• Structural Engineering and Mechanics
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• 제58권6호
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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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• 제16권1호
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• pp.45-58
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• 2014

EC3 provides several methodologies for the stability verification of members and frames. However, when dealing with the verification of non-uniform members in general, with tapered cross-section, irregular distribution of restraints, non-linear axis, castellated, etc., several difficulties are noted. Because there are yet no guidelines to overcome any of these issues, safety verification is conservative. In recent research from the authors of this paper, an Ayrton-Perry based procedure was proposed for the flexural buckling verification of web-tapered columns. However, in order to apply this procedure, Linear Buckling Analysis (LBA) of the tapered column must be performed for determination of the critical load. Because tapered members should lead to efficient structural solutions, it is therefore of major importance to provide simple and accurate formula for determination of the critical axial force of tapered columns. In this paper, firstly, the fourth order differential equation for non-uniform columns is derived. For the particular case of simply supported web-tapered columns subject to in-plane buckling, the Rayleigh-Ritz method is applied. Finally, and followed by a numerical parametric study, a formula for determination of the critical axial force of simply supported linearly web-tapered columns buckling in plane is proposed leading to differences up to 8% relatively to the LBA model.

• Structural Engineering and Mechanics
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• 제65권1호
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• pp.111-120
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• 2018

This paper presents a new and simple solution for determining the natural frequencies of framed tube combined with shear-walls and tube-in-tube systems. The novelty of the presented approach is based on the bending moment function approximation instead of the mode shape function approximation. This novelty makes the presented solution very simpler and very shorter in the mathematical calculations process. The shear stiffness, flexural stiffness and mass per unit length of the structure are variable along the height. The effect of the structure weight on its natural frequencies is considered using a variable axial force. The effects of shear lag phenomena has been investigated on the natural frequencies of the structure. The whole structure is modeled by an equivalent non-prismatic shear-flexural cantilever beam under variable axial forces. The governing differential equation of motion is converted into a system of linear algebraic equations and the natural frequencies are calculated by determining a non-trivial solution for the system of equations. The accuracy of the proposed method is verified through several numerical examples and the results are compared with the literature.

• Advances in Computational Design
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• 제5권4호
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• pp.397-416
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• 2020

Functionally graded material (FGM) illustrates a novel class of composites that consists of a graded pattern of material composition. FGM is engineered to have a continuously varying spatial composition profile. Current work focused on buckling analysis of beam made of stepwise linear and quadratic graded material in axial direction subjected to axial span-load with piecewise function and rested on shear layer based on classical beam theory. The various boundary and natural conditions including simply supported (S-S), pinned - clamped (P-C), axial hinge - pinned (AH-P), axial hinge - clamped (AH-C), pinned - shear hinge (P-SHH), pinned - shear force released (P-SHR), axial hinge - shear force released (AH-SHR) and axial hinge - shear hinge (AH-SHH) are considered. To the best of the author's knowledge, buckling behavior of this kind of Euler-Bernoulli beams has not been studied yet. The equilibrium differential equation is derived by minimizing total potential energy via variational calculus and solved analytically. The boundary conditions, natural conditions and deformation continuity at concentrated load insertion point are expressed in matrix form and nontrivial solution is employed to calculate first buckling loads and corresponding mode shapes. By increasing truncation order, the relative error reduction and convergence of solution are observed. Fast convergence and good compatibility with various conditions are advantages of the proposed method. A MATLAB code is provided in appendix to employ the numerical procedure based on proposed method.

• 한국지구과학회지
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• 제30권5호
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• pp.671-681
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• 2009

In the equilibrium theory of tides by Newton, tide on the Earth is a phenomenon driven by differential gravity contributed both by the Sun and the Moon. Due to the direct link of the generic tidal effect to the oceanic tides, college students in the earth science education department are exposed to this theory through oceanography lectures as well as astronomy lectures. Common oceanography textbooks adopt a non-inertial reference frame fixed to the Earth in which the fictitious, centrifugal force appears. This has a potential risk to provide misconceptions among students in various aspects including the followings: 1) this is how Newton originally derived the equilibrium theory of tides, and 2) the tide is a phenomenon appearing only in rotating systems. We show that in astronomy, a much simpler description, which employs the inertial frame, is generally used to explain tides and thus causes less confusion. We argue that the description used in astronomy is preferable both in the viewpoints of simplicity and ease of interpretation. Moreover, on a historical basis, an inertial frame was adopted by Newton in Principia to explain tides. Thus, the description used in astronomy is consistent with Newton's original approach. We also present various astrophysical tides which do not comply with the concept of centrifugal force in general. We therefore argue that the description used in oceanography should be compensated by that in astronomy, due to its complexity, historical inconsistency and limited applicability.

• 대한기계학회논문집B
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• 제24권6호
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• pp.760-768
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• 2000

Filter efficiency of electrically charged particle in uncharged fibrous filter was measured. In previous studies, the effect of charged particle on filter efficiency was investigated but there was difficulty in measuring of image effect that is appeared at the charged small particle. We could easily measure the image effect with charging small particles by photoelectric charging. The spark discharge aerosol generator and a differential mobility analyzer (DMA) were used to generate sub-micron monodisperse particles (${\leq}200$ nm). The generated particles were charged in photoelectric charging process using ultraviolet lamp and electric field. The filter efficiency of the charged particles, classified by another DMA, was measured in filter tester using a condensation nucleus counter (CNC) as function of particle diameter, particle charge and airflow velocity. It is shown that the filter efficiency increases with increasing charge number of the particle and is affected by particle size and flow velocity. Single fiber filter efficiency mainly depends on image force parameter and peclet number. The peclet number was not considered at previous other papers. We propose a modi fied experimental correlation as function of image force parameter and peclet number.

• Journal of Electrical Engineering and Technology
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• 제13권5호
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• pp.1935-1944
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• 2018

With the increase of the production of energy from renewable, it becomes important to look at techniques to store this energy. Therefore, a single winding bearingless flywheel motor (SWBFM) specially for flywheel energy storage system is introduced. For the control system of SWBFM, coupling between the torque and the suspension subsystems exists inevitably. It is necessary to build a reasonable radial force mathematical model to precisely control SWBFM. However, SWBFM has twelve independently controlled windings which leads to high-order matrix transformation and complex differential calculation in the process of mathematical modeling based on virtual displacement method. In this frame, a Maxwell tensor modeling method which is no need the detailed derivation and complex theoretical computation is present. Moreover, it possesses advantages of universality, accuracy, and directness. The fringing magnetic path is improved from straight and circular lines to elliptical line and the rationality of elliptical line is verified by virtual displacement theory according to electromagnetic torque characteristics. A correction function is taken to increase the model accuracy based on finite element analysis. Simulation and experimental results show that the control system of SWBFM with radial force mathematical model based on Maxwell tensor method is feasible and has high precision.

• 한국기계가공학회지
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• 제20권9호
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• pp.11-19
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• 2021

Linear variable differential transformer (LVDT) is a displacement sensor and is commonly used owing to its wide measurement range, excellent linearity, high sensitivity, and precision. To improve the output characteristics of LVDT, a few studies have been conducted to analyze the output using a theoretical method or a finite element method. However, the material properties of the core and the electromagnetic force acting on the core were not considered in the previous studies. In this study, a finite element analysis model was proposed considering the characteristics of the LVDT composed of coils, core, magnetic shell and electric circuit, and the core displacement. Using the proposed model, changes in sensitivity and linear region of LVDT according to changes in process and material parameters were analyzed. The outputs of the LVDT model were compared with those of the theoretical analysis, and then, the proposed analysis model was validated. When the electrical conductivity of the core was high and the relative magnetic permeability was low, the decrease in sensitivity was large. Additionally, an increase in the frequency of the power led to further decrease in sensitivity. The electromagnetic force applied on the core increased as the voltage increased, the frequency decreased, and the core displacement increased.

• 한국축산식품학회지
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• 제39권1호
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• pp.65-72
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• 2019

This study investigated the effects of temperature ($50^{\circ}C$, $55^{\circ}C$, and $60^{\circ}C$) and time (12 and 24 h) on the cookery properties of sous-vide (SV) processed pork loin. As an indicator of cookery properties, cooking loss, expressible moisture (EM), pH, differential scanning calorimetry (DSC), shear force, total plate count (TPC) and CIE color were measured and compared with fresh (FC) and cooked control (CC, $75^{\circ}C$ for 30 min). SV treatments at $50^{\circ}C$ showed higher tenderness and lower cooking loss comparing to CC. DSC result indicated that thermal transition of collagen was a key factor affecting the cooking loss and shear force of meat. In comparison of CC, risks of insufficient pasteurization and uncooked color generation were not shown in SV processed meat. Therefore, the results indicated that SV had a potential advantage to produce tender and moist meat, and the best SV condition of pork loin was estimated at $50^{\circ}C$ for 24 h.

• 한국기계가공학회지
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• 제19권11호
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• pp.29-34
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• 2020

In this study, a sensitivity formulation was applied to analyze the dynamic response due to the effect of the excitation force for the undamped vibration of the cantilever beam. The theoretically fundamental formulations were derived considering an eigenvalue problem and its modal analysis to govern the second order algebraic differential equation in terms of the change in the modal coordinate with respect to the design parameters. A representative physical quantity pertaining to the dynamic response, that is, the rate of change in the dynamic displacement, was observed by changing the design variables, such as the cross-sectional area of the beam. The numerical results were obtained at various locations, considering the application of the external forces and observation of the dynamic displacement. When the detection position was closer to the free end of the cantilever beam, the sensitivity of the dynamic displacement was higher, as predicted through the oscillating motion of the beam. The presented findings can provide guidance to compute the dynamic sensitivity for a flexibly connected structure under dynamic excitations.