• Structural Engineering and Mechanics
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• v.53 no.3
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• pp.537-573
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• 2015

Multiple-step beams carrying intermediate lumped masses with/without rotary inertias are widely used in engineering applications, but in the literature for free vibration analysis of such structural systems; Bernoulli-Euler Beam Theory (BEBT) without axial force effect is used. The literature regarding the free vibration analysis of Bernoulli-Euler single-span beams carrying a number of spring-mass systems, Bernoulli-Euler multiple-step and multi-span beams carrying multiple spring-mass systems and multiple point masses are plenty, but that of Timoshenko multiple-step beams carrying intermediate lumped masses and/or rotary inertias with axial force effect is fewer. The purpose of this paper is to utilize Numerical Assembly Technique (NAT) and Differential Transform Method (DTM) to determine the exact natural frequencies and mode shapes of the axial-loaded Timoshenko multiple-step beam carrying a number of intermediate lumped masses and/or rotary inertias. The model allows analyzing the influence of the shear and axial force effects, intermediate lumped masses and rotary inertias on the free vibration analysis of the multiple-step beams by using Timoshenko Beam Theory (TBT). At first, the coefficient matrices for the intermediate lumped mass with rotary inertia, the step change in cross-section, left-end support and right-end support of the multiple-step Timoshenko beam are derived from the analytical solution. After the derivation of the coefficient matrices, NAT is used to establish the overall coefficient matrix for the whole vibrating system. Finally, equating the overall coefficient matrix to zero one determines the natural frequencies of the vibrating system and substituting the corresponding values of integration constants into the related eigenfunctions one determines the associated mode shapes. After the analytical solution, an efficient and easy mathematical technique called DTM is used to solve the differential equations of the motion. The calculated natural frequencies of Timoshenko multiple-step beam carrying intermediate lumped masses and/or rotary inertias for the different values of axial force are given in tables. The first five mode shapes are presented in graphs. The effects of axial force, intermediate lumped masses and rotary inertias on the free vibration analysis of Timoshenko multiple-step beam are investigated.

• Structural Engineering and Mechanics
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• v.17 no.5
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• pp.671-690
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• 2004

A meshless method with novel variation of point collocation by finite mixture approximation is developed in this paper, termed the meshless finite mixture (MFM) method. It is based on the finite mixture theorem and consists of two or more existing meshless techniques for exploitation of their respective merits for the numerical solution of partial differential boundary value (PDBV) problems. In this representation, the classical reproducing kernel particle and differential quadrature techniques are mixed in a point collocation framework. The least-square method is used to optimize the value of the weight coefficient to construct the final finite mixture approximation with higher accuracy and numerical stability. In order to validate the developed MFM method, several one- and two-dimensional PDBV problems are studied with different mixed boundary conditions. From the numerical results, it is observed that the optimized MFM weight coefficient can improve significantly the numerical stability and accuracy of the newly developed MFM method for the various PDBV problems.

• Journal of Internet Computing and Services
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• v.22 no.2
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• pp.19-27
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• 2021

Fireworks Algorithm (FWA) is a new heuristic swarm intelligent algorithm inspired by the natural phenomenon of the fireworks explosion. Though it is an effective algorithm for solving optimization problems, FWA has a slow convergence rate and less information sharing between individuals. In this paper, we improve the FWA. Firstly, explosion operator and explosion amplitude are analyzed in detail. The coefficient of explosion amplitude and explosion operator change dynamically with iteration to balance the exploitation and exploration. The convergence performance of FWA is improved. Secondly, differential evolution and commensal learning (CDE) significantly increase the information sharing between individuals, and the diversity of fireworks is enhanced. Comprehensive experiment and comparison with CDE, FWA, and VACUFWA for the 13 benchmark functions show that the improved algorithm was highly competitive.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.4
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• pp.1501-1509
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• 1996

Differential pressure devices such as an orifice and Venturi are widely used in the measurement of flow rate of fluid mainly due to cost effectiveness and easy installation. In the current study, the viscoelastic effect on discharge and loss coefficients of those flow meters were investigated experimentally. Aqueous solutions of Polyacrylamide (200, 500, and 800 ppm) as viscoelastic fluids were used. Discharge coefficient of an orifice for viscoelastic fluids increased significantly up to approximately 15-20% when compared with that for water, while loss coefficient decreased up to 10-25% depending on the diameter ratio, .betha.. Also, pressure recovery for viscoelastic fluids was extended much longer than that for water. On the other hand, discharge and loss coefficients of Venturi for viscoelastic fluids were found to be strongly dependent on the Reynolds number. In both flow meters, the concentration effect for discharge and loss coefficients was not observed at more over than 200 ppm of aqueous solution. Conclusively, orifice and Venturi flow meters should be calibrated very carefully in the flow rate measurement for viscoelastic fluids.

• School Mathematics
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• v.19 no.4
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• pp.639-661
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• 2017

The purpose of this study is to investigate the relationship between the distance function average speed and the speed function. Particularly, in this study, we investigate the process of constructing the speed function in the distance function (irrational function, exponential function) which is difficult to weaken the argument in the denominator. In this process, students showed various anxieties and expressions about the procedural knowledge that they constructed first. In particular, if student B can not explain all the knowledge he already knows in this process, he showed his reflection on the process of calculating the differential coefficient. This study adds an understanding of the calculation method of students in differential coefficient learning. In addition, it is meaningful that the students who construct procedural knowledge at the time of calculating the differential coefficient have thought about how to provide opportunities to reflect on the procedure they constructed.

• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.807-816
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• 2014

The asymptotic behavior of solutions of Lyapunov type matrix Volterra integro differential equation, in which the coefficient matrices are not stable, is studied by the method of reduction.

• Steel and Composite Structures
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• v.41 no.6
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• pp.821-829
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• 2021

Nonlinear dynamic response of a sandwich beam considering porous core and nano-composite face sheet on nonlinear viscoelastic foundation with temperature-variable material properties is investigated in this research. The Hamilton's principle and beam theory are used to drive the equations of motion. The nonlinear differential equations of sandwich beam respect to time are obtained to solve nonlinear differential equations by Homotopy perturbation method (HPM). The effects of various parameters such as linear and nonlinear damping coefficient, linear and nonlinear spring constant, shear constant of Pasternak type for elastic foundation, temperature variation, volume fraction of carbon nanotube, porosity distribution and porosity coefficient on nonlinear dynamic response of sandwich beam are presented. The results of this paper could be used to analysis of dynamic modeling for a flexible structure in many industries such as automobiles, Shipbuilding, aircrafts and spacecraft with solar easured at current time step and the velocity and displacement were estimated through linear integration.

• Journal of the Korean Society of Clothing and Textiles
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• v.25 no.3
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• pp.560-568
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• 2001

The aim of the present study was to measure intra-individual consistency in clothing and fabric evaluation and to examine its relation to the ratings. A sample of 93 female and 97 male university students rated clothing of 4 styles of daytime wear and 2 fabrics on 15 pairs of polar adjectives twice in 7-days interval. Correlation coefficients between the two ratings for each subject, intra-individual consistency in the evaluation, ranged from -0.12 to 0.89 and mean coefficient was 0.63 of female and -0.01 to 0.78 and mean coefficient was 0.54 of male. Based on the coefficients, the subjects were classified into three groups: high, medium, and low intra-individual consistency. Analysis of variance of mean ratings by the three groups revealed that significant difference existed in 24% of female and 23% of male in 90 combinations of 6 clothing and 15 semantic differential scales. Female of subjects with high intra-individual consistency were most likely definite to evaluate clothing, whereas the ones with low were least. But male subjects were not definite. Mean correlation coefficients for style evaluation subscales of female was 0.39, but male was 0.44. Among the semantic differential scales, high stability in the two ratings was observed for the synthetic clothing evaluation. Correlation coefficients for each clothing obtained from the mean score of the subjects in each semantics differential scale were around 0.98, including that the mean scores of the subjects in each scale could yield excellent stability in clothing evaluation.

• Journal of the Korean Society of Safety
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• v.25 no.3
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• pp.15-21
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• 2010

A differential case equipped with LSD(limited slip differential) has several advantages over a normal type for rear wheel drive vehicles. Specially, the torque distribution can be done between left and right drive wheel in the state of limited slip differential. Also although LSD types are very various according to operating type, medium and torque distribution, a multi-clutch type is generally applied to rear wheel drive vehicles. So, this study presents the analysis of design parameters for development of a friction plate for multi-clutch type LSD using vehicle road test, the simulation of analytical model and the development of vehicle dynamics model by a benchmark product. According to this investigation, the design parameters which are pre-load of coil spring, friction plate and contact area quantity, friction coefficient and TBR(torque bias ratio) for a friction plate are derived from experiment and simulation and consequently, vehicle dynamics model has been constructed for the development of friction plate for multi-clutch type LSD.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1143-1155
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• 2011

In this paper, we shall establish a new theorem on the existence and uniqueness of the solution to a backward doubly stochastic differential equations under a weaker condition than the Lipschitz coefficient. We also show a comparison theorem for this kind of equations.