• 대한기계학회논문집
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• 제2권3호
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• pp.62-68
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• 1978

The influences of the large amplitude free vibrations of simply supported Timoshenko beams with ends restrained to remain a fixed distance apart and with no axial restraints, which cause a longitudinal elastic force and a longitudinal inertia force, respectively, are investigated. The equations of motion derived by an appropriate linearizarion of the nonlinear strain- displacement relation have nonlinear terms arising from large curvature, longitudinal elastic force and longitudinal inertia force. The fourth order nonlinear partial differential equations for the deflection, can be reduced to the nonlinear ordinary differential equations by means of Galerkin procedure and a modal expansion. The general response and frequensy-amplitude relations are derived by the perturbation method of strained parameters. Comparison with previously published results is made.

• Structural Engineering and Mechanics
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• 제31권4호
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• pp.453-475
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• 2009

The literature regarding the free vibration analysis of Bernoulli-Euler and Timoshenko beams on elastic soil is plenty, but the free vibration analysis of Reddy-Bickford beams on elastic soil with/without axial force effect using the Differential Transform Method (DTM) has not been investigated by any of the studies in open literature so far. In this study, the free vibration analysis of axially loaded Reddy-Bickford beam on elastic soil is carried out by using DTM. The model has six degrees of freedom at the two ends, one transverse displacement and two rotations, and the end forces are a shear force and two end moments in this study. The governing differential equations of motion of the rectangular beam in free vibration are derived using Hamilton's principle and considering rotatory inertia. Parameters for the relative stiffness, stiffness ratio and nondimensionalized multiplication factor for the axial compressive force are incorporated into the equations of motion in order to investigate their effects on the natural frequencies. At first, the terms are found directly from the analytical solutions of the differential equations that describe the deformations of the cross-section according to the high-order theory. After the analytical solution, an efficient and easy mathematical technique called DTM is used to solve the governing differential equations of the motion. The calculated natural frequencies of one end fixed and the other end simply supported Reddy-Bickford beam on elastic soil using DTM are tabulated in several tables and figures and are compared with the results of the analytical solution where a very good agreement is observed and the mode shapes are presented in graphs.

• Coupled systems mechanics
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• 제12권6호
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• pp.519-530
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• 2023

This paper presents a mathematical model suitable for the calculation of laminated glass, i.e. glass plates combined with an interlayer material. The model is based on a beam differential equation for each glass plate and a separate differential equation for the slip in the interlayer. In addition to slip, the model takes into account prestressing force in the interlayer. It is possible to combine the two contributions arbitrarily, which is important because the glass sheet fabrication process changes the stiffness of the interlayer in ways that are not easily predictable and could introduce prestressing of varying magnitude. The model is suitable for reformulation into an inverse procedure for calculation of the relevant parameters. Model consisting of a system of differential-algebraic equations, proved too stiff for cases with the thin interlayer. This novel approach covers the full range of possible stiffnesses of layered glass sheets, i.e., from zero to infinite stiffness of the interlayer. The comparison of numerical and experimental results contributes to the validation of the model.

• Structural Engineering and Mechanics
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• 제53권3호
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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.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2004년도 추계학술대회 논문집
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• pp.131-136
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• 2004

The limited slip differential(LSD) is a device which enables the driving force to be transmitted from one slipping wheel to another wheel in such case that the car is stuck in clay or snow. When the unwanted slipping occurs on one wheel, the LSD temporarily restraints the differential motion to transmit the driving force in the other wheel. So far, many types of LSD were developed such as mechanical lock type, disk clutch type, viscous coupling type, torsion type and multiple clutch type. However these types of LSD is too complicated and expensive, so it is used only for 4WD outdoor vehicles, military vehicles, and a portion of deluxe car. So, many studies has been devoted to improve new types of LSD to cover those demerits of existing LSDs that the hydraulic LSD is developed as arepresentative result of that. The hydraulic LSD which uses the principle of gear pump is packed with viscous oil in tight container. When a slip occurs on one wheel, the hydraulic LSD generates torque caused by high oil pressure in the container. This study has been devoted to suggest an improved hydraulic LSD. In order to achieve it, we designed a new type of hydraulic LSD, produced it and did a rig test with it on real vehicle. From the rig test, it has been confirmed that the new type of hydraulic LSD can be directly applied to exiting vehicles without changing the design criteria

• Structural Engineering and Mechanics
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• 제19권1호
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• pp.73-96
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• 2005

For the spatially coupled free vibration analysis of shear deformable thin-walled non-symmetric curved beam subjected to initial axial force, an exact dynamic element stiffness matrix of curved beam is evaluated. Firstly equations of motion and force-deformation relations are rigorously derived from the total potential energy for a curved beam element. Next a system of linear algebraic equations are constructed by introducing 14 displacement parameters and transforming the second order simultaneous differential equations into the first order simultaneous differential equations. And then explicit expressions for displacement parameters are numerically evaluated via eigensolutions and the exact $14{\times}14$ dynamic element stiffness matrix is determined using force-deformation relations. To demonstrate the accuracy and the reliability of this study, the spatially coupled natural frequencies of shear deformable thin-walled non-symmetric curved beams subjected to initial axial forces are evaluated and compared with analytical and FE solutions using isoparametric and Hermitian curved beam elements and results by ABAQUS's shell elements.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2005년도 추계학술대회논문집
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• pp.903-906
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• 2005

The purpose of this paper is to investigate free vibrations and critical loads of the uniform Beck's columns with a tip spring, carrying a tip mass. The ordinary differential equation governing free vibrations of such Beck's column subjected to a follower force is derived based on the Bernoulli-Euler beam theory. Both the divergence and flutter critical loads are calculated from the load-frequency curves that are obtained by solving the differential equation numerically. The critical loads are presented in the figures as functions of various non-dimensional system parameters such as the mass moment of inertia and spring parameter.

• Structural Engineering and Mechanics
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• 제80권5호
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• pp.491-501
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• 2021

A difference in subgrade settlement between two rails of a track manifests as lateral differential subgrade settlement. This settlement causes unsteadiness in the motion of trains passing through the corresponding area. To illustrate the effect of lateral differential subgrade settlement on the dynamic response of a vehicle-track coupling system, a three-dimensional vehicle-track-subgrade coupling model was formulated by combining the vehicle-track dynamics theory and the finite element method. The wheel/rail force, car body acceleration, and derailment factor are chosen as evaluation indices of the system dynamic response. The effects of the amplitude and wavelength of lateral differential subgrade settlement as well as the driving speed of the vehicle are analyzed. The study reveals the following: The dynamic responses of the vehicle-track system generally increase linearly with the driving speed when the train passes through a lateral subgrade settlement area. The wheel/rail force acting on a rail with a large settlement exceeds that on a rail with a small settlement. The dynamic responses of the vehicle-track system increase with the amplitude of the lateral differential subgrade settlement. For a 250-km/h train speed, the proposed maximum amplitude for a lateral differential settlement with a wavelength of 20 m is 10 mm. The dynamic responses of the vehicle-track system decrease with an increase in the wavelength of the lateral differential subgrade settlement. To achieve a good operation quality of a train at a 250-km/h driving speed, the wavelength of a lateral differential subgrade settlement with an amplitude of 20 mm should not be less than 15 m. Monitoring lateral differential settlements should be given more emphasis in routine high-speed railway maintenance and repairs.

• 한국산업정보학회논문지
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• 제21권1호
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• pp.61-70
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• 2016

본 논문은 자동 시험 장비(ATE : automatic test equipment)를 위한 새로운 파라메터 측정기(PMU : parametric measurement unit) 설계 기술을 설명한다. 기존의 설계는 피 시험 소자(DUT : device under test)에 신호를 인가하기 위해 두 개 혹은 그 이상의 증폭기를 사용하지만, 본 연구에서는 오직 하나의 차동 차이 증폭기(DDA : differential difference amplifier)를 사용한다. 제안된 기술은 귀환 경로에 추가적인 증폭기가 필요하지 않기 때문에, PMU는 안정적인 동작을 보장한다. 또한 DUT의 응답 신호를 측정하기 위한 기존의 계측 증폭기(IA : instrument amplifier)가 3개의 증폭기와 다수의 저항을 사용하는 것에 반해, 제안된 기술은 오직하나의 DDA를 IA로 적용했다. DDA는 전 범위의 차동 신호를 다루기 위해 두 개의 rail-to-rail 차동 입력 단을 적용하였다. 100 dB의 개 루프 이득을 얻기 위해 folded-cascode 형태의 DDA 안에 추가적인 이득 증가 기술이 사용되었다. 제안된 PMU 설계는 더 작은 면적과 더 적은 전력 소모를 가지고 정확하고 안정적인 동작을 가능하게 한다. PMU는 0.18 um CMOS 공정으로 구현되었고 공급 전압은 1.8 V이다. 입력 범위는 전압인가 시 0.25~1.55 V이고, 전류인가 시 0.9~0.935 V이다.

• 한국화재소방학회논문지
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• 제27권3호
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• pp.66-71
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• 2013

본 연구의 목적은 제연구역 출입문의 최적 설계를 위한 플로어힌지(floor-hinge) 및 도어클로저(door closer)의 기준을 제시하는데 있다. 차압에 대한 개방력은 60 Pa일 때 60.75 N, 40 Pa일 때 40.5 N, 32.5 Pa일 때 32.91 N, 12.5 Pa일 때 12.66 N 등이다. KS F 2806의 기준을 적용한 플로어힌지 및 도어클로저의 개방력은 No.1은 27.5 N, No. 2는 40 N, No. 3는 75 N, No. 4는 100 N, No. 5는 125 N 등이다. 차압과 플로어힌지 및 도어클로저의 개방력을 NFSC 501A의 개방력 제한값과 비교한 결과 기준을 초과하는 것으로 확인되었다. 따라서 NFSC 501A 차압과 방연 풍속을 설계에 반영하는 것뿐만 아니라 개방력도 설계에 반영할 필요가 있다. 제연댐퍼의 종류에 따라 출입문의 플로어힌지 및 도어클로저의 설치 조건은 호칭에 따라 다르다. 저차압용의 경우는 No. 1, No. 2, No. 3의 설치가 가능하며, 일반 차압용의 경우에는 No. 1, No. 2의 설치가 가능하였다.