from which a user may choose. When running a program, the user is asked to enter the system parameters according to a specified control system configurations are; 1. A control system with a nonlinear element followed by a plant in a feedback configurations(NLSVF1). 2. A control system with a nonlinear device situated between two plants in a feedback configurations(NLSVF2). 3. A control system with a nonlinear element followed by a plant, followed by a the dealy in feedback configurations(TLAG). 4. A motor and load with a backlash nonlinearity between dynamic portions of the motor/load configurations (BACKLASH). The matrix from state equations are integrated using combination the trapezoidal method and fixed point iteration. Several cases which have nonlinearity were implemented on the computer and the results were discussed.

• Structural Engineering and Mechanics
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• v.4 no.4
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• pp.397-413
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• 1996

In this paper the elastic post-buckling behaviour of plates under non-uniform compressive edge stress is investigated. The compatibility differential equations is first solved analytically and then an approximate solution of the equilibrium equation is obtained using the Galerkin method. Explicit expressions are derived for the load-deflection, ultimate strength and membrane stress distributions. Analytical effective width formulations, based on the characteristics of the stress field of the buckled plate, are proposed for this general loading condition. The predicted load-deflection expression is compared with independent test results. Results are also presented detailing the load-deflection behaviour and stress distribution for various aspect ratios.

• Steel and Composite Structures
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• v.28 no.3
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• pp.349-362
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• 2018

This paper presents a semi-analytical solution for the creep analysis and life assessment of 304L austenitic stainless steel thick truncated conical shells using multilayered method based on the first order shear deformation theory (FSDT). The cone is subjected to the non-uniform internal pressure and temperature gradient. Damages are obtained in thick truncated conical shell using Robinson's linear life fraction damage rule, and time to rupture and remaining life assessment is determined by Larson-Miller Parameter (LMP). The creep response of the material is described by Norton's law. In the multilayer method, the truncated cone is divided into n homogeneous disks, and n sets of differential equations with constant coefficients. This set of equations is solved analytically by applying boundary and continuity conditions between the layers. The results obtained analytically have been compared with the numerical results of the finite element method. The results show that the multilayered method based on FSDT has an acceptable amount of accuracy when one wants to obtain radial displacement, radial, circumferential and shear stresses. It is shown that non-uniform pressure has significant influences on the creep damages and remaining life of the truncated cone.

• Journal of the Korean Society of Food Science and Nutrition
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• v.28 no.1
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• pp.178-190
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• 1999

This study was conducted to develop a simulation model for the growth dynamics of pigs and to describe quantitatively protein deposition depending on the amino acid composition of feed protein. In the model it is assumed that the essential processes that determine the utilization of feed protein in the whole body are protein synthesis, breakdown of protein, and oxidation of amino acid. Besides, it is also assumed that occurrence of protein deposition depends on genetic potential and amino acid composition of feed protein. The genetic potential for the protein deposition is the maximum capacity of protein synthesis, being dependent on the protein mass of the whole body. To describe the effect of amino acid composition of feed on the protein deposition, a factor, which consist of ten amino acid functions and lie between 0 and 1, is introduced. Accordingly a model was developed, which is described with 15 flux equations and 11 differential equations and is composed of two compartments. The model describes non linear structure of the protein utilization system of an organism, which is in non steady state. The objective function for the simulation was protein deposition(g/day) cal culated according to the empirical model, PAF(product of amino acid functions) of Menke. The mean of relative difference between the simulated protein deposition and PAF calculated values, lied in a range of 11.8%. The simulated protein synthesis and breakdown rates(g/day) in the whole body showed a parallel behavior in the course of growth.

• Smart Structures and Systems
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• v.18 no.2
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• pp.335-354
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• 2016

This contribution presents an extended one-dimensional theory for piezoelectric beam-type structures with non-ideal electrodes. For these types of electrodes the equipotential area condition is not satisfied. The main motivation of our research is originated from passive vibration control: when an elastic structure is covered by several piezoelectric patches that are linked via resistances and inductances, vibrational energy is efficiently dissipated if the electric network is properly designed. Assuming infinitely small piezoelectric patches that are connected by an infinite number of electrical, in particular resistive and inductive elements, one obtains the Telegrapher's equation for the voltage across the piezoelectric transducer. Embedding this outcome into the framework of Bernoulli-Euler, the final equations are coupled to the wave equations for the longitudinal motion of a bar and to the partial differential equations for the lateral motion of the beam. We present results for the wave propagation of a longitudinal bar for several types of electrode properties. The frequency spectra are computed (phase angle, wave number, wave speed), which point out the effect of resistive and inductive electrodes on wave characteristics. Our results show that electrical damping due to the resistivity of the electrodes is different from internal (=strain velocity dependent) or external (=velocity dependent) mechanical damping. Finally, results are presented, when the structure is excited by a harmonic single force, yielding that resistive-inductive electrodes are suitable candidates for passive vibration control that might be of great interest for practical applications in the future.

• Structural Engineering and Mechanics
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• v.58 no.6
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• pp.949-966
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• 2016

The second order analysis taking place due to non-linear behavior of the structures under the mechanical and geometric factors through implementing exact and approximate methods is an indispensible issue in the analysis of such structures. Among the exact methods is the slope-deflection method that due to its simplicity and efficiency of its relationships has always been in consideration. By solving the differential equations of the modified slope-deflection method in which the effect of axial compressive force is considered, the stiffness matrix including trigonometric entries would be obtained. The complexity of computations with trigonometric functions causes replacement with their Maclaurin expansion. In most cases only the first two terms of this expansion are used but to obtain more accurate results, more elements are needed. In this paper, the effect of utilizing higher order terms of Maclaurin expansion on reducing the number of required elements and attaining more rapid convergence with less error is investigated for the Bernoulli beam with various boundary conditions. The results indicate that when using only one element along the beam length, utilizing higher order terms in Maclaurin expansion would reduce the relative error in determining the critical buckling load and kinematic parameters in the second order analysis.

• Steel and Composite Structures
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• v.52 no.5
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• pp.557-569
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• 2024

Nonlinear internal modals interactions analysis of axially functionally graded nanorods is evaluated on the basis of nonlocal elasticity theory and Rayleigh beam model for the first time. Functionally graded materials can be determined as nonhomogeneous composites which are obtained by combining of two various materials in order to get a new ideal material. In this research, material properties of nanorods are supposed to be calmly varied along the axial direction. Hamilton's principle is used to derive the equations with consideration of Von-Kármán's geometrically nonlinearity. Harmonic Differential Quadrature (HDQ) and Multiple Scale (MS) solution techniques are used to derive an approximate-analytic solution to the linear and nonlinear free axial vibration problem of non-classical nanorods for clamped-clamped and clamped-free boundary conditions. A parametric study is carried out to indicate the effects of index of AFG, aspect ratio, mode number, internal resonances and nonlinear amplitude on nonlinear nonlocal frequencies of axially functionally graded nanorods. Also, the effects of nonlocal and nonlinear coefficients and AFG index on relationships of internal resonances have been investigated. The presented theatrical-semi analytical model has the ability to predict very suitable results for extracting the internal modal interactions in the AFG nanorod.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.6A
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• pp.617-624
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• 2009

This study deals with the free vibrations of the elastica shaped arch with linear taper. The shape of elastica is obtained from the Bernoulli-Euler beam theory. Differential equations governing free vibrations of such arch are derived and numerically solved to determine natural frequencies, in which three kinds of taper type and two kinds of end constraint, respectively, are considered. For validating the theories presented herein, the frequency parameters obtained in this study are compared to those of SAP 2000. As results of the numerical analyses, effects of end constraint, taper type, slenderness ratio and section ratio on the lowest four non-dimensional frequency parameters are extensively investigated.

• Wind and Structures
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• v.4 no.3
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• pp.177-196
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• 2001

At present the most popular turbulence models used for engineering solutions to flow problems are the $k-{\varepsilon}$ and Reynolds stress models. The shortcoming of these models based on the isotropic eddy viscosity concept and Reynolds averaging in flow fields of the type found in the field of Wind Engineering are well documented. In view of these shortcomings this paper presents the implementation of a non-linear model and its evaluation for flow around a building. Tests were undertaken using the classical bluff body shape, a surface mounted cube, with orientations both normal and skewed at $45^{\circ}$ to the incident wind. Full-scale investigations have been undertaken at the Silsoe Research Institute with a 6 m surface mounted cube and a fetch of roughness height equal to 0.01 m. All tests were originally undertaken for a number of turbulence models including the standard, RNG and MMK $k-{\varepsilon}$ models and the differential stress model. The sensitivity of the CFD results to a number of solver parameters was tested. The accuracy of the turbulence model used was deduced by comparison to the full-scale predicted roof and wake recirculation zone lengths. Mean values of the predicted pressure coefficients were used to further validate the turbulence models. Preliminary comparisons have also been made with available published experimental and large eddy simulation data. Initial investigations suggested that a suitable turbulence model should be able to model the anisotropy of turbulent flow such as the Reynolds stress model whilst maintaining the ease of use and computational stability of the two equations models. Therefore development work concentrated on non-linear quadratic and cubic expansions of the Boussinesq eddy viscosity assumption. Comparisons of these with models based on an isotropic assumption are presented along with comparisons with measured data.