• Transactions of the Korean Society of Mechanical Engineers
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• v.2 no.3
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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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• v.31 no.4
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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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• v.12 no.6
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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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• 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.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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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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• v.19 no.1
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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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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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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• v.80 no.5
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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.

• Journal of Korea Society of Industrial Information Systems
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• v.21 no.1
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• pp.61-70
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• 2016

This paper describes a new PMU(parametric measurement unit) design technique for automatic test equipment(ATE). Only one DDA(differential difference amplifier) is used to force the test signals to DUT(device under test), while conventional design uses two or more amplifiers to force test signals. Since the proposed technique does not need extra amplifiers in feedback path, the proposed PMU inherently guarantees stable operation. Moreover, to measure the response signals from DUT, proposed technique also adopted only one DDA amplifier as an IA(instrument amplifier), while conventional IA uses 3 amplifiers and several resistors. The DDA adopted two rail-to-rail differential input stages to handle full-range differential signals. Gain enhancement technique is used in folded-cascode type DDA to get open loop gain of 100 dB. Proposed PMU design enables accurate and stable operation with smaller hardware and lower power consumption. This PMU is implemented with 0.18 um CMOS process and supply voltage is 1.8 V. Input ranges for each force mode are 0.25~1.55 V at voltage force and 0.9~0.935 V at current force mode.

• Fire Science and Engineering
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• v.27 no.3
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• pp.66-71
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• 2013

The purpose of this study is to assess the criteria on a floor hinge and door closer for the optimum design of the access door of a smoke control room. The door opening force due to differential pressure is 60.75 N, 40.5 N, 32.91 N and 12.66 N when the differential pressure is 60 Pa, 40 Pa, 32.5 Pa and 12.5 Pa, respectively. The door opening force of the floor hinge and door closer to which the criteria of KS F 2806 are applied is 27.5 N, 40 N, 75 N, 100 N and 125 N for the Nos. 1, 2, 3, 4 and 5 class floor hinges and door closers, respectively. This study compared the differential pressure and opening force limits of floor hinges and door closers with the values specified in NFSC 501A and found that they exceeded the criteria specified in NFSC 501A. Therefore, it is necessary to reflect the differential pressure and smoke control wind speeds as well as the opening forces specified in NFSC 501A on the design of floor hinges and door closers. The installation conditions of floor hinges and door closers of access doors differ depending on the type and name of a smoke control damper. This study found that Nos. 1, 2 and 3 floor hinges and door closers could be installed for access doors with low differential pressure and that Nos. 1 and 2 floor hinges and door closers could be installed for access doors with normal differential pressure.